diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json
index 28f6aaa43..16904e357 100644
--- a/dev/.documenter-siteinfo.json
+++ b/dev/.documenter-siteinfo.json
@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-09T15:50:26","documenter_version":"1.2.1"}}
\ No newline at end of file
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-19T11:56:11","documenter_version":"1.5.0"}}
\ No newline at end of file
diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js
index f5311607b..b2bdd43ee 100644
--- a/dev/assets/documenter.js
+++ b/dev/assets/documenter.js
@@ -4,7 +4,6 @@ requirejs.config({
'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
- 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min',
'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
@@ -103,9 +102,10 @@ $(document).on("click", ".docstring header", function () {
});
});
-$(document).on("click", ".docs-article-toggle-button", function () {
+$(document).on("click", ".docs-article-toggle-button", function (event) {
let articleToggleTitle = "Expand docstring";
let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
debounce(() => {
if (isExpanded) {
@@ -116,7 +116,7 @@ $(document).on("click", ".docs-article-toggle-button", function () {
isExpanded = false;
- $(".docstring section").slideUp();
+ $(".docstring section").slideUp(animationSpeed);
} else {
$(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
$(".docstring-article-toggle-button")
@@ -127,7 +127,7 @@ $(document).on("click", ".docs-article-toggle-button", function () {
articleToggleTitle = "Collapse docstring";
navArticleToggleTitle = "Collapse all docstrings";
- $(".docstring section").slideDown();
+ $(".docstring section").slideDown(animationSpeed);
}
$(this).prop("title", navArticleToggleTitle);
@@ -224,224 +224,474 @@ $(document).ready(function () {
})
////////////////////////////////////////////////////////////////////////////////
-require(['jquery', 'minisearch'], function($, minisearch) {
-
-// In general, most search related things will have "search" as a prefix.
-// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+require(['jquery'], function($) {
-let results = [];
-let timer = undefined;
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
-let data = documenterSearchIndex["docs"].map((x, key) => {
- x["id"] = key; // minisearch requires a unique for each object
- return x;
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
});
-// list below is the lunr 2.1.3 list minus the intersect with names(Base)
-// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
-// ideally we'd just filter the original list but it's not available as a variable
-const stopWords = new Set([
- "a",
- "able",
- "about",
- "across",
- "after",
- "almost",
- "also",
- "am",
- "among",
- "an",
- "and",
- "are",
- "as",
- "at",
- "be",
- "because",
- "been",
- "but",
- "by",
- "can",
- "cannot",
- "could",
- "dear",
- "did",
- "does",
- "either",
- "ever",
- "every",
- "from",
- "got",
- "had",
- "has",
- "have",
- "he",
- "her",
- "hers",
- "him",
- "his",
- "how",
- "however",
- "i",
- "if",
- "into",
- "it",
- "its",
- "just",
- "least",
- "like",
- "likely",
- "may",
- "me",
- "might",
- "most",
- "must",
- "my",
- "neither",
- "no",
- "nor",
- "not",
- "of",
- "off",
- "often",
- "on",
- "or",
- "other",
- "our",
- "own",
- "rather",
- "said",
- "say",
- "says",
- "she",
- "should",
- "since",
- "so",
- "some",
- "than",
- "that",
- "the",
- "their",
- "them",
- "then",
- "there",
- "these",
- "they",
- "this",
- "tis",
- "to",
- "too",
- "twas",
- "us",
- "wants",
- "was",
- "we",
- "were",
- "what",
- "when",
- "who",
- "whom",
- "why",
- "will",
- "would",
- "yet",
- "you",
- "your",
-]);
-
-let index = new minisearch({
- fields: ["title", "text"], // fields to index for full-text search
- storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results
- processTerm: (term) => {
- let word = stopWords.has(term) ? null : term;
- if (word) {
- // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
- word = word
- .replace(/^[^a-zA-Z0-9@!]+/, "")
- .replace(/[^a-zA-Z0-9@!]+$/, "");
- }
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
- return word ?? null;
- },
- // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification
- tokenize: (string) => string.split(/[\s\-\.]+/),
- // options which will be applied during the search
- searchOptions: {
- boost: { title: 100 },
- fuzzy: 2,
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
processTerm: (term) => {
let word = stopWords.has(term) ? null : term;
if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
word = word
.replace(/^[^a-zA-Z0-9@!]+/, "")
.replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
}
return word ?? null;
},
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
tokenize: (string) => string.split(/[\s\-\.]+/),
- },
-});
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * RegX escape function from MDN
+ * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+ function escapeRegExp(string) {
+ return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+ }
-index.addAll(data);
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
-
-
- ${search_modal_header}
-
- ${initial_search_body}
-
- ${search_modal_footer}
+$(document).ready(function () {
+ let search_modal_header = `
+
- `
-);
+
+
+
+
+ `;
-document.querySelector(".docs-search-query").addEventListener("click", () => {
- openModal();
-});
+ let initial_search_body = `
+
Type something to get started!
+ `;
-document.querySelector(".close-search-modal").addEventListener("click", () => {
- closeModal();
-});
+ let search_modal_footer = `
+
+ `;
-$(document).on("click", ".search-result-link", function () {
- closeModal();
-});
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
-document.addEventListener("keydown", (event) => {
- if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
openModal();
- } else if (event.key === "Escape") {
- closeModal();
- }
+ });
- return false;
-});
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
-// Functions to open and close a modal
-function openModal() {
- let searchModal = document.querySelector("#search-modal");
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
- searchModal.classList.add("is-active");
- document.querySelector(".documenter-search-input").focus();
-}
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
-function closeModal() {
- let searchModal = document.querySelector("#search-modal");
- let initial_search_body = `
-
Type something to get started!
- `;
+ return false;
+ });
- searchModal.classList.remove("is-active");
- document.querySelector(".documenter-search-input").blur();
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
- if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
- $(".search-modal-card-body").addClass("is-justify-content-center");
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
}
- $(".documenter-search-input").val("");
- $(".search-modal-card-body").html(initial_search_body);
-}
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+
Type something to get started!
+ `;
-document
- .querySelector("#search-modal .modal-background")
- .addEventListener("click", () => {
- closeModal();
- });
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
})
////////////////////////////////////////////////////////////////////////////////
diff --git a/dev/assets/themes/catppuccin-frappe.css b/dev/assets/themes/catppuccin-frappe.css
new file mode 100644
index 000000000..54a5b77ea
--- /dev/null
+++ b/dev/assets/themes/catppuccin-frappe.css
@@ -0,0 +1 @@
+html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis,html.theme--catppuccin-frappe .file-cta,html.theme--catppuccin-frappe .file-name,html.theme--catppuccin-frappe .select select,html.theme--catppuccin-frappe .textarea,html.theme--catppuccin-frappe .input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-frappe .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--catppuccin-frappe .pagination-previous:focus,html.theme--catppuccin-frappe .pagination-next:focus,html.theme--catppuccin-frappe .pagination-link:focus,html.theme--catppuccin-frappe .pagination-ellipsis:focus,html.theme--catppuccin-frappe .file-cta:focus,html.theme--catppuccin-frappe .file-name:focus,html.theme--catppuccin-frappe .select select:focus,html.theme--catppuccin-frappe .textarea:focus,html.theme--catppuccin-frappe .input:focus,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input:focus,html.theme--catppuccin-frappe .button:focus,html.theme--catppuccin-frappe .is-focused.pagination-previous,html.theme--catppuccin-frappe .is-focused.pagination-next,html.theme--catppuccin-frappe .is-focused.pagination-link,html.theme--catppuccin-frappe .is-focused.pagination-ellipsis,html.theme--catppuccin-frappe .is-focused.file-cta,html.theme--catppuccin-frappe .is-focused.file-name,html.theme--catppuccin-frappe .select select.is-focused,html.theme--catppuccin-frappe .is-focused.textarea,html.theme--catppuccin-frappe .is-focused.input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-frappe .is-focused.button,html.theme--catppuccin-frappe .pagination-previous:active,html.theme--catppuccin-frappe .pagination-next:active,html.theme--catppuccin-frappe .pagination-link:active,html.theme--catppuccin-frappe .pagination-ellipsis:active,html.theme--catppuccin-frappe .file-cta:active,html.theme--catppuccin-frappe .file-name:active,html.theme--catppuccin-frappe .select select:active,html.theme--catppuccin-frappe .textarea:active,html.theme--catppuccin-frappe .input:active,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input:active,html.theme--catppuccin-frappe .button:active,html.theme--catppuccin-frappe .is-active.pagination-previous,html.theme--catppuccin-frappe .is-active.pagination-next,html.theme--catppuccin-frappe .is-active.pagination-link,html.theme--catppuccin-frappe .is-active.pagination-ellipsis,html.theme--catppuccin-frappe .is-active.file-cta,html.theme--catppuccin-frappe .is-active.file-name,html.theme--catppuccin-frappe .select select.is-active,html.theme--catppuccin-frappe .is-active.textarea,html.theme--catppuccin-frappe .is-active.input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--catppuccin-frappe .is-active.button{outline:none}html.theme--catppuccin-frappe .pagination-previous[disabled],html.theme--catppuccin-frappe .pagination-next[disabled],html.theme--catppuccin-frappe .pagination-link[disabled],html.theme--catppuccin-frappe .pagination-ellipsis[disabled],html.theme--catppuccin-frappe .file-cta[disabled],html.theme--catppuccin-frappe .file-name[disabled],html.theme--catppuccin-frappe .select select[disabled],html.theme--catppuccin-frappe .textarea[disabled],html.theme--catppuccin-frappe .input[disabled],html.theme--catppuccin-frappe #documenter .docs-sidebar 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kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe 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html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content 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.button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe .image.is-3by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-frappe .image.is-5by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-frappe .image.is-16by9,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-frappe .image.is-2by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-frappe .image.is-3by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-frappe .image.is-4by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-frappe .image.is-3by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-frappe .image.is-2by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-frappe .image.is-3by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-frappe .image.is-9by16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-frappe .image.is-1by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-frappe .image.is-1by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-frappe .image.is-16x16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-frappe .image.is-24x24,html.theme--catppuccin-frappe #documenter 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diff --git a/dev/assets/themes/catppuccin-latte.css b/dev/assets/themes/catppuccin-latte.css
new file mode 100644
index 000000000..ca172b630
--- /dev/null
+++ b/dev/assets/themes/catppuccin-latte.css
@@ -0,0 +1 @@
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!important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-link.is-light{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:hover,html.theme--catppuccin-latte .button.is-link.is-light.is-hovered{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:active,html.theme--catppuccin-latte .button.is-link.is-light.is-active{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:hover,html.theme--catppuccin-latte .button.is-info.is-hovered{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus,html.theme--catppuccin-latte .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus:not(:active),html.theme--catppuccin-latte .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(23,146,153,0.25)}html.theme--catppuccin-latte .button.is-info:active,html.theme--catppuccin-latte .button.is-info.is-active{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:#179299;box-shadow:none}html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;color:#179299}html.theme--catppuccin-latte .button.is-info.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-outlined.is-focused{background-color:#179299;border-color:#179299;color:#fff}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte .content.is-normal{font-size:1rem}html.theme--catppuccin-latte .content.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .content.is-large{font-size:1.5rem}html.theme--catppuccin-latte .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-latte .icon.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-latte .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-latte .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-latte .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-latte .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-latte .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-latte div.icon-text{display:flex}html.theme--catppuccin-latte .image,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-latte .image img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-latte .image img.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-latte .image.is-fullwidth,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-latte .image.is-square img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-latte .image.is-square .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-latte .image.is-1by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-latte .image.is-1by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-latte .image.is-5by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-latte .image.is-5by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-latte .image.is-4by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-latte .image.is-4by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-latte .image.is-3by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-latte .image.is-5by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-latte .image.is-5by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-latte .image.is-16by9 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-latte .image.is-16by9 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-latte .image.is-2by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-latte .image.is-2by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-latte .image.is-3by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-latte .image.is-3by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-latte .image.is-4by5 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-latte .image.is-4by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-latte .image.is-3by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-latte .image.is-3by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-latte .image.is-2by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-latte .image.is-2by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by5 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-latte .image.is-3by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-latte .image.is-9by16 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-latte .image.is-9by16 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-latte .image.is-1by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-latte .image.is-1by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-latte .image.is-1by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-latte .image.is-1by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-latte .image.is-square,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-latte .image.is-1by1,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-latte .image.is-5by4,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-latte .image.is-4by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-latte .image.is-3by2,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-latte .image.is-5by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-latte .image.is-16by9,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-latte .image.is-2by1,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-latte .image.is-3by1,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-latte .image.is-4by5,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-latte .image.is-3by4,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-latte .image.is-2by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-latte .image.is-3by5,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-latte .image.is-9by16,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-latte .image.is-1by2,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-latte .image.is-1by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-latte .image.is-16x16,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-latte .image.is-24x24,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-24x24{height:24px;width:24px}html.theme--catppuccin-latte .image.is-32x32,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-32x32{height:32px;width:32px}html.theme--catppuccin-latte .image.is-48x48,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-48x48{height:48px;width:48px}html.theme--catppuccin-latte .image.is-64x64,html.theme--catppuccin-latte 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.navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte 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a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte 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.pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte 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diff --git a/dev/assets/themes/catppuccin-macchiato.css b/dev/assets/themes/catppuccin-macchiato.css
new file mode 100644
index 000000000..6ed16f8eb
--- /dev/null
+++ b/dev/assets/themes/catppuccin-macchiato.css
@@ -0,0 +1 @@
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.button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:hover,html.theme--catppuccin-macchiato .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus,html.theme--catppuccin-macchiato .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus:not(:active),html.theme--catppuccin-macchiato .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-macchiato .button.is-light:active,html.theme--catppuccin-macchiato .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-dark,html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:hover,html.theme--catppuccin-macchiato .content kbd.button:hover,html.theme--catppuccin-macchiato .button.is-dark.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-hovered{background-color:#313447;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus,html.theme--catppuccin-macchiato .content kbd.button:focus,html.theme--catppuccin-macchiato .button.is-dark.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus:not(:active),html.theme--catppuccin-macchiato .content kbd.button:focus:not(:active),html.theme--catppuccin-macchiato .button.is-dark.is-focused:not(:active),html.theme--catppuccin-macchiato .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,58,79,0.25)}html.theme--catppuccin-macchiato .button.is-dark:active,html.theme--catppuccin-macchiato .content kbd.button:active,html.theme--catppuccin-macchiato .button.is-dark.is-active,html.theme--catppuccin-macchiato .content kbd.button.is-active{background-color:#2c2f40;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark[disabled],html.theme--catppuccin-macchiato .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:#363a4f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-dark.is-inverted,html.theme--catppuccin-macchiato .content kbd.button.is-inverted{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted:hover,html.theme--catppuccin-macchiato 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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-primary,html.theme--catppuccin-macchiato .docstring>section>a.button.docs-sourcelink{background-color:#8aadf4;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-primary:hover,html.theme--catppuccin-macchiato .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-macchiato .button.is-primary.is-hovered,html.theme--catppuccin-macchiato .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#7ea5f3;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato 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.button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato 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diff --git a/dev/assets/themes/catppuccin-mocha.css b/dev/assets/themes/catppuccin-mocha.css
new file mode 100644
index 000000000..6f27b4c5f
--- /dev/null
+++ b/dev/assets/themes/catppuccin-mocha.css
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.button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-outlined:hover,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-white.is-outlined:focus,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black:hover,html.theme--catppuccin-mocha .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black:focus,html.theme--catppuccin-mocha .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black:focus:not(:active),html.theme--catppuccin-mocha .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-mocha .button.is-black:active,html.theme--catppuccin-mocha .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-mocha .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted:hover,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-outlined:hover,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-black.is-outlined:focus,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha 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.button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted:hover,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-outlined:hover,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-light.is-outlined:focus,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-dark,html.theme--catppuccin-mocha .content kbd.button{background-color:#313244;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:hover,html.theme--catppuccin-mocha .content kbd.button:hover,html.theme--catppuccin-mocha .button.is-dark.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-hovered{background-color:#2c2d3d;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus,html.theme--catppuccin-mocha .content kbd.button:focus,html.theme--catppuccin-mocha .button.is-dark.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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kbd.button.is-inverted{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-dark.is-inverted[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-focused{background-color:#313244;border-color:#313244;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha 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.button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha 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diff --git a/dev/assets/themes/documenter-dark.css b/dev/assets/themes/documenter-dark.css
index 9f5449f4b..2892b385e 100644
--- a/dev/assets/themes/documenter-dark.css
+++ b/dev/assets/themes/documenter-dark.css
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span{font-style:inherit;font-weight:inherit}html.theme--documenter-dark strong{color:#f2f2f2;font-weight:700}html.theme--documenter-dark fieldset{border:none}html.theme--documenter-dark pre{-webkit-overflow-scrolling:touch;background-color:#282f2f;color:#fff;font-size:.875em;overflow-x:auto;padding:1.25rem 1.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark pre code{background-color:transparent;color:currentColor;font-size:1em;padding:0}html.theme--documenter-dark table td,html.theme--documenter-dark table th{vertical-align:top}html.theme--documenter-dark table td:not([align]),html.theme--documenter-dark table th:not([align]){text-align:inherit}html.theme--documenter-dark table th{color:#f2f2f2}html.theme--documenter-dark .box{background-color:#343c3d;border-radius:8px;box-shadow:none;color:#fff;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 0.5em 1em -0.125em rgba(10,10,10,0.1),0 0 0 1px 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#cb3c33;border-color:#cb3c33;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 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diff --git a/dev/assets/themes/documenter-light.css b/dev/assets/themes/documenter-light.css
index 2f168c77b..a435b3b63 100644
--- a/dev/assets/themes/documenter-light.css
+++ b/dev/assets/themes/documenter-light.css
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Author: (c) Ivan Sagalaev
diff --git a/dev/custom/custom-addons/index.html b/dev/custom/custom-addons/index.html
index ba09a1fbf..41c6a6551 100644
--- a/dev/custom/custom-addons/index.html
+++ b/dev/custom/custom-addons/index.html
@@ -1,5 +1,5 @@
-Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
count :: T
end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
@@ -21,4 +21,8 @@
end
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
return AddonCount(left_addon.count + right_addon.count + 1)
-end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
Theme
documenter-light documenter-dark Automatic (OS)
This document was generated with Documenter.jl version 1.2.1 on Tuesday 9 January 2024 . Using Julia version 1.10.0.
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
Theme
Automatic (OS) documenter-light documenter-dark catppuccin-latte catppuccin-frappe catppuccin-macchiato catppuccin-mocha
This document was generated with Documenter.jl version 1.5.0 on Friday 19 July 2024 . Using Julia version 1.10.4.
diff --git a/dev/custom/custom-functional-form/index.html b/dev/custom/custom-functional-form/index.html
index c811d6f53..996db501b 100644
--- a/dev/custom/custom-functional-form/index.html
+++ b/dev/custom/custom-functional-form/index.html
@@ -1,21 +1,59 @@
-Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
See also: CompositeFormConstraint
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
. Any functional form constraint that defines is_point_mass_form_constraint() = true
may be used only as the last element of the composition.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
Every custom functional form may implement a new method for the is_point_mass_form_constraint
function that returns either true
or false
. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.
To make custom functional form constraint compatible with the @constraints
macro, it must implement a new method for the make_form_constraint
function.
make_form_constraint(::Type, args...; kwargs...)
Creates form constraint object based on passed type
with given args
and kwargs
. Used to simplify form constraint specification.
As an example:
make_form_constraint(PointMass)
creates an instance of PointMassFormConstraint
and
make_form_constraint(SampleList, 5000, LeftProposal())
should create an instance of SampleListFormConstraint
.
See also: AbstractFormConstraint
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source preprocess_form_constraints(constraints)
This function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint
object. Wraps unknown form constraints into a WrappedFormConstraint
object.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(constraint, something)
This function applies a given form constraint to a given object.
source In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional form constraint implementation is the prod
function in the BayesBase
package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.
Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint
functional form constraint:
using ReactiveMP, ExponentialFamily, Distributions, BayesBase
-# First we define our functional form structure with no fields
-struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false
-ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
-ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+# First, we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
+
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
- # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
- # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ # This assumes that the given `distribution` object has `mean` and `precision` defined.
+ # These quantities might be approximated using other methods, such as Laplace approximation.
m = mean(distribution) # or approximate with some other method
p = precision(distribution) # or approximate with some other method
return NormalMeanPrecision(m, p)
end
function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
- # ProductOf is the special case, read about this type more in the corresponding documentation section
- # of the `BayesBase` package
+ # `ProductOf` is a special case. Read more about this type in the corresponding
+ # documentation section of the `BayesBase` package.
# ...
-end
Theme
documenter-light documenter-dark Automatic (OS)
This document was generated with Documenter.jl version 1.2.1 on Tuesday 9 January 2024 . Using Julia version 1.10.0.
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())
+
+constrain_form(constraint, NormalMeanVariance(0, 2))
ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=0.5)
Some constraint objects might not be subtypes of AbstractFormConstraint
. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP
expects users to pass a WrappedFormConstraint
object, which wraps the original object and makes it compatible with the ReactiveMP
inference backend. Note that the ReactiveMP.preprocess_form_constraints
function automatically wraps all objects that are not subtypes of AbstractFormConstraint
.
Additionally, objects wrapped by WrappedFormConstraints
may implement the ReactiveMP.prepare_context
function. This function's output will be stored in the WrappedFormConstraints
along with the original object. If prepare_context
is implemented, the constrain_form
function will take three arguments: the original constraint, the context, and the object that needs to be constrained.
WrappedFormConstraint(constraint, context)
This is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form
function. By default all objects that are not sub-typed from AbstractFormConstraint
are wrapped into this object. Use ReactiveMP.prepare_context
to provide an extra context for a given form constraint, that can be reused between multiple constrain_form
calls.
source prepare_context(constraint)
This function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext
if no context is needed (the default behaviour).
source constrain_form(wrapped::WrappedFormConstraint, something)
This function unwraps the wrapped
object and calls constrain_form
function with the provided context. If the context is not provided, simply calls constrain_form
with the wrapped constraint. Otherwise passes the context to the constrain_form
function as the second argument.
source using ReactiveMP, Distributions, BayesBase, Random
+
+# First, we define our custom form constraint that creates a set of samples
+# Note that this is not a subtype of `AbstractFormConstraint`
+struct MyCustomSampleListFormConstraint end
+
+# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions
+# which are necessary for the `ReactiveMP` inference backend
+ReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()
+
+# We implement the `prepare_context` function, which returns a random number generator
+function ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)
+ return Random.default_rng()
+end
+
+# We implement the `constrain_form` function, which returns a set of samples
+function ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)
+ return rand(context, distribution, 10)
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())
+
+constrain_form(constraint, Normal(0, 10))
10-element Vector{Float64}:
+ 2.765243267225301
+ -7.743664432791434
+ 10.096949510991
+ -1.3807891286455332
+ -18.759821147850232
+ -1.124102268938954
+ -3.2910988879476175
+ 0.5901898664125939
+ -8.740494042415495
+ 8.248243206462803
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diff --git a/dev/extra/contributing/index.html b/dev/extra/contributing/index.html
index 0fabacb09..551089cea 100644
--- a/dev/extra/contributing/index.html
+++ b/dev/extra/contributing/index.html
@@ -1,2 +1,2 @@
-Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, as_variable
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
Theme
documenter-light documenter-dark Automatic (OS)
This document was generated with Documenter.jl version 1.2.1 on Tuesday 9 January 2024 . Using Julia version 1.10.0.
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/dev/extra/extensions/index.html b/dev/extra/extensions/index.html
index 98a275f6d..c6712441f 100644
--- a/dev/extra/extensions/index.html
+++ b/dev/extra/extensions/index.html
@@ -1,2 +1,2 @@
-Extensions and interaction with the Julia ecosystem · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/dev/extra/methods/index.html b/dev/extra/methods/index.html
new file mode 100644
index 000000000..628c847a2
--- /dev/null
+++ b/dev/extra/methods/index.html
@@ -0,0 +1,179 @@
+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CVIProjection
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NodeFunctionRuleFallback
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/dev/index.html b/dev/index.html
index c2957c3aa..37701390e 100644
--- a/dev/index.html
+++ b/dev/index.html
@@ -1,2 +1,2 @@
-Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
Tutorials and examples are available in the RxInfer documentation .
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+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/dev/lib/algebra/index.html b/dev/lib/algebra/index.html
new file mode 100644
index 000000000..9a504e3c0
--- /dev/null
+++ b/dev/lib/algebra/index.html
@@ -0,0 +1,5 @@
+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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diff --git a/dev/lib/helpers/index.html b/dev/lib/helpers/index.html
index d5b12df7d..3c94b4cd0 100644
--- a/dev/lib/helpers/index.html
+++ b/dev/lib/helpers/index.html
@@ -1,5 +1,5 @@
-Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
1
3
@@ -7,4 +7,8 @@
julia> collect(s)
2-element Vector{Int64}:
1
- 3
See also: SkipIndexIterator
source FunctionalIndex
A special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex
can be firstindex
or lastindex
, but more complex use cases are possible too, e.g. firstindex + 1
. Important part of the implementation is that the resulting structure is isbitstype(...) = true
, that allows to store it in parametric type as valtype.
One use case for this structure is to dispatch on and to replace begin
or end
(or more complex use cases, e.g. begin + 1
) markers in constraints specification language.
source
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+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/dev/lib/marginal/index.html b/dev/lib/marginal/index.html
new file mode 100644
index 000000000..abcb0141b
--- /dev/null
+++ b/dev/lib/marginal/index.html
@@ -0,0 +1,21 @@
+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/dev/lib/message/index.html b/dev/lib/message/index.html
index e310743ed..82fefacf5 100644
--- a/dev/lib/message/index.html
+++ b/dev/lib/message/index.html
@@ -1,5 +1,59 @@
-Messages · ReactiveMP.jl In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.
Both belief propagation and variational messages are subtypes of a AbstractMessage
supertype.
AbstractMessage
An abstract supertype for all concrete message types.
See also: Message
source Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
Message{D, A} <: AbstractMessage
Message
structure encodes a Belief Propagation message, which holds some data
that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data
object and proxies most of the statistical functions, e.g. mean
, mode
, cov
etc.
Arguments
data::D
: message always holds some data object associated with itis_clamped::Bool
, specifies if this message is clampedis_initial::Bool
, specifies if this message is initialaddons::A
, specifies the addons of the messageExample
julia> distribution = Gamma(10.0, 2.0)
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
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+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
Distributions.Gamma{Float64}(α=10.0, θ=2.0)
julia> message = Message(distribution, false, true, nothing)
@@ -16,5 +70,7 @@
julia> is_initial(message)
true
-
See also: AbstractMessage
, ReactiveMP.materialize!
source materialize!(message::AbstractMessage)
Materializes an abstract message and converts it to be of type Message
.
See also: Message
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
distribution = NormalMeanPrecision(0.0, 1.0)
-message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
The user should not really interact with Message
structure while working with ReactiveMP
unless doing some advanced inference procedures that involve prediction.
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+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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diff --git a/dev/lib/nodes/ar/index.html b/dev/lib/nodes/ar/index.html
new file mode 100644
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/dev/lib/nodes/bifm/index.html b/dev/lib/nodes/bifm/index.html
new file mode 100644
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--- /dev/null
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@@ -0,0 +1,22 @@
+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/dev/lib/nodes/ctransition/index.html b/dev/lib/nodes/ctransition/index.html
new file mode 100644
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--- /dev/null
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+
+Continuous transition · ReactiveMP.jl The functional form of the ContinuousTransition node is given by: y ~ Normal(K(a) * x, W⁻¹)
This node transforms an m-dimensional vector x into an n-dimensional vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
via a transformation K(a). ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
The ContinuousTransition node support two factorizations:
Mean-field factorization: @constraints begin
+ q(y, x, a, W) = q(y)q(x)q(a)q(W)
+end
Structured factorization: @constraints begin
+ q(y, x, a, W) = q(y, x)q(a)q(W)
+end
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/dev/lib/nodes/delta/index.html b/dev/lib/nodes/delta/index.html
new file mode 100644
index 000000000..309504c2b
--- /dev/null
+++ b/dev/lib/nodes/delta/index.html
@@ -0,0 +1,6 @@
+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
ProdCVI
is deprecated in favor of CVIProjection
.
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source CVIProjection(; parameters...)
A structure representing the parameters for the Conjugate Variational Inference (CVI) projection method. This structure is a subtype of AbstractApproximationMethod
and is used to configure the settings for CVI.
The CVIProjection
method requires ExponentialFamilyProjection
package installed in the current environment.
Parameters
rng::R
: The random number generator used for sampling. Default is Random.MersenneTwister(42)
.marginalsamples::S
: The number of samples used for approximating marginal distributions. Default is 10
.outsamples::S
: The number of samples used for approximating output message distributions. Default is 100
.prjparams::P
: Parameters for the exponential family projection. Default is nothing
, in which case it will use ExponentialFamilyProjection.DefaultProjectionParameters()
.The CVIProjection
method is an experimental enhancement of the now-deprecated CVI
, offering better stability and improved accuracy. Note that the parameters of this structure, as well as their defaults, are subject to change during the experimentation phase.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/dev/lib/nodes/equality/index.html b/dev/lib/nodes/equality/index.html
new file mode 100644
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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diff --git a/dev/lib/nodes/flow/index.html b/dev/lib/nodes/flow/index.html
index 057e8d29d..552615e28 100644
--- a/dev/lib/nodes/flow/index.html
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@@ -1,9 +1,9 @@
-Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+
Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
y_1 &= x_1 \\
y_2 &= x_2 + f(x_1)
\end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
x_1 &= y_1 \\
x_2 &= y_2 - f(y_1)
\end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
-layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
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+
+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
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-
-Overview · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
To quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node
or Base.doc(make_node)
.
ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:
struct MyNewCustomNode end
-
-@node MyNewCustomNode Stochastic [ x, y, z ]
-# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
-# Node's tag/name Node's type A fixed set of edges
-# Another possible The very first edge (in this example `x`) is considered
-# value is to be the output of the node
-# `Deterministic`
This expression registers a new node that can be used with the inference engine. Note howeve, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
plus_node = make_node(+)
-
-println("Is `+` node deterministic: ", isdeterministic(plus_node))
-println("Is `+` node stochastic: ", isstochastic(plus_node))
Is `+` node deterministic: true
-Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
bernoulli_node = make_node(Bernoulli)
-
-println("Is `Bernoulli` node deterministic: ", isdeterministic(bernoulli_node))
-println("Is `Bernoulli` node stochastic: ", isstochastic(bernoulli_node))
Is `Bernoulli` node deterministic: false
-Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(plus_node))
-println("sdtype() of `Bernoulli` node is ", sdtype(bernoulli_node))
sdtype() of `+` node is Deterministic()
-sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require inbound messagesstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial inbound messages for edges in indices
Note: start_with
uses setmessage!
mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
- # ...
- y ~ NormalMeanVariance(x, τ) where {
- pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)
- # ^^^ ^^^
- # request 'inbound' for 'x' we may do the same for 'τ',
- # and initialise with `vague(...)` but here we skip initialisation
- }
- # ...
-end
Deprecation warning: RequireInboundFunctionalDependencies
has been deprecated in favor of RequireMessageFunctionalDependencies
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)
Similar to DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the posterior marginal on that edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require their own marginalsstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial marginal for edges in indices
Note: start_with
uses the setmarginal!
mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
- # ...
- y ~ NormalMeanVariance(x, τ) where {
- pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)
- # ^^^ ^^^
- # request 'marginal' for 'x' we may do the same for 'τ',
- # and initialise with `vague(...)` but here we skip initialisation
- }
- # ...
-end
Note: The simplified construction in @model
macro syntax is only available in GraphPPL.jl
of version >2.2.0
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.as_node_functional_form
trait function and to specify a ReactiveMP.ValidNodeFunctionalForm
singleton as a return object. By default ReactiveMP.as_node_functional_form
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
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diff --git a/dev/lib/rules/index.html b/dev/lib/rules/index.html
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
fallback
- specifies the fallback rule to use in case the rule is not defined for the given NodeType
and specified argumentsSee also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source NodeFunctionRuleFallback(extractfn = mean)
A fallback rule for Stochastic
nodes that uses a specified function (default: mean) to transform messages and marginals into a value. It calls the nodefunction
method to create the message.
When a node is defined with the @node
macro:
1. The nodefunction
typically calls logpdf
associated with the node's distribution. 2. The first edge in the @node
specification is used to evaluate logpdf
at. 3. Other edges are used to instantiate the associated distribution object.
julia> using ReactiveMP, BayesBase, Distributions
+
+julia> struct MyBeta{A, B} <: ContinuousUnivariateDistribution
+ a::A
+ b::B
+ end
+
+julia> BayesBase.logpdf(d::MyBeta, x) = logpdf(Beta(d.a, d.b), x)
+
+julia> BayesBase.insupport(d::MyBeta, x::Real) = true
+
+julia> @node MyBeta Stochastic [out, a, b]
+
+julia> message = @call_rule [fallback = NodeFunctionRuleFallback()] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2));
+
+julia> logpdf(message, 0.5)
+-0.5017644952110732
+
+julia> message = @call_rule [fallback = NodeFunctionRuleFallback(mode)] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2)); # evaluate at `mode`
+
+julia> logpdf(message, 0.5)
+-0.5954237415153454
source nodefunction(::Type{T}) where {T}
Returns a function that represents a node of type T
. The function typically takes arguments that represent the node's input and output variables in the same order as defined in the @node
macro.
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing SoftDot γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(θ) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot x μ(y) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(θ) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y μ(x) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper out q(in) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any HalfNormal out q(v) :: BayesBase.PointMass Nothing GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.GammaShapeRate β q(out) :: Any Nothing q(α) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Any Nothing q(β) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.GammaShapeRate out q(α) :: Any Nothing q(β) :: Any ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ContinuousTransition W q(y) :: Any ContinuousTransitionMeta q(x) :: Any q(a) :: Any ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y) :: Any ContinuousTransitionMeta q(x) :: Any q(a) :: Any q(W) :: Any ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x q(y) :: Any ContinuousTransitionMeta q(a) :: Any q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y q(x) :: Any ContinuousTransitionMeta q(a) :: Any q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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-
-Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
- # rule body
- return ...
-end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
- m_μ_mean, m_μ_cov = mean_cov(m_μ)
- return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
-end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source Prints a table of all message passing update rules in ReactiveMP.
-
-Use `Markdown.parse` on the output of this function to get a prettified table.
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
- # rule body
- return ...
-end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
- xi_out, W_out = weightedmean_precision(m_out)
- xi_μ, W_μ = weightedmean_precision(m_μ)
-
- W_bar = mean(q_τ)
-
- W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
- xi = [xi_out; xi_μ]
-
- return MvNormalWeightedMeanPrecision(xi, W)
-end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
- return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
-end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
-@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
- (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
- (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
- (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
-]
-
-@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
- (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
- (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
- (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
-]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source using ReactiveMP, Markdown
-Markdown.parse(ReactiveMP.print_rules_table())
Node Output Inputs Meta * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing HalfNormal out q(v) :: BayesBase.PointMass Nothing ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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var documenterSearchIndex = {"docs":
-[{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/#lib-helpers-skip-index-iterator","page":"Helper utils","title":"SkipIndexIterator","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#lib-helpers-functional-index","page":"Helper utils","title":"FunctionalIndex","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.FunctionalIndex","category":"page"},{"location":"lib/helpers/#ReactiveMP.FunctionalIndex","page":"Helper utils","title":"ReactiveMP.FunctionalIndex","text":"FunctionalIndex\n\nA special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex can be firstindex or lastindex, but more complex use cases are possible too, e.g. firstindex + 1. Important part of the implementation is that the resulting structure is isbitstype(...) = true, that allows to store it in parametric type as valtype.\n\nOne use case for this structure is to dispatch on and to replace begin or end (or more complex use cases, e.g. begin + 1) markers in constraints specification language.\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.print_rules_table","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.print_rules_table","page":"Message update rules","title":"ReactiveMP.print_rules_table","text":"Prints a table of all message passing update rules in ReactiveMP.\n\nUse `Markdown.parse` on the output of this function to get a prettified table.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.","category":"page"},{"location":"lib/message/#Abstract-message-type","page":"Messages","title":"Abstract message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Both belief propagation and variational messages are subtypes of a AbstractMessage supertype.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"AbstractMessage\n\nAn abstract supertype for all concrete message types.\n\nSee also: Message\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Message\nReactiveMP.materialize!","category":"page"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message{D, A} <: AbstractMessage\n\nMessage structure encodes a Belief Propagation message, which holds some data that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data object and proxies most of the statistical functions, e.g. mean, mode, cov etc.\n\nArguments\n\ndata::D: message always holds some data object associated with it\nis_clamped::Bool, specifies if this message is clamped\nis_initial::Bool, specifies if this message is initial\naddons::A, specifies the addons of the message\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\nSee also: AbstractMessage, ReactiveMP.materialize!\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.materialize!","page":"Messages","title":"ReactiveMP.materialize!","text":"materialize!(message::AbstractMessage)\n\nMaterializes an abstract message and converts it to be of type Message.\n\nSee also: Message\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"distribution = NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The user should not really interact with Message structure while working with ReactiveMP unless doing some advanced inference procedures that involve prediction.","category":"page"},{"location":"lib/nodes/nodes/#lib-node","page":"Overview","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\nTo quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node or Base.doc(make_node).","category":"page"},{"location":"lib/nodes/nodes/#lib-custom-node","page":"Overview","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, z ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic`","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"This expression registers a new node that can be used with the inference engine. Note howeve, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro.","category":"page"},{"location":"lib/nodes/nodes/#lib-node-types","page":"Overview","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.Deterministic","page":"Overview","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.Stochastic","page":"Overview","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.isdeterministic","page":"Overview","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.isstochastic","page":"Overview","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.sdtype","page":"Overview","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"plus_node = make_node(+)\n\nprintln(\"Is `+` node deterministic: \", isdeterministic(plus_node))\nprintln(\"Is `+` node stochastic: \", isstochastic(plus_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"bernoulli_node = make_node(Bernoulli)\n\nprintln(\"Is `Bernoulli` node deterministic: \", isdeterministic(bernoulli_node))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(bernoulli_node))","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"println(\"sdtype() of `+` node is \", sdtype(plus_node))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(bernoulli_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/#lib-node-functional-dependencies-pipeline","page":"Overview","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Overview","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis pipeline translates directly to enforcing a variational message passing scheme. In order to compute a message out of some edge, this pipeline requires messages from edges within the same edge-cluster and marginals over other edge-clusters.\n\nSee also: ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require inbound messages\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial inbound messages for edges in indices\n\nNote: start_with uses setmessage! mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nDeprecation warning: RequireInboundFunctionalDependencies has been deprecated in favor of RequireMessageFunctionalDependencies.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nSimilar to DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the posterior marginal on that edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require their own marginals\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial marginal for edges in indices\n\nNote: start_with uses the setmarginal! mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nNote: The simplified construction in @model macro syntax is only available in GraphPPL.jl of version >2.2.0.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#lib-node-traits","page":"Overview","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Each factor node has to define the ReactiveMP.as_node_functional_form trait function and to specify a ReactiveMP.ValidNodeFunctionalForm singleton as a return object. By default ReactiveMP.as_node_functional_form returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.ValidNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.as_node_functional_form","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.ValidNodeFunctionalForm","page":"Overview","title":"ReactiveMP.ValidNodeFunctionalForm","text":"ValidNodeFunctionalForm\n\nTrait specification for an object that can be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Overview","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that can not be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.ValidNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.as_node_functional_form","page":"Overview","title":"ReactiveMP.as_node_functional_form","text":"as_node_functional_form(object)\n\nDetermines object node functional form trait specification. Returns either ValidNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.ValidNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, as_variable, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions and interaction with the Julia ecosystem","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions and interaction with the Julia ecosystem","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\nSee also: CompositeFormConstraint\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. Any functional form constraint that defines is_point_mass_form_constraint() = true may be used only as the last element of the composition.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, default_form_check_strategy, is_point_mass_form_constraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Is-point-mass-form-constraint-(optional)","page":"Custom functional form","title":"Is point mass form constraint (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form may implement a new method for the is_point_mass_form_constraint function that returns either true or false. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"is_point_mass_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.is_point_mass_form_constraint","page":"Custom functional form","title":"ReactiveMP.is_point_mass_form_constraint","text":"is_point_mass_form_constraint(form_constraint)\n\nSpecifies whether form constraint always returns PointMass estimates or not. For a given form_constraint returns either true or false.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Compatibility-with-@constraints-macro-(optional)","page":"Custom functional form","title":"Compatibility with @constraints macro (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"To make custom functional form constraint compatible with the @constraints macro, it must implement a new method for the make_form_constraint function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"make_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.make_form_constraint","page":"Custom functional form","title":"ReactiveMP.make_form_constraint","text":"make_form_constraint(::Type, args...; kwargs...)\n\nCreates form constraint object based on passed type with given args and kwargs. Used to simplify form constraint specification.\n\nAs an example:\n\nmake_form_constraint(PointMass)\n\ncreates an instance of PointMassFormConstraint and \n\nmake_form_constraint(SampleList, 5000, LeftProposal())\n\nshould create an instance of SampleListFormConstraint.\n\nSee also: AbstractFormConstraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"lib/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"lib/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/message.md\",\n \"lib/node.md\",\n \"lib/math.md\",\n \"extra/contributing.md\"\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/algebra/common/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/common/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/common/","page":"Algebra utils","title":"Algebra utils","text":"diageye","category":"page"},{"location":"lib/algebra/common/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"}]
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.CVIProjection\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nnote: Note\nProdCVI is deprecated in favor of CVIProjection.\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVIProjection","page":"Delta","title":"ReactiveMP.CVIProjection","text":"CVIProjection(; parameters...)\n\nA structure representing the parameters for the Conjugate Variational Inference (CVI) projection method. This structure is a subtype of AbstractApproximationMethod and is used to configure the settings for CVI.\n\nnote: Note\nThe CVIProjection method requires ExponentialFamilyProjection package installed in the current environment.\n\nParameters\n\nrng::R: The random number generator used for sampling. Default is Random.MersenneTwister(42).\nmarginalsamples::S: The number of samples used for approximating marginal distributions. Default is 10.\noutsamples::S: The number of samples used for approximating output message distributions. Default is 100.\nprjparams::P: Parameters for the exponential family projection. Default is nothing, in which case it will use ExponentialFamilyProjection.DefaultProjectionParameters().\n\nnote: Note\nThe CVIProjection method is an experimental enhancement of the now-deprecated CVI, offering better stability and improved accuracy. Note that the parameters of this structure, as well as their defaults, are subject to change during the experimentation phase.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The functional form of the ContinuousTransition node is given by: y ~ Normal(K(a) * x, W⁻¹)\n\nThis node transforms an m-dimensional vector x into an n-dimensional vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a via a transformation K(a). ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\nThe ContinuousTransition node support two factorizations:\n\nMean-field factorization:\n\n@constraints begin\n q(y, x, a, W) = q(y)q(x)q(a)q(W)\nend\n\nStructured factorization:\n\n@constraints begin\n q(y, x, a, W) = q(y, x)q(a)q(W)\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint\nReactiveMP.preprocess_form_constraints","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.preprocess_form_constraints","page":"Custom functional form","title":"ReactiveMP.preprocess_form_constraints","text":"preprocess_form_constraints(constraints)\n\nThis function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint object. Wraps unknown form constraints into a WrappedFormConstraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(constraint, something)\n\nThis function applies a given form constraint to a given object. \n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional form constraint implementation is the prod function in the BayesBase package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, ExponentialFamily, Distributions, BayesBase\n\n# First, we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end\n\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This assumes that the given `distribution` object has `mean` and `precision` defined.\n # These quantities might be approximated using other methods, such as Laplace approximation.\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # `ProductOf` is a special case. Read more about this type in the corresponding \n # documentation section of the `BayesBase` package.\n # ... \nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())\n\nconstrain_form(constraint, NormalMeanVariance(0, 2))","category":"page"},{"location":"custom/custom-functional-form/#Wrapped-Form-Constraints","page":"Custom functional form","title":"Wrapped Form Constraints","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Some constraint objects might not be subtypes of AbstractFormConstraint. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP expects users to pass a WrappedFormConstraint object, which wraps the original object and makes it compatible with the ReactiveMP inference backend. Note that the ReactiveMP.preprocess_form_constraints function automatically wraps all objects that are not subtypes of AbstractFormConstraint.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Additionally, objects wrapped by WrappedFormConstraints may implement the ReactiveMP.prepare_context function. This function's output will be stored in the WrappedFormConstraints along with the original object. If prepare_context is implemented, the constrain_form function will take three arguments: the original constraint, the context, and the object that needs to be constrained.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.WrappedFormConstraint\nReactiveMP.prepare_context\nReactiveMP.constrain_form(::ReactiveMP.WrappedFormConstraint, something)","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.WrappedFormConstraint","page":"Custom functional form","title":"ReactiveMP.WrappedFormConstraint","text":"WrappedFormConstraint(constraint, context)\n\nThis is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form function. By default all objects that are not sub-typed from AbstractFormConstraint are wrapped into this object. Use ReactiveMP.prepare_context to provide an extra context for a given form constraint, that can be reused between multiple constrain_form calls.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.prepare_context","page":"Custom functional form","title":"ReactiveMP.prepare_context","text":"prepare_context(constraint)\n\nThis function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext if no context is needed (the default behaviour).\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form-Tuple{ReactiveMP.WrappedFormConstraint, Any}","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(wrapped::WrappedFormConstraint, something)\n\nThis function unwraps the wrapped object and calls constrain_form function with the provided context. If the context is not provided, simply calls constrain_form with the wrapped constraint. Otherwise passes the context to the constrain_form function as the second argument.\n\n\n\n\n\n","category":"method"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, Distributions, BayesBase, Random\n\n# First, we define our custom form constraint that creates a set of samples\n# Note that this is not a subtype of `AbstractFormConstraint`\nstruct MyCustomSampleListFormConstraint end\n\n# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions\n# which are necessary for the `ReactiveMP` inference backend\nReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()\n\n# We implement the `prepare_context` function, which returns a random number generator\nfunction ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)\n return Random.default_rng()\nend\n\n# We implement the `constrain_form` function, which returns a set of samples\nfunction ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)\n return rand(context, distribution, 10)\nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())\n\nconstrain_form(constraint, Normal(0, 10))","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\nfallback - specifies the fallback rule to use in case the rule is not defined for the given NodeType and specified arguments\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-fallbacks","page":"Message update rules","title":"Rule fallbacks","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.NodeFunctionRuleFallback\nReactiveMP.nodefunction","category":"page"},{"location":"lib/rules/#ReactiveMP.NodeFunctionRuleFallback","page":"Message update rules","title":"ReactiveMP.NodeFunctionRuleFallback","text":"NodeFunctionRuleFallback(extractfn = mean)\n\nA fallback rule for Stochastic nodes that uses a specified function (default: mean) to transform messages and marginals into a value. It calls the nodefunction method to create the message.\n\nWhen a node is defined with the @node macro:\n\n1.\tThe nodefunction typically calls logpdf associated with the node's distribution. 2.\tThe first edge in the @node specification is used to evaluate logpdf at. 3.\tOther edges are used to instantiate the associated distribution object.\n\njulia> using ReactiveMP, BayesBase, Distributions\n\njulia> struct MyBeta{A, B} <: ContinuousUnivariateDistribution\n a::A\n b::B\n end\n\njulia> BayesBase.logpdf(d::MyBeta, x) = logpdf(Beta(d.a, d.b), x)\n\njulia> BayesBase.insupport(d::MyBeta, x::Real) = true\n\njulia> @node MyBeta Stochastic [out, a, b]\n\njulia> message = @call_rule [fallback = NodeFunctionRuleFallback()] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2));\n\njulia> logpdf(message, 0.5)\n-0.5017644952110732\n\njulia> message = @call_rule [fallback = NodeFunctionRuleFallback(mode)] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2)); # evaluate at `mode`\n\njulia> logpdf(message, 0.5)\n-0.5954237415153454\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/#ReactiveMP.nodefunction","page":"Message update rules","title":"ReactiveMP.nodefunction","text":"nodefunction(::Type{T}) where {T}\n\nReturns a function that represents a node of type T. The function typically takes arguments that represent the node's input and output variables in the same order as defined in the @node macro.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
}
diff --git a/stable b/stable
index 516ff7a78..1ddc0f604 120000
--- a/stable
+++ b/stable
@@ -1 +1 @@
-v3.13.0
\ No newline at end of file
+v4.3.0
\ No newline at end of file
diff --git a/v3 b/v3
index 516ff7a78..46dcedd50 120000
--- a/v3
+++ b/v3
@@ -1 +1 @@
-v3.13.0
\ No newline at end of file
+v3.14.0
\ No newline at end of file
diff --git a/v3.13 b/v3.13
index 516ff7a78..6afce1303 120000
--- a/v3.13
+++ b/v3.13
@@ -1 +1 @@
-v3.13.0
\ No newline at end of file
+v3.13.3
\ No newline at end of file
diff --git a/v3.13.1/.documenter-siteinfo.json b/v3.13.1/.documenter-siteinfo.json
new file mode 100644
index 000000000..4bc5b782a
--- /dev/null
+++ b/v3.13.1/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-12T15:00:45","documenter_version":"1.2.1"}}
\ No newline at end of file
diff --git a/v3.13.1/assets/documenter.js b/v3.13.1/assets/documenter.js
new file mode 100644
index 000000000..f5311607b
--- /dev/null
+++ b/v3.13.1/assets/documenter.js
@@ -0,0 +1,889 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
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+ 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function () {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp();
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown();
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'minisearch'], function($, minisearch) {
+
+// In general, most search related things will have "search" as a prefix.
+// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+let results = [];
+let timer = undefined;
+
+let data = documenterSearchIndex["docs"].map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+});
+
+// list below is the lunr 2.1.3 list minus the intersect with names(Base)
+// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+// ideally we'd just filter the original list but it's not available as a variable
+const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+]);
+
+let index = new minisearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ boost: { title: 100 },
+ fuzzy: 2,
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+ }
+
+ return word ?? null;
+ },
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ },
+});
+
+index.addAll(data);
+
+let filters = [...new Set(data.map((x) => x.category))];
+var modal_filters = make_modal_body_filters(filters);
+var filter_results = [];
+
+$(document).on("keyup", ".documenter-search-input", function (event) {
+ // Adding a debounce to prevent disruptions from super-speed typing!
+ debounce(() => update_search(filter_results), 300);
+});
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ $(this).removeClass("search-filter-selected");
+ } else {
+ $(this).addClass("search-filter-selected");
+ }
+
+ // Adding a debounce to prevent disruptions from crazy clicking!
+ debounce(() => get_filters(), 300);
+});
+
+/**
+ * A debounce function, takes a function and an optional timeout in milliseconds
+ *
+ * @function callback
+ * @param {number} timeout
+ */
+function debounce(callback, timeout = 300) {
+ clearTimeout(timer);
+ timer = setTimeout(callback, timeout);
+}
+
+/**
+ * Make/Update the search component
+ *
+ * @param {string[]} selected_filters
+ */
+function update_search(selected_filters = []) {
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ results = index.search(querystring, {
+ filter: (result) => {
+ // Filtering results
+ if (selected_filters.length === 0) {
+ return result.score >= 1;
+ } else {
+ return (
+ result.score >= 1 && selected_filters.includes(result.category)
+ );
+ }
+ },
+ });
+
+ let search_result_container = ``;
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ results.forEach(function (result) {
+ if (result.location) {
+ // Checking for duplication of results for the same page
+ if (!links.includes(result.location)) {
+ search_results += make_search_result(result, querystring);
+ count++;
+ }
+
+ links.push(result.location);
+ }
+ });
+
+ let result_count = `${count} result(s)
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ filter_results = [];
+ modal_filters = make_modal_body_filters(filters, filter_results);
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @param {string[]} filters
+ * @param {string[]} selected_filters
+ * @returns string
+ */
+function make_modal_body_filters(filters, selected_filters = []) {
+ let str = ``;
+
+ filters.forEach((val) => {
+ if (selected_filters.includes(val)) {
+ str += `${val} `;
+ } else {
+ str += `${val} `;
+ }
+ });
+
+ let filter_html = `
+
+ Filters:
+ ${str}
+
+ `;
+
+ return filter_html;
+}
+
+/**
+ * Make the result component given a minisearch result data object and the value of the search input as queryString.
+ * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${result.title}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+}
+
+/**
+ * Get selected filters, remake the filter html and lastly update the search modal
+ */
+function get_filters() {
+ let ele = $(".search-filters .search-filter-selected").get();
+ filter_results = ele.map((x) => $(x).text().toLowerCase());
+ modal_filters = make_modal_body_filters(filters, filter_results);
+ update_search(filter_results);
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let search_modal_header = `
+
+`;
+
+let initial_search_body = `
+ Type something to get started!
+`;
+
+let search_modal_footer = `
+
+`;
+
+$(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+);
+
+document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+});
+
+document.querySelector(".close-search-modal").addEventListener("click", () => {
+ closeModal();
+});
+
+$(document).on("click", ".search-result-link", function () {
+ closeModal();
+});
+
+document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+});
+
+// Functions to open and close a modal
+function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+}
+
+function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+}
+
+document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v3.13.1/assets/img/bp-message.svg b/v3.13.1/assets/img/bp-message.svg
new file mode 100644
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--- /dev/null
+++ b/v3.13.1/assets/img/bp-message.svg
@@ -0,0 +1 @@
+
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new file mode 100644
index 000000000..a85960c12
--- /dev/null
+++ b/v3.13.1/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/v3.13.1/assets/img/vmp-message.svg b/v3.13.1/assets/img/vmp-message.svg
new file mode 100644
index 000000000..475cd7f49
--- /dev/null
+++ b/v3.13.1/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
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diff --git a/v3.13.1/assets/themes/documenter-dark.css b/v3.13.1/assets/themes/documenter-dark.css
new file mode 100644
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@@ -0,0 +1,7 @@
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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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diff --git a/v3.13.1/assets/themes/documenter-light.css b/v3.13.1/assets/themes/documenter-light.css
new file mode 100644
index 000000000..2f168c77b
--- /dev/null
+++ b/v3.13.1/assets/themes/documenter-light.css
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span.sgr42{background-color:#066f00}.ansi span.sgr43{background-color:#856b00}.ansi span.sgr44{background-color:#2149b0}.ansi span.sgr45{background-color:#7d4498}.ansi span.sgr46{background-color:#007989}.ansi span.sgr47{background-color:gray}.ansi span.sgr90{color:#616161}.ansi span.sgr91{color:#cb3c33}.ansi span.sgr92{color:#0e8300}.ansi span.sgr93{color:#a98800}.ansi span.sgr94{color:#3c5dcd}.ansi span.sgr95{color:#9256af}.ansi span.sgr96{color:#008fa3}.ansi span.sgr97{color:#f5f5f5}.ansi span.sgr100{background-color:#616161}.ansi span.sgr101{background-color:#cb3c33}.ansi span.sgr102{background-color:#0e8300}.ansi span.sgr103{background-color:#a98800}.ansi span.sgr104{background-color:#3c5dcd}.ansi span.sgr105{background-color:#9256af}.ansi span.sgr106{background-color:#008fa3}.ansi span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*!
+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v3.13.1/assets/themeswap.js b/v3.13.1/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v3.13.1/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v3.13.1/assets/warner.js b/v3.13.1/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v3.13.1/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
+ document.body.appendChild(div);
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+if (document.readyState === "loading") {
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diff --git a/v3.13.1/custom/custom-addons/index.html b/v3.13.1/custom/custom-addons/index.html
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+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
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diff --git a/v3.13.1/custom/custom-functional-form/index.html b/v3.13.1/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
See also: CompositeFormConstraint
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
. Any functional form constraint that defines is_point_mass_form_constraint() = true
may be used only as the last element of the composition.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
Every custom functional form may implement a new method for the is_point_mass_form_constraint
function that returns either true
or false
. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.
To make custom functional form constraint compatible with the @constraints
macro, it must implement a new method for the make_form_constraint
function.
make_form_constraint(::Type, args...; kwargs...)
Creates form constraint object based on passed type
with given args
and kwargs
. Used to simplify form constraint specification.
As an example:
make_form_constraint(PointMass)
creates an instance of PointMassFormConstraint
and
make_form_constraint(SampleList, 5000, LeftProposal())
should create an instance of SampleListFormConstraint
.
See also: AbstractFormConstraint
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v3.13.1/extra/contributing/index.html b/v3.13.1/extra/contributing/index.html
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@@ -0,0 +1,2 @@
+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, as_variable
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v3.13.1/extra/extensions/index.html b/v3.13.1/extra/extensions/index.html
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+
+Extensions and interaction with the Julia ecosystem · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v3.13.1/index.html b/v3.13.1/index.html
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+++ b/v3.13.1/index.html
@@ -0,0 +1,2 @@
+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
Tutorials and examples are available in the RxInfer documentation .
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diff --git a/v3.13.1/lib/algebra/common/index.html b/v3.13.1/lib/algebra/common/index.html
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+++ b/v3.13.1/lib/algebra/common/index.html
@@ -0,0 +1,2 @@
+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source
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diff --git a/v3.13.1/lib/helpers/index.html b/v3.13.1/lib/helpers/index.html
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@@ -0,0 +1,10 @@
+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source FunctionalIndex
A special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex
can be firstindex
or lastindex
, but more complex use cases are possible too, e.g. firstindex + 1
. Important part of the implementation is that the resulting structure is isbitstype(...) = true
, that allows to store it in parametric type as valtype.
One use case for this structure is to dispatch on and to replace begin
or end
(or more complex use cases, e.g. begin + 1
) markers in constraints specification language.
source
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diff --git a/v3.13.1/lib/message/index.html b/v3.13.1/lib/message/index.html
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+
+Messages · ReactiveMP.jl In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.
Both belief propagation and variational messages are subtypes of a AbstractMessage
supertype.
AbstractMessage
An abstract supertype for all concrete message types.
See also: Message
source Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
Message{D, A} <: AbstractMessage
Message
structure encodes a Belief Propagation message, which holds some data
that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data
object and proxies most of the statistical functions, e.g. mean
, mode
, cov
etc.
Arguments
data::D
: message always holds some data object associated with itis_clamped::Bool
, specifies if this message is clampedis_initial::Bool
, specifies if this message is initialaddons::A
, specifies the addons of the messageExample
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
See also: AbstractMessage
, ReactiveMP.materialize!
source materialize!(message::AbstractMessage)
Materializes an abstract message and converts it to be of type Message
.
See also: Message
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
distribution = NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
The user should not really interact with Message
structure while working with ReactiveMP
unless doing some advanced inference procedures that involve prediction.
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diff --git a/dev/lib/methods/index.html b/v3.13.1/lib/methods/index.html
similarity index 84%
rename from dev/lib/methods/index.html
rename to v3.13.1/lib/methods/index.html
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--- a/dev/lib/methods/index.html
+++ b/v3.13.1/lib/methods/index.html
@@ -1,5 +1,5 @@
-Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
import Distributions: mean as mean_from_distributions
import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
# Julia will not overwrite `mean` that is coming from both packages
@@ -194,4 +194,4 @@
softdot
srcubature
tiny
-update!
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documenter-light documenter-dark Automatic (OS)
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+update!
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documenter-light documenter-dark Automatic (OS)
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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diff --git a/v3.13.1/lib/nodes/nodes/index.html b/v3.13.1/lib/nodes/nodes/index.html
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+
+Overview · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
To quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node
or Base.doc(make_node)
.
ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, z ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic`
This expression registers a new node that can be used with the inference engine. Note howeve, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
plus_node = make_node(+)
+
+println("Is `+` node deterministic: ", isdeterministic(plus_node))
+println("Is `+` node stochastic: ", isstochastic(plus_node))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
bernoulli_node = make_node(Bernoulli)
+
+println("Is `Bernoulli` node deterministic: ", isdeterministic(bernoulli_node))
+println("Is `Bernoulli` node stochastic: ", isstochastic(bernoulli_node))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(plus_node))
+println("sdtype() of `Bernoulli` node is ", sdtype(bernoulli_node))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require inbound messagesstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial inbound messages for edges in indices
Note: start_with
uses setmessage!
mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Deprecation warning: RequireInboundFunctionalDependencies
has been deprecated in favor of RequireMessageFunctionalDependencies
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)
Similar to DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the posterior marginal on that edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require their own marginalsstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial marginal for edges in indices
Note: start_with
uses the setmarginal!
mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Note: The simplified construction in @model
macro syntax is only available in GraphPPL.jl
of version >2.2.0
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.as_node_functional_form
trait function and to specify a ReactiveMP.ValidNodeFunctionalForm
singleton as a return object. By default ReactiveMP.as_node_functional_form
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
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diff --git a/v3.13.1/lib/rules/rules/index.html b/v3.13.1/lib/rules/rules/index.html
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source Prints a table of all message passing update rules in ReactiveMP.
+
+Use `Markdown.parse` on the output of this function to get a prettified table.
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source using ReactiveMP, Markdown
+Markdown.parse(ReactiveMP.print_rules_table())
Node Output Inputs Meta * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} HalfNormal out q(v) :: BayesBase.PointMass Nothing GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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This document was generated with Documenter.jl version 1.2.1 on Friday 12 January 2024 . Using Julia version 1.10.0.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/#lib-helpers-skip-index-iterator","page":"Helper utils","title":"SkipIndexIterator","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#lib-helpers-functional-index","page":"Helper utils","title":"FunctionalIndex","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.FunctionalIndex","category":"page"},{"location":"lib/helpers/#ReactiveMP.FunctionalIndex","page":"Helper utils","title":"ReactiveMP.FunctionalIndex","text":"FunctionalIndex\n\nA special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex can be firstindex or lastindex, but more complex use cases are possible too, e.g. firstindex + 1. Important part of the implementation is that the resulting structure is isbitstype(...) = true, that allows to store it in parametric type as valtype.\n\nOne use case for this structure is to dispatch on and to replace begin or end (or more complex use cases, e.g. begin + 1) markers in constraints specification language.\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.print_rules_table","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.print_rules_table","page":"Message update rules","title":"ReactiveMP.print_rules_table","text":"Prints a table of all message passing update rules in ReactiveMP.\n\nUse `Markdown.parse` on the output of this function to get a prettified table.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.","category":"page"},{"location":"lib/message/#Abstract-message-type","page":"Messages","title":"Abstract message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Both belief propagation and variational messages are subtypes of a AbstractMessage supertype.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"AbstractMessage\n\nAn abstract supertype for all concrete message types.\n\nSee also: Message\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Message\nReactiveMP.materialize!","category":"page"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message{D, A} <: AbstractMessage\n\nMessage structure encodes a Belief Propagation message, which holds some data that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data object and proxies most of the statistical functions, e.g. mean, mode, cov etc.\n\nArguments\n\ndata::D: message always holds some data object associated with it\nis_clamped::Bool, specifies if this message is clamped\nis_initial::Bool, specifies if this message is initial\naddons::A, specifies the addons of the message\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\nSee also: AbstractMessage, ReactiveMP.materialize!\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.materialize!","page":"Messages","title":"ReactiveMP.materialize!","text":"materialize!(message::AbstractMessage)\n\nMaterializes an abstract message and converts it to be of type Message.\n\nSee also: Message\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"distribution = NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The user should not really interact with Message structure while working with ReactiveMP unless doing some advanced inference procedures that involve prediction.","category":"page"},{"location":"lib/nodes/nodes/#lib-node","page":"Overview","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\nTo quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node or Base.doc(make_node).","category":"page"},{"location":"lib/nodes/nodes/#lib-custom-node","page":"Overview","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, z ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic`","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"This expression registers a new node that can be used with the inference engine. Note howeve, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro.","category":"page"},{"location":"lib/nodes/nodes/#lib-node-types","page":"Overview","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.Deterministic","page":"Overview","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.Stochastic","page":"Overview","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.isdeterministic","page":"Overview","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.isstochastic","page":"Overview","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.sdtype","page":"Overview","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"plus_node = make_node(+)\n\nprintln(\"Is `+` node deterministic: \", isdeterministic(plus_node))\nprintln(\"Is `+` node stochastic: \", isstochastic(plus_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"bernoulli_node = make_node(Bernoulli)\n\nprintln(\"Is `Bernoulli` node deterministic: \", isdeterministic(bernoulli_node))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(bernoulli_node))","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"println(\"sdtype() of `+` node is \", sdtype(plus_node))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(bernoulli_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/#lib-node-functional-dependencies-pipeline","page":"Overview","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Overview","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis pipeline translates directly to enforcing a variational message passing scheme. In order to compute a message out of some edge, this pipeline requires messages from edges within the same edge-cluster and marginals over other edge-clusters.\n\nSee also: ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require inbound messages\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial inbound messages for edges in indices\n\nNote: start_with uses setmessage! mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nDeprecation warning: RequireInboundFunctionalDependencies has been deprecated in favor of RequireMessageFunctionalDependencies.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nSimilar to DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the posterior marginal on that edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require their own marginals\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial marginal for edges in indices\n\nNote: start_with uses the setmarginal! mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nNote: The simplified construction in @model macro syntax is only available in GraphPPL.jl of version >2.2.0.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#lib-node-traits","page":"Overview","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Each factor node has to define the ReactiveMP.as_node_functional_form trait function and to specify a ReactiveMP.ValidNodeFunctionalForm singleton as a return object. By default ReactiveMP.as_node_functional_form returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.ValidNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.as_node_functional_form","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.ValidNodeFunctionalForm","page":"Overview","title":"ReactiveMP.ValidNodeFunctionalForm","text":"ValidNodeFunctionalForm\n\nTrait specification for an object that can be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Overview","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that can not be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.ValidNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.as_node_functional_form","page":"Overview","title":"ReactiveMP.as_node_functional_form","text":"as_node_functional_form(object)\n\nDetermines object node functional form trait specification. Returns either ValidNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.ValidNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, as_variable, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions and interaction with the Julia ecosystem","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions and interaction with the Julia ecosystem","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\nSee also: CompositeFormConstraint\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. Any functional form constraint that defines is_point_mass_form_constraint() = true may be used only as the last element of the composition.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, default_form_check_strategy, is_point_mass_form_constraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Is-point-mass-form-constraint-(optional)","page":"Custom functional form","title":"Is point mass form constraint (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form may implement a new method for the is_point_mass_form_constraint function that returns either true or false. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"is_point_mass_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.is_point_mass_form_constraint","page":"Custom functional form","title":"ReactiveMP.is_point_mass_form_constraint","text":"is_point_mass_form_constraint(form_constraint)\n\nSpecifies whether form constraint always returns PointMass estimates or not. For a given form_constraint returns either true or false.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Compatibility-with-@constraints-macro-(optional)","page":"Custom functional form","title":"Compatibility with @constraints macro (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"To make custom functional form constraint compatible with the @constraints macro, it must implement a new method for the make_form_constraint function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"make_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.make_form_constraint","page":"Custom functional form","title":"ReactiveMP.make_form_constraint","text":"make_form_constraint(::Type, args...; kwargs...)\n\nCreates form constraint object based on passed type with given args and kwargs. Used to simplify form constraint specification.\n\nAs an example:\n\nmake_form_constraint(PointMass)\n\ncreates an instance of PointMassFormConstraint and \n\nmake_form_constraint(SampleList, 5000, LeftProposal())\n\nshould create an instance of SampleListFormConstraint.\n\nSee also: AbstractFormConstraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"lib/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"lib/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/message.md\",\n \"lib/node.md\",\n \"lib/math.md\",\n \"extra/contributing.md\"\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/algebra/common/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/common/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/common/","page":"Algebra utils","title":"Algebra utils","text":"diageye","category":"page"},{"location":"lib/algebra/common/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v3.13.1/siteinfo.js b/v3.13.1/siteinfo.js
new file mode 100644
index 000000000..9bfffb7e3
--- /dev/null
+++ b/v3.13.1/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v3.13.1";
diff --git a/v3.13.2/.documenter-siteinfo.json b/v3.13.2/.documenter-siteinfo.json
new file mode 100644
index 000000000..91e14ca9c
--- /dev/null
+++ b/v3.13.2/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-25T11:28:31","documenter_version":"1.2.1"}}
\ No newline at end of file
diff --git a/v3.13.2/assets/documenter.js b/v3.13.2/assets/documenter.js
new file mode 100644
index 000000000..f5311607b
--- /dev/null
+++ b/v3.13.2/assets/documenter.js
@@ -0,0 +1,889 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function () {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp();
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown();
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'minisearch'], function($, minisearch) {
+
+// In general, most search related things will have "search" as a prefix.
+// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+let results = [];
+let timer = undefined;
+
+let data = documenterSearchIndex["docs"].map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+});
+
+// list below is the lunr 2.1.3 list minus the intersect with names(Base)
+// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+// ideally we'd just filter the original list but it's not available as a variable
+const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+]);
+
+let index = new minisearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ boost: { title: 100 },
+ fuzzy: 2,
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+ }
+
+ return word ?? null;
+ },
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ },
+});
+
+index.addAll(data);
+
+let filters = [...new Set(data.map((x) => x.category))];
+var modal_filters = make_modal_body_filters(filters);
+var filter_results = [];
+
+$(document).on("keyup", ".documenter-search-input", function (event) {
+ // Adding a debounce to prevent disruptions from super-speed typing!
+ debounce(() => update_search(filter_results), 300);
+});
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ $(this).removeClass("search-filter-selected");
+ } else {
+ $(this).addClass("search-filter-selected");
+ }
+
+ // Adding a debounce to prevent disruptions from crazy clicking!
+ debounce(() => get_filters(), 300);
+});
+
+/**
+ * A debounce function, takes a function and an optional timeout in milliseconds
+ *
+ * @function callback
+ * @param {number} timeout
+ */
+function debounce(callback, timeout = 300) {
+ clearTimeout(timer);
+ timer = setTimeout(callback, timeout);
+}
+
+/**
+ * Make/Update the search component
+ *
+ * @param {string[]} selected_filters
+ */
+function update_search(selected_filters = []) {
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ results = index.search(querystring, {
+ filter: (result) => {
+ // Filtering results
+ if (selected_filters.length === 0) {
+ return result.score >= 1;
+ } else {
+ return (
+ result.score >= 1 && selected_filters.includes(result.category)
+ );
+ }
+ },
+ });
+
+ let search_result_container = ``;
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ results.forEach(function (result) {
+ if (result.location) {
+ // Checking for duplication of results for the same page
+ if (!links.includes(result.location)) {
+ search_results += make_search_result(result, querystring);
+ count++;
+ }
+
+ links.push(result.location);
+ }
+ });
+
+ let result_count = `${count} result(s)
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ filter_results = [];
+ modal_filters = make_modal_body_filters(filters, filter_results);
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @param {string[]} filters
+ * @param {string[]} selected_filters
+ * @returns string
+ */
+function make_modal_body_filters(filters, selected_filters = []) {
+ let str = ``;
+
+ filters.forEach((val) => {
+ if (selected_filters.includes(val)) {
+ str += `${val} `;
+ } else {
+ str += `${val} `;
+ }
+ });
+
+ let filter_html = `
+
+ Filters:
+ ${str}
+
+ `;
+
+ return filter_html;
+}
+
+/**
+ * Make the result component given a minisearch result data object and the value of the search input as queryString.
+ * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${result.title}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+}
+
+/**
+ * Get selected filters, remake the filter html and lastly update the search modal
+ */
+function get_filters() {
+ let ele = $(".search-filters .search-filter-selected").get();
+ filter_results = ele.map((x) => $(x).text().toLowerCase());
+ modal_filters = make_modal_body_filters(filters, filter_results);
+ update_search(filter_results);
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let search_modal_header = `
+
+`;
+
+let initial_search_body = `
+ Type something to get started!
+`;
+
+let search_modal_footer = `
+
+`;
+
+$(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+);
+
+document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+});
+
+document.querySelector(".close-search-modal").addEventListener("click", () => {
+ closeModal();
+});
+
+$(document).on("click", ".search-result-link", function () {
+ closeModal();
+});
+
+document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+});
+
+// Functions to open and close a modal
+function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+}
+
+function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+}
+
+document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v3.13.2/assets/img/bp-message.svg b/v3.13.2/assets/img/bp-message.svg
new file mode 100644
index 000000000..259b70803
--- /dev/null
+++ b/v3.13.2/assets/img/bp-message.svg
@@ -0,0 +1 @@
+
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diff --git a/v3.13.2/assets/img/coin-flip.png b/v3.13.2/assets/img/coin-flip.png
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diff --git a/v3.13.2/assets/img/coin-flip.svg b/v3.13.2/assets/img/coin-flip.svg
new file mode 100644
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--- /dev/null
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diff --git a/v3.13.2/assets/img/vmp-message.svg b/v3.13.2/assets/img/vmp-message.svg
new file mode 100644
index 000000000..475cd7f49
--- /dev/null
+++ b/v3.13.2/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v3.13.2/assets/themes/documenter-dark.css b/v3.13.2/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..9f5449f4b
--- /dev/null
+++ b/v3.13.2/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark 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+ Theme: a11y-dark
+ Author: @ericwbailey
+ Maintainer: @ericwbailey
+
+ Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css
+*/}html.theme--documenter-dark html{background-color:#1f2424;font-size:16px;-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased;min-width:300px;overflow-x:auto;overflow-y:scroll;text-rendering:optimizeLegibility;text-size-adjust:100%}html.theme--documenter-dark article,html.theme--documenter-dark aside,html.theme--documenter-dark figure,html.theme--documenter-dark footer,html.theme--documenter-dark header,html.theme--documenter-dark hgroup,html.theme--documenter-dark section{display:block}html.theme--documenter-dark body,html.theme--documenter-dark button,html.theme--documenter-dark input,html.theme--documenter-dark optgroup,html.theme--documenter-dark select,html.theme--documenter-dark textarea{font-family:"Lato Medium",-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue","Helvetica","Arial",sans-serif}html.theme--documenter-dark code,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark 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.button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--documenter-dark .image.is-16x16,html.theme--documenter-dark #documenter .docs-sidebar 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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v3.13.2/assets/themeswap.js b/v3.13.2/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v3.13.2/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v3.13.2/assets/warner.js b/v3.13.2/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v3.13.2/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
+ document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+ maybeAddWarning();
+}
diff --git a/v3.13.2/custom/custom-addons/index.html b/v3.13.2/custom/custom-addons/index.html
new file mode 100644
index 000000000..fe4dfc3d2
--- /dev/null
+++ b/v3.13.2/custom/custom-addons/index.html
@@ -0,0 +1,24 @@
+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
Theme
documenter-light documenter-dark Automatic (OS)
This document was generated with Documenter.jl version 1.2.1 on Thursday 25 January 2024 . Using Julia version 1.10.0.
diff --git a/v3.13.2/custom/custom-functional-form/index.html b/v3.13.2/custom/custom-functional-form/index.html
new file mode 100644
index 000000000..23476fff3
--- /dev/null
+++ b/v3.13.2/custom/custom-functional-form/index.html
@@ -0,0 +1,21 @@
+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
See also: CompositeFormConstraint
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
. Any functional form constraint that defines is_point_mass_form_constraint() = true
may be used only as the last element of the composition.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
Every custom functional form may implement a new method for the is_point_mass_form_constraint
function that returns either true
or false
. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.
To make custom functional form constraint compatible with the @constraints
macro, it must implement a new method for the make_form_constraint
function.
make_form_constraint(::Type, args...; kwargs...)
Creates form constraint object based on passed type
with given args
and kwargs
. Used to simplify form constraint specification.
As an example:
make_form_constraint(PointMass)
creates an instance of PointMassFormConstraint
and
make_form_constraint(SampleList, 5000, LeftProposal())
should create an instance of SampleListFormConstraint
.
See also: AbstractFormConstraint
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
Theme
documenter-light documenter-dark Automatic (OS)
This document was generated with Documenter.jl version 1.2.1 on Thursday 25 January 2024 . Using Julia version 1.10.0.
diff --git a/v3.13.2/extra/contributing/index.html b/v3.13.2/extra/contributing/index.html
new file mode 100644
index 000000000..65bc1f4d6
--- /dev/null
+++ b/v3.13.2/extra/contributing/index.html
@@ -0,0 +1,2 @@
+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, as_variable
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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+
+Extensions and interaction with the Julia ecosystem · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
Tutorials and examples are available in the RxInfer documentation .
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source FunctionalIndex
A special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex
can be firstindex
or lastindex
, but more complex use cases are possible too, e.g. firstindex + 1
. Important part of the implementation is that the resulting structure is isbitstype(...) = true
, that allows to store it in parametric type as valtype.
One use case for this structure is to dispatch on and to replace begin
or end
(or more complex use cases, e.g. begin + 1
) markers in constraints specification language.
source
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+Messages · ReactiveMP.jl In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.
Both belief propagation and variational messages are subtypes of a AbstractMessage
supertype.
AbstractMessage
An abstract supertype for all concrete message types.
See also: Message
source Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
Message{D, A} <: AbstractMessage
Message
structure encodes a Belief Propagation message, which holds some data
that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data
object and proxies most of the statistical functions, e.g. mean
, mode
, cov
etc.
Arguments
data::D
: message always holds some data object associated with itis_clamped::Bool
, specifies if this message is clampedis_initial::Bool
, specifies if this message is initialaddons::A
, specifies the addons of the messageExample
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
See also: AbstractMessage
, ReactiveMP.materialize!
source materialize!(message::AbstractMessage)
Materializes an abstract message and converts it to be of type Message
.
See also: Message
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
distribution = NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
The user should not really interact with Message
structure while working with ReactiveMP
unless doing some advanced inference procedures that involve prediction.
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ConstraintsSpecification
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DefaultConstraints
+DefaultMeta
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNodeCreationOptions
+FactorNodesCollection
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+FullFactorisation
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+MeanField
+Message
+MetaSpecification
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableCreationOptions
+ReactiveMP
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedConstraints
+UnspecifiedFormConstraint
+UnspecifiedMeta
+VariableBoundEntropy
+VariablesCollection
+VariationalMessage
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+as_variable
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+functional_dependencies
+functionalform
+getapproximation
+getconst
+getconstant
+getdata
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getnode_ids
+getnodes
+getprediction
+getpredictions
+getrandom
+getvardict
+ghcubature
+hasconstvar
+hasdatavar
+hasrandomvar
+huge
+interfaces
+is_clamped
+is_initial
+is_marginalisation
+is_moment_matching
+is_point_mass_form_constraint
+isconnected
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+make_form_constraint
+make_node
+marginalrule
+metadata
+name
+nr_params
+randomvar
+rule
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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+
+Overview · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
To quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node
or Base.doc(make_node)
.
ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, z ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic`
This expression registers a new node that can be used with the inference engine. Note howeve, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
plus_node = make_node(+)
+
+println("Is `+` node deterministic: ", isdeterministic(plus_node))
+println("Is `+` node stochastic: ", isstochastic(plus_node))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
bernoulli_node = make_node(Bernoulli)
+
+println("Is `Bernoulli` node deterministic: ", isdeterministic(bernoulli_node))
+println("Is `Bernoulli` node stochastic: ", isstochastic(bernoulli_node))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(plus_node))
+println("sdtype() of `Bernoulli` node is ", sdtype(bernoulli_node))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require inbound messagesstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial inbound messages for edges in indices
Note: start_with
uses setmessage!
mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Deprecation warning: RequireInboundFunctionalDependencies
has been deprecated in favor of RequireMessageFunctionalDependencies
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)
Similar to DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the posterior marginal on that edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require their own marginalsstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial marginal for edges in indices
Note: start_with
uses the setmarginal!
mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Note: The simplified construction in @model
macro syntax is only available in GraphPPL.jl
of version >2.2.0
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.as_node_functional_form
trait function and to specify a ReactiveMP.ValidNodeFunctionalForm
singleton as a return object. By default ReactiveMP.as_node_functional_form
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
Theme
documenter-light documenter-dark Automatic (OS)
This document was generated with Documenter.jl version 1.2.1 on Thursday 25 January 2024 . Using Julia version 1.10.0.
diff --git a/v3.13.2/lib/rules/rules/index.html b/v3.13.2/lib/rules/rules/index.html
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--- /dev/null
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@@ -0,0 +1,38 @@
+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source Prints a table of all message passing update rules in ReactiveMP.
+
+Use `Markdown.parse` on the output of this function to get a prettified table.
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source using ReactiveMP, Markdown
+Markdown.parse(ReactiveMP.print_rules_table())
Node Output Inputs Meta * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass HalfNormal out q(v) :: BayesBase.PointMass Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper out q(in) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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This document was generated with Documenter.jl version 1.2.1 on Thursday 25 January 2024 . Using Julia version 1.10.0.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/#lib-helpers-skip-index-iterator","page":"Helper utils","title":"SkipIndexIterator","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#lib-helpers-functional-index","page":"Helper utils","title":"FunctionalIndex","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.FunctionalIndex","category":"page"},{"location":"lib/helpers/#ReactiveMP.FunctionalIndex","page":"Helper utils","title":"ReactiveMP.FunctionalIndex","text":"FunctionalIndex\n\nA special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex can be firstindex or lastindex, but more complex use cases are possible too, e.g. firstindex + 1. Important part of the implementation is that the resulting structure is isbitstype(...) = true, that allows to store it in parametric type as valtype.\n\nOne use case for this structure is to dispatch on and to replace begin or end (or more complex use cases, e.g. begin + 1) markers in constraints specification language.\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.print_rules_table","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.print_rules_table","page":"Message update rules","title":"ReactiveMP.print_rules_table","text":"Prints a table of all message passing update rules in ReactiveMP.\n\nUse `Markdown.parse` on the output of this function to get a prettified table.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.","category":"page"},{"location":"lib/message/#Abstract-message-type","page":"Messages","title":"Abstract message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Both belief propagation and variational messages are subtypes of a AbstractMessage supertype.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"AbstractMessage\n\nAn abstract supertype for all concrete message types.\n\nSee also: Message\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Message\nReactiveMP.materialize!","category":"page"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message{D, A} <: AbstractMessage\n\nMessage structure encodes a Belief Propagation message, which holds some data that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data object and proxies most of the statistical functions, e.g. mean, mode, cov etc.\n\nArguments\n\ndata::D: message always holds some data object associated with it\nis_clamped::Bool, specifies if this message is clamped\nis_initial::Bool, specifies if this message is initial\naddons::A, specifies the addons of the message\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\nSee also: AbstractMessage, ReactiveMP.materialize!\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.materialize!","page":"Messages","title":"ReactiveMP.materialize!","text":"materialize!(message::AbstractMessage)\n\nMaterializes an abstract message and converts it to be of type Message.\n\nSee also: Message\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"distribution = NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The user should not really interact with Message structure while working with ReactiveMP unless doing some advanced inference procedures that involve prediction.","category":"page"},{"location":"lib/nodes/nodes/#lib-node","page":"Overview","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\nTo quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node or Base.doc(make_node).","category":"page"},{"location":"lib/nodes/nodes/#lib-custom-node","page":"Overview","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, z ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic`","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"This expression registers a new node that can be used with the inference engine. Note howeve, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro.","category":"page"},{"location":"lib/nodes/nodes/#lib-node-types","page":"Overview","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.Deterministic","page":"Overview","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.Stochastic","page":"Overview","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.isdeterministic","page":"Overview","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.isstochastic","page":"Overview","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.sdtype","page":"Overview","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"plus_node = make_node(+)\n\nprintln(\"Is `+` node deterministic: \", isdeterministic(plus_node))\nprintln(\"Is `+` node stochastic: \", isstochastic(plus_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"bernoulli_node = make_node(Bernoulli)\n\nprintln(\"Is `Bernoulli` node deterministic: \", isdeterministic(bernoulli_node))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(bernoulli_node))","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"println(\"sdtype() of `+` node is \", sdtype(plus_node))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(bernoulli_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/#lib-node-functional-dependencies-pipeline","page":"Overview","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Overview","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis pipeline translates directly to enforcing a variational message passing scheme. In order to compute a message out of some edge, this pipeline requires messages from edges within the same edge-cluster and marginals over other edge-clusters.\n\nSee also: ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require inbound messages\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial inbound messages for edges in indices\n\nNote: start_with uses setmessage! mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nDeprecation warning: RequireInboundFunctionalDependencies has been deprecated in favor of RequireMessageFunctionalDependencies.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nSimilar to DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the posterior marginal on that edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require their own marginals\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial marginal for edges in indices\n\nNote: start_with uses the setmarginal! mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nNote: The simplified construction in @model macro syntax is only available in GraphPPL.jl of version >2.2.0.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#lib-node-traits","page":"Overview","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Each factor node has to define the ReactiveMP.as_node_functional_form trait function and to specify a ReactiveMP.ValidNodeFunctionalForm singleton as a return object. By default ReactiveMP.as_node_functional_form returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.ValidNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.as_node_functional_form","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.ValidNodeFunctionalForm","page":"Overview","title":"ReactiveMP.ValidNodeFunctionalForm","text":"ValidNodeFunctionalForm\n\nTrait specification for an object that can be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Overview","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that can not be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.ValidNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.as_node_functional_form","page":"Overview","title":"ReactiveMP.as_node_functional_form","text":"as_node_functional_form(object)\n\nDetermines object node functional form trait specification. Returns either ValidNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.ValidNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, as_variable, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions and interaction with the Julia ecosystem","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions and interaction with the Julia ecosystem","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\nSee also: CompositeFormConstraint\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. Any functional form constraint that defines is_point_mass_form_constraint() = true may be used only as the last element of the composition.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, default_form_check_strategy, is_point_mass_form_constraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Is-point-mass-form-constraint-(optional)","page":"Custom functional form","title":"Is point mass form constraint (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form may implement a new method for the is_point_mass_form_constraint function that returns either true or false. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"is_point_mass_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.is_point_mass_form_constraint","page":"Custom functional form","title":"ReactiveMP.is_point_mass_form_constraint","text":"is_point_mass_form_constraint(form_constraint)\n\nSpecifies whether form constraint always returns PointMass estimates or not. For a given form_constraint returns either true or false.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Compatibility-with-@constraints-macro-(optional)","page":"Custom functional form","title":"Compatibility with @constraints macro (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"To make custom functional form constraint compatible with the @constraints macro, it must implement a new method for the make_form_constraint function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"make_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.make_form_constraint","page":"Custom functional form","title":"ReactiveMP.make_form_constraint","text":"make_form_constraint(::Type, args...; kwargs...)\n\nCreates form constraint object based on passed type with given args and kwargs. Used to simplify form constraint specification.\n\nAs an example:\n\nmake_form_constraint(PointMass)\n\ncreates an instance of PointMassFormConstraint and \n\nmake_form_constraint(SampleList, 5000, LeftProposal())\n\nshould create an instance of SampleListFormConstraint.\n\nSee also: AbstractFormConstraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"lib/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"lib/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/message.md\",\n \"lib/node.md\",\n \"lib/math.md\",\n \"extra/contributing.md\"\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/algebra/common/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/common/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/common/","page":"Algebra utils","title":"Algebra utils","text":"diageye","category":"page"},{"location":"lib/algebra/common/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"}]
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+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'minisearch'], function($, minisearch) {
+
+// In general, most search related things will have "search" as a prefix.
+// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+let results = [];
+let timer = undefined;
+
+let data = documenterSearchIndex["docs"].map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+});
+
+// list below is the lunr 2.1.3 list minus the intersect with names(Base)
+// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+// ideally we'd just filter the original list but it's not available as a variable
+const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+]);
+
+let index = new minisearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ boost: { title: 100 },
+ fuzzy: 2,
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+ }
+
+ return word ?? null;
+ },
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ },
+});
+
+index.addAll(data);
+
+let filters = [...new Set(data.map((x) => x.category))];
+var modal_filters = make_modal_body_filters(filters);
+var filter_results = [];
+
+$(document).on("keyup", ".documenter-search-input", function (event) {
+ // Adding a debounce to prevent disruptions from super-speed typing!
+ debounce(() => update_search(filter_results), 300);
+});
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ $(this).removeClass("search-filter-selected");
+ } else {
+ $(this).addClass("search-filter-selected");
+ }
+
+ // Adding a debounce to prevent disruptions from crazy clicking!
+ debounce(() => get_filters(), 300);
+});
+
+/**
+ * A debounce function, takes a function and an optional timeout in milliseconds
+ *
+ * @function callback
+ * @param {number} timeout
+ */
+function debounce(callback, timeout = 300) {
+ clearTimeout(timer);
+ timer = setTimeout(callback, timeout);
+}
+
+/**
+ * Make/Update the search component
+ *
+ * @param {string[]} selected_filters
+ */
+function update_search(selected_filters = []) {
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ results = index.search(querystring, {
+ filter: (result) => {
+ // Filtering results
+ if (selected_filters.length === 0) {
+ return result.score >= 1;
+ } else {
+ return (
+ result.score >= 1 && selected_filters.includes(result.category)
+ );
+ }
+ },
+ });
+
+ let search_result_container = ``;
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ results.forEach(function (result) {
+ if (result.location) {
+ // Checking for duplication of results for the same page
+ if (!links.includes(result.location)) {
+ search_results += make_search_result(result, querystring);
+ count++;
+ }
+
+ links.push(result.location);
+ }
+ });
+
+ let result_count = `${count} result(s)
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ filter_results = [];
+ modal_filters = make_modal_body_filters(filters, filter_results);
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @param {string[]} filters
+ * @param {string[]} selected_filters
+ * @returns string
+ */
+function make_modal_body_filters(filters, selected_filters = []) {
+ let str = ``;
+
+ filters.forEach((val) => {
+ if (selected_filters.includes(val)) {
+ str += `${val} `;
+ } else {
+ str += `${val} `;
+ }
+ });
+
+ let filter_html = `
+
+ Filters:
+ ${str}
+
+ `;
+
+ return filter_html;
+}
+
+/**
+ * Make the result component given a minisearch result data object and the value of the search input as queryString.
+ * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${result.title}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+}
+
+/**
+ * Get selected filters, remake the filter html and lastly update the search modal
+ */
+function get_filters() {
+ let ele = $(".search-filters .search-filter-selected").get();
+ filter_results = ele.map((x) => $(x).text().toLowerCase());
+ modal_filters = make_modal_body_filters(filters, filter_results);
+ update_search(filter_results);
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let search_modal_header = `
+
+`;
+
+let initial_search_body = `
+ Type something to get started!
+`;
+
+let search_modal_footer = `
+
+`;
+
+$(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+);
+
+document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+});
+
+document.querySelector(".close-search-modal").addEventListener("click", () => {
+ closeModal();
+});
+
+$(document).on("click", ".search-result-link", function () {
+ closeModal();
+});
+
+document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+});
+
+// Functions to open and close a modal
+function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+}
+
+function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+}
+
+document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v3.13.3/assets/img/bp-message.svg b/v3.13.3/assets/img/bp-message.svg
new file mode 100644
index 000000000..259b70803
--- /dev/null
+++ b/v3.13.3/assets/img/bp-message.svg
@@ -0,0 +1 @@
+
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diff --git a/v3.13.3/assets/img/coin-flip.png b/v3.13.3/assets/img/coin-flip.png
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diff --git a/v3.13.3/assets/img/coin-flip.svg b/v3.13.3/assets/img/coin-flip.svg
new file mode 100644
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--- /dev/null
+++ b/v3.13.3/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
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+
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+
+
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+
+
+
diff --git a/v3.13.3/assets/img/vmp-message.svg b/v3.13.3/assets/img/vmp-message.svg
new file mode 100644
index 000000000..475cd7f49
--- /dev/null
+++ b/v3.13.3/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v3.13.3/assets/themes/documenter-dark.css b/v3.13.3/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..9f5449f4b
--- /dev/null
+++ b/v3.13.3/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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diff --git a/v3.13.3/assets/themes/documenter-light.css b/v3.13.3/assets/themes/documenter-light.css
new file mode 100644
index 000000000..2f168c77b
--- /dev/null
+++ b/v3.13.3/assets/themes/documenter-light.css
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span.sgr42{background-color:#066f00}.ansi span.sgr43{background-color:#856b00}.ansi span.sgr44{background-color:#2149b0}.ansi span.sgr45{background-color:#7d4498}.ansi span.sgr46{background-color:#007989}.ansi span.sgr47{background-color:gray}.ansi span.sgr90{color:#616161}.ansi span.sgr91{color:#cb3c33}.ansi span.sgr92{color:#0e8300}.ansi span.sgr93{color:#a98800}.ansi span.sgr94{color:#3c5dcd}.ansi span.sgr95{color:#9256af}.ansi span.sgr96{color:#008fa3}.ansi span.sgr97{color:#f5f5f5}.ansi span.sgr100{background-color:#616161}.ansi span.sgr101{background-color:#cb3c33}.ansi span.sgr102{background-color:#0e8300}.ansi span.sgr103{background-color:#a98800}.ansi span.sgr104{background-color:#3c5dcd}.ansi span.sgr105{background-color:#9256af}.ansi span.sgr106{background-color:#008fa3}.ansi span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*!
+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v3.13.3/assets/themeswap.js b/v3.13.3/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v3.13.3/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
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+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v3.13.3/assets/warner.js b/v3.13.3/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v3.13.3/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
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diff --git a/v3.13.3/custom/custom-addons/index.html b/v3.13.3/custom/custom-addons/index.html
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+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
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diff --git a/v3.13.3/custom/custom-functional-form/index.html b/v3.13.3/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
See also: CompositeFormConstraint
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
. Any functional form constraint that defines is_point_mass_form_constraint() = true
may be used only as the last element of the composition.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
Every custom functional form may implement a new method for the is_point_mass_form_constraint
function that returns either true
or false
. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.
To make custom functional form constraint compatible with the @constraints
macro, it must implement a new method for the make_form_constraint
function.
make_form_constraint(::Type, args...; kwargs...)
Creates form constraint object based on passed type
with given args
and kwargs
. Used to simplify form constraint specification.
As an example:
make_form_constraint(PointMass)
creates an instance of PointMassFormConstraint
and
make_form_constraint(SampleList, 5000, LeftProposal())
should create an instance of SampleListFormConstraint
.
See also: AbstractFormConstraint
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v3.13.3/extra/contributing/index.html b/v3.13.3/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, as_variable
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v3.13.3/extra/extensions/index.html b/v3.13.3/extra/extensions/index.html
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+
+Extensions and interaction with the Julia ecosystem · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v3.13.3/index.html b/v3.13.3/index.html
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
Tutorials and examples are available in the RxInfer documentation .
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diff --git a/v3.13.3/lib/algebra/common/index.html b/v3.13.3/lib/algebra/common/index.html
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source
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diff --git a/v3.13.3/lib/helpers/index.html b/v3.13.3/lib/helpers/index.html
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source FunctionalIndex
A special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex
can be firstindex
or lastindex
, but more complex use cases are possible too, e.g. firstindex + 1
. Important part of the implementation is that the resulting structure is isbitstype(...) = true
, that allows to store it in parametric type as valtype.
One use case for this structure is to dispatch on and to replace begin
or end
(or more complex use cases, e.g. begin + 1
) markers in constraints specification language.
source
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diff --git a/v3.13.3/lib/message/index.html b/v3.13.3/lib/message/index.html
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+
+Messages · ReactiveMP.jl In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.
Both belief propagation and variational messages are subtypes of a AbstractMessage
supertype.
AbstractMessage
An abstract supertype for all concrete message types.
See also: Message
source Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
Message{D, A} <: AbstractMessage
Message
structure encodes a Belief Propagation message, which holds some data
that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data
object and proxies most of the statistical functions, e.g. mean
, mode
, cov
etc.
Arguments
data::D
: message always holds some data object associated with itis_clamped::Bool
, specifies if this message is clampedis_initial::Bool
, specifies if this message is initialaddons::A
, specifies the addons of the messageExample
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
See also: AbstractMessage
, ReactiveMP.materialize!
source materialize!(message::AbstractMessage)
Materializes an abstract message and converts it to be of type Message
.
See also: Message
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
distribution = NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
The user should not really interact with Message
structure while working with ReactiveMP
unless doing some advanced inference procedures that involve prediction.
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diff --git a/v3.13.3/lib/methods/index.html b/v3.13.3/lib/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ConstraintsSpecification
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DefaultConstraints
+DefaultMeta
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNodeCreationOptions
+FactorNodesCollection
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+FullFactorisation
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+MeanField
+Message
+MetaSpecification
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableCreationOptions
+ReactiveMP
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedConstraints
+UnspecifiedFormConstraint
+UnspecifiedMeta
+VariableBoundEntropy
+VariablesCollection
+VariationalMessage
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+as_variable
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+functional_dependencies
+functionalform
+getapproximation
+getconst
+getconstant
+getdata
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getnode_ids
+getnodes
+getprediction
+getpredictions
+getrandom
+getvardict
+ghcubature
+hasconstvar
+hasdatavar
+hasrandomvar
+huge
+interfaces
+is_clamped
+is_initial
+is_marginalisation
+is_moment_matching
+is_point_mass_form_constraint
+isconnected
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+make_form_constraint
+make_node
+marginalrule
+metadata
+name
+nr_params
+randomvar
+rule
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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documenter-light documenter-dark Automatic (OS)
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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+
+Overview · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
To quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node
or Base.doc(make_node)
.
ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, z ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic`
This expression registers a new node that can be used with the inference engine. Note howeve, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
plus_node = make_node(+)
+
+println("Is `+` node deterministic: ", isdeterministic(plus_node))
+println("Is `+` node stochastic: ", isstochastic(plus_node))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
bernoulli_node = make_node(Bernoulli)
+
+println("Is `Bernoulli` node deterministic: ", isdeterministic(bernoulli_node))
+println("Is `Bernoulli` node stochastic: ", isstochastic(bernoulli_node))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(plus_node))
+println("sdtype() of `Bernoulli` node is ", sdtype(bernoulli_node))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require inbound messagesstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial inbound messages for edges in indices
Note: start_with
uses setmessage!
mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Deprecation warning: RequireInboundFunctionalDependencies
has been deprecated in favor of RequireMessageFunctionalDependencies
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)
Similar to DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the posterior marginal on that edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require their own marginalsstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial marginal for edges in indices
Note: start_with
uses the setmarginal!
mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Note: The simplified construction in @model
macro syntax is only available in GraphPPL.jl
of version >2.2.0
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.as_node_functional_form
trait function and to specify a ReactiveMP.ValidNodeFunctionalForm
singleton as a return object. By default ReactiveMP.as_node_functional_form
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
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diff --git a/v3.13.3/lib/rules/rules/index.html b/v3.13.3/lib/rules/rules/index.html
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source Prints a table of all message passing update rules in ReactiveMP.
+
+Use `Markdown.parse` on the output of this function to get a prettified table.
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source using ReactiveMP, Markdown
+Markdown.parse(ReactiveMP.print_rules_table())
Node Output Inputs Meta * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass HalfNormal out q(v) :: BayesBase.PointMass Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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This document was generated with Documenter.jl version 1.2.1 on Friday 9 February 2024 . Using Julia version 1.10.0.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/#lib-helpers-skip-index-iterator","page":"Helper utils","title":"SkipIndexIterator","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#lib-helpers-functional-index","page":"Helper utils","title":"FunctionalIndex","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.FunctionalIndex","category":"page"},{"location":"lib/helpers/#ReactiveMP.FunctionalIndex","page":"Helper utils","title":"ReactiveMP.FunctionalIndex","text":"FunctionalIndex\n\nA special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex can be firstindex or lastindex, but more complex use cases are possible too, e.g. firstindex + 1. Important part of the implementation is that the resulting structure is isbitstype(...) = true, that allows to store it in parametric type as valtype.\n\nOne use case for this structure is to dispatch on and to replace begin or end (or more complex use cases, e.g. begin + 1) markers in constraints specification language.\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.print_rules_table","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.print_rules_table","page":"Message update rules","title":"ReactiveMP.print_rules_table","text":"Prints a table of all message passing update rules in ReactiveMP.\n\nUse `Markdown.parse` on the output of this function to get a prettified table.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.","category":"page"},{"location":"lib/message/#Abstract-message-type","page":"Messages","title":"Abstract message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Both belief propagation and variational messages are subtypes of a AbstractMessage supertype.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"AbstractMessage\n\nAn abstract supertype for all concrete message types.\n\nSee also: Message\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Message\nReactiveMP.materialize!","category":"page"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message{D, A} <: AbstractMessage\n\nMessage structure encodes a Belief Propagation message, which holds some data that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data object and proxies most of the statistical functions, e.g. mean, mode, cov etc.\n\nArguments\n\ndata::D: message always holds some data object associated with it\nis_clamped::Bool, specifies if this message is clamped\nis_initial::Bool, specifies if this message is initial\naddons::A, specifies the addons of the message\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\nSee also: AbstractMessage, ReactiveMP.materialize!\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.materialize!","page":"Messages","title":"ReactiveMP.materialize!","text":"materialize!(message::AbstractMessage)\n\nMaterializes an abstract message and converts it to be of type Message.\n\nSee also: Message\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"distribution = NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The user should not really interact with Message structure while working with ReactiveMP unless doing some advanced inference procedures that involve prediction.","category":"page"},{"location":"lib/nodes/nodes/#lib-node","page":"Overview","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\nTo quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node or Base.doc(make_node).","category":"page"},{"location":"lib/nodes/nodes/#lib-custom-node","page":"Overview","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, z ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic`","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"This expression registers a new node that can be used with the inference engine. Note howeve, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro.","category":"page"},{"location":"lib/nodes/nodes/#lib-node-types","page":"Overview","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.Deterministic","page":"Overview","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.Stochastic","page":"Overview","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.isdeterministic","page":"Overview","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.isstochastic","page":"Overview","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.sdtype","page":"Overview","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"plus_node = make_node(+)\n\nprintln(\"Is `+` node deterministic: \", isdeterministic(plus_node))\nprintln(\"Is `+` node stochastic: \", isstochastic(plus_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"bernoulli_node = make_node(Bernoulli)\n\nprintln(\"Is `Bernoulli` node deterministic: \", isdeterministic(bernoulli_node))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(bernoulli_node))","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"println(\"sdtype() of `+` node is \", sdtype(plus_node))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(bernoulli_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/#lib-node-functional-dependencies-pipeline","page":"Overview","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Overview","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis pipeline translates directly to enforcing a variational message passing scheme. In order to compute a message out of some edge, this pipeline requires messages from edges within the same edge-cluster and marginals over other edge-clusters.\n\nSee also: ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require inbound messages\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial inbound messages for edges in indices\n\nNote: start_with uses setmessage! mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nDeprecation warning: RequireInboundFunctionalDependencies has been deprecated in favor of RequireMessageFunctionalDependencies.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nSimilar to DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the posterior marginal on that edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require their own marginals\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial marginal for edges in indices\n\nNote: start_with uses the setmarginal! mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nNote: The simplified construction in @model macro syntax is only available in GraphPPL.jl of version >2.2.0.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#lib-node-traits","page":"Overview","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Each factor node has to define the ReactiveMP.as_node_functional_form trait function and to specify a ReactiveMP.ValidNodeFunctionalForm singleton as a return object. By default ReactiveMP.as_node_functional_form returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.ValidNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.as_node_functional_form","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.ValidNodeFunctionalForm","page":"Overview","title":"ReactiveMP.ValidNodeFunctionalForm","text":"ValidNodeFunctionalForm\n\nTrait specification for an object that can be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Overview","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that can not be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.ValidNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.as_node_functional_form","page":"Overview","title":"ReactiveMP.as_node_functional_form","text":"as_node_functional_form(object)\n\nDetermines object node functional form trait specification. Returns either ValidNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.ValidNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, as_variable, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions and interaction with the Julia ecosystem","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions and interaction with the Julia ecosystem","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\nSee also: CompositeFormConstraint\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. Any functional form constraint that defines is_point_mass_form_constraint() = true may be used only as the last element of the composition.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, default_form_check_strategy, is_point_mass_form_constraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Is-point-mass-form-constraint-(optional)","page":"Custom functional form","title":"Is point mass form constraint (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form may implement a new method for the is_point_mass_form_constraint function that returns either true or false. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"is_point_mass_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.is_point_mass_form_constraint","page":"Custom functional form","title":"ReactiveMP.is_point_mass_form_constraint","text":"is_point_mass_form_constraint(form_constraint)\n\nSpecifies whether form constraint always returns PointMass estimates or not. For a given form_constraint returns either true or false.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Compatibility-with-@constraints-macro-(optional)","page":"Custom functional form","title":"Compatibility with @constraints macro (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"To make custom functional form constraint compatible with the @constraints macro, it must implement a new method for the make_form_constraint function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"make_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.make_form_constraint","page":"Custom functional form","title":"ReactiveMP.make_form_constraint","text":"make_form_constraint(::Type, args...; kwargs...)\n\nCreates form constraint object based on passed type with given args and kwargs. Used to simplify form constraint specification.\n\nAs an example:\n\nmake_form_constraint(PointMass)\n\ncreates an instance of PointMassFormConstraint and \n\nmake_form_constraint(SampleList, 5000, LeftProposal())\n\nshould create an instance of SampleListFormConstraint.\n\nSee also: AbstractFormConstraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"lib/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"lib/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/message.md\",\n \"lib/node.md\",\n \"lib/math.md\",\n \"extra/contributing.md\"\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/algebra/common/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/common/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/common/","page":"Algebra utils","title":"Algebra utils","text":"diageye","category":"page"},{"location":"lib/algebra/common/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v3.13.3/siteinfo.js b/v3.13.3/siteinfo.js
new file mode 100644
index 000000000..0ad6c49a4
--- /dev/null
+++ b/v3.13.3/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v3.13.3";
diff --git a/v3.14 b/v3.14
new file mode 120000
index 000000000..46dcedd50
--- /dev/null
+++ b/v3.14
@@ -0,0 +1 @@
+v3.14.0
\ No newline at end of file
diff --git a/v3.14.0/.documenter-siteinfo.json b/v3.14.0/.documenter-siteinfo.json
new file mode 100644
index 000000000..ab430e859
--- /dev/null
+++ b/v3.14.0/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-18T13:08:09","documenter_version":"1.3.0"}}
\ No newline at end of file
diff --git a/v3.14.0/assets/documenter.js b/v3.14.0/assets/documenter.js
new file mode 100644
index 000000000..c6562b558
--- /dev/null
+++ b/v3.14.0/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v3.14.0/assets/img/bp-message.svg b/v3.14.0/assets/img/bp-message.svg
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+++ b/v3.14.0/assets/img/bp-message.svg
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+
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diff --git a/v3.14.0/assets/img/coin-flip.png b/v3.14.0/assets/img/coin-flip.png
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index 000000000..a85960c12
--- /dev/null
+++ b/v3.14.0/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
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+
+
+
+
+
+
+
+
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+
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diff --git a/v3.14.0/assets/img/vmp-message.svg b/v3.14.0/assets/img/vmp-message.svg
new file mode 100644
index 000000000..475cd7f49
--- /dev/null
+++ b/v3.14.0/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v3.14.0/assets/themes/documenter-dark.css b/v3.14.0/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..53889fb99
--- /dev/null
+++ b/v3.14.0/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter 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form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark 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.subtitle:not(:last-child),html.theme--documenter-dark .table-container:not(:last-child),html.theme--documenter-dark .table:not(:last-child),html.theme--documenter-dark .progress:not(:last-child),html.theme--documenter-dark .notification:not(:last-child),html.theme--documenter-dark .content:not(:last-child),html.theme--documenter-dark .box:not(:last-child){margin-bottom:1.5rem}html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;-moz-appearance:none;-webkit-appearance:none;background-color:rgba(10,10,10,0.2);border:none;border-radius:9999px;cursor:pointer;pointer-events:auto;display:inline-block;flex-grow:0;flex-shrink:0;font-size:0;height:20px;max-height:20px;max-width:20px;min-height:20px;min-width:20px;outline:none;position:relative;vertical-align:top;width:20px}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark 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+ Author: @ericwbailey
+ Maintainer: @ericwbailey
+
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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--documenter-dark .image.is-3by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--documenter-dark .image.is-2by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--documenter-dark .image.is-2by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--documenter-dark .image.is-3by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--documenter-dark .image.is-3by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--documenter-dark .image.is-9by16 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--documenter-dark .image.is-9by16 .has-ratio,html.theme--documenter-dark #documenter 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diff --git a/v3.14.0/assets/themes/documenter-light.css b/v3.14.0/assets/themes/documenter-light.css
new file mode 100644
index 000000000..2f168c77b
--- /dev/null
+++ b/v3.14.0/assets/themes/documenter-light.css
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v3.14.0/assets/themeswap.js b/v3.14.0/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v3.14.0/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v3.14.0/assets/warner.js b/v3.14.0/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v3.14.0/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
+ document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+ maybeAddWarning();
+}
diff --git a/v3.14.0/custom/custom-addons/index.html b/v3.14.0/custom/custom-addons/index.html
new file mode 100644
index 000000000..34d1f9b1b
--- /dev/null
+++ b/v3.14.0/custom/custom-addons/index.html
@@ -0,0 +1,24 @@
+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
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diff --git a/v3.14.0/custom/custom-functional-form/index.html b/v3.14.0/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
See also: CompositeFormConstraint
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
. Any functional form constraint that defines is_point_mass_form_constraint() = true
may be used only as the last element of the composition.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
See also: FormConstraintCheckLast
, default_form_check_strategy
, constrain_form
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
Every custom functional form may implement a new method for the is_point_mass_form_constraint
function that returns either true
or false
. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.
To make custom functional form constraint compatible with the @constraints
macro, it must implement a new method for the make_form_constraint
function.
make_form_constraint(::Type, args...; kwargs...)
Creates form constraint object based on passed type
with given args
and kwargs
. Used to simplify form constraint specification.
As an example:
make_form_constraint(PointMass)
creates an instance of PointMassFormConstraint
and
make_form_constraint(SampleList, 5000, LeftProposal())
should create an instance of SampleListFormConstraint
.
See also: AbstractFormConstraint
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v3.14.0/extra/contributing/index.html b/v3.14.0/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, as_variable
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v3.14.0/extra/extensions/index.html b/v3.14.0/extra/extensions/index.html
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+
+Extensions and interaction with the Julia ecosystem · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
Tutorials and examples are available in the RxInfer documentation .
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diff --git a/dev/lib/algebra/common/index.html b/v3.14.0/lib/algebra/common/index.html
similarity index 53%
rename from dev/lib/algebra/common/index.html
rename to v3.14.0/lib/algebra/common/index.html
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+++ b/v3.14.0/lib/algebra/common/index.html
@@ -1,2 +1,2 @@
-Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source
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+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source FunctionalIndex
A special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex
can be firstindex
or lastindex
, but more complex use cases are possible too, e.g. firstindex + 1
. Important part of the implementation is that the resulting structure is isbitstype(...) = true
, that allows to store it in parametric type as valtype.
One use case for this structure is to dispatch on and to replace begin
or end
(or more complex use cases, e.g. begin + 1
) markers in constraints specification language.
source
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diff --git a/v3.14.0/lib/message/index.html b/v3.14.0/lib/message/index.html
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+
+Messages · ReactiveMP.jl In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.
Both belief propagation and variational messages are subtypes of a AbstractMessage
supertype.
AbstractMessage
An abstract supertype for all concrete message types.
See also: Message
source Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
Message{D, A} <: AbstractMessage
Message
structure encodes a Belief Propagation message, which holds some data
that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data
object and proxies most of the statistical functions, e.g. mean
, mode
, cov
etc.
Arguments
data::D
: message always holds some data object associated with itis_clamped::Bool
, specifies if this message is clampedis_initial::Bool
, specifies if this message is initialaddons::A
, specifies the addons of the messageExample
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
See also: AbstractMessage
, ReactiveMP.materialize!
source materialize!(message::AbstractMessage)
Materializes an abstract message and converts it to be of type Message
.
See also: Message
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
distribution = NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
The user should not really interact with Message
structure while working with ReactiveMP
unless doing some advanced inference procedures that involve prediction.
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diff --git a/v3.14.0/lib/methods/index.html b/v3.14.0/lib/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+BetheFactorisation
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ConstraintsSpecification
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DefaultConstraints
+DefaultMeta
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNodeCreationOptions
+FactorNodesCollection
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+MeanField
+Message
+MetaSpecification
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableCreationOptions
+ReactiveMP
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedConstraints
+UnspecifiedFormConstraint
+UnspecifiedMeta
+VariableBoundEntropy
+VariablesCollection
+VariationalMessage
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+as_variable
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+functional_dependencies
+functionalform
+getapproximation
+getconst
+getconstant
+getdata
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getnode_ids
+getnodes
+getprediction
+getpredictions
+getrandom
+getvardict
+ghcubature
+hasconstvar
+hasdatavar
+hasrandomvar
+huge
+interfaces
+is_clamped
+is_initial
+is_marginalisation
+is_moment_matching
+is_point_mass_form_constraint
+isconnected
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+make_form_constraint
+make_node
+marginalrule
+metadata
+name
+nr_params
+randomvar
+rule
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Monday 18 March 2024 . Using Julia version 1.10.2.
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+
+Overview · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
To quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node
or Base.doc(make_node)
.
ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, z ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic`
This expression registers a new node that can be used with the inference engine. Note howeve, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
plus_node = make_node(+)
+
+println("Is `+` node deterministic: ", isdeterministic(plus_node))
+println("Is `+` node stochastic: ", isstochastic(plus_node))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
bernoulli_node = make_node(Bernoulli)
+
+println("Is `Bernoulli` node deterministic: ", isdeterministic(bernoulli_node))
+println("Is `Bernoulli` node stochastic: ", isstochastic(bernoulli_node))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(plus_node))
+println("sdtype() of `Bernoulli` node is ", sdtype(bernoulli_node))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require inbound messagesstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial inbound messages for edges in indices
Note: start_with
uses setmessage!
mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Deprecation warning: RequireInboundFunctionalDependencies
has been deprecated in favor of RequireMessageFunctionalDependencies
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)
Similar to DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the posterior marginal on that edge.
Arguments
indices
::Tuple, tuple of integers, which indicates what edges should require their own marginalsstart_with::Tuple
, tuple of nothing
or <:Distribution
, which specifies the initial marginal for edges in indices
Note: start_with
uses the setmarginal!
mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal!
overwrites whatever has been passed in start_with
.
@model
macro accepts a simplified construction of this pipeline:
@model function some_model()
+ # ...
+ y ~ NormalMeanVariance(x, τ) where {
+ pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
+ }
+ # ...
+end
Note: The simplified construction in @model
macro syntax is only available in GraphPPL.jl
of version >2.2.0
.
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.as_node_functional_form
trait function and to specify a ReactiveMP.ValidNodeFunctionalForm
singleton as a return object. By default ReactiveMP.as_node_functional_form
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Monday 18 March 2024 . Using Julia version 1.10.2.
diff --git a/v3.14.0/lib/rules/rules/index.html b/v3.14.0/lib/rules/rules/index.html
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source Prints a table of all message passing update rules in ReactiveMP.
+
+Use `Markdown.parse` on the output of this function to get a prettified table.
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source using ReactiveMP, Markdown
+Markdown.parse(ReactiveMP.print_rules_table())
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in2 μ(out) :: Any μ(in1) :: Any * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass HalfNormal out q(v) :: BayesBase.PointMass Nothing ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper out q(in) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing BIFMHelper in μ(out) :: Any Nothing Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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This document was generated with Documenter.jl version 1.3.0 on Monday 18 March 2024 . Using Julia version 1.10.2.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/#lib-helpers-skip-index-iterator","page":"Helper utils","title":"SkipIndexIterator","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#lib-helpers-functional-index","page":"Helper utils","title":"FunctionalIndex","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.FunctionalIndex","category":"page"},{"location":"lib/helpers/#ReactiveMP.FunctionalIndex","page":"Helper utils","title":"ReactiveMP.FunctionalIndex","text":"FunctionalIndex\n\nA special type of an index that represents a function that can be used only in pair with a collection. An example of a FunctionalIndex can be firstindex or lastindex, but more complex use cases are possible too, e.g. firstindex + 1. Important part of the implementation is that the resulting structure is isbitstype(...) = true, that allows to store it in parametric type as valtype.\n\nOne use case for this structure is to dispatch on and to replace begin or end (or more complex use cases, e.g. begin + 1) markers in constraints specification language.\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.print_rules_table","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.print_rules_table","page":"Message update rules","title":"ReactiveMP.print_rules_table","text":"Prints a table of all message passing update rules in ReactiveMP.\n\nUse `Markdown.parse` on the output of this function to get a prettified table.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In our message passing framework one of the most important concepts is the message (wow!). Messages flow along edges of a factor graph and hold information about the part of the graph that it originates from. Usually this information is in a form of a probability distribution. Two common messages are belief propagation messages and variational messages, with are computed differently as shown below.","category":"page"},{"location":"lib/message/#Abstract-message-type","page":"Messages","title":"Abstract message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Both belief propagation and variational messages are subtypes of a AbstractMessage supertype.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"AbstractMessage\n\nAn abstract supertype for all concrete message types.\n\nSee also: Message\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Message\nReactiveMP.materialize!","category":"page"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message{D, A} <: AbstractMessage\n\nMessage structure encodes a Belief Propagation message, which holds some data that usually a probability distribution, but can also be an arbitrary object. Message acts as a proxy structure to data object and proxies most of the statistical functions, e.g. mean, mode, cov etc.\n\nArguments\n\ndata::D: message always holds some data object associated with it\nis_clamped::Bool, specifies if this message is clamped\nis_initial::Bool, specifies if this message is initial\naddons::A, specifies the addons of the message\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\nSee also: AbstractMessage, ReactiveMP.materialize!\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.materialize!","page":"Messages","title":"ReactiveMP.materialize!","text":"materialize!(message::AbstractMessage)\n\nMaterializes an abstract message and converts it to be of type Message.\n\nSee also: Message\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"distribution = NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The user should not really interact with Message structure while working with ReactiveMP unless doing some advanced inference procedures that involve prediction.","category":"page"},{"location":"lib/nodes/nodes/#lib-node","page":"Overview","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\nTo quickly check the list of all available factor nodes that can be used in the model specification language, call ?make_node or Base.doc(make_node).","category":"page"},{"location":"lib/nodes/nodes/#lib-custom-node","page":"Overview","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The interface is the following:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, z ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic`","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"This expression registers a new node that can be used with the inference engine. Note howeve, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro.","category":"page"},{"location":"lib/nodes/nodes/#lib-node-types","page":"Overview","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.Deterministic","page":"Overview","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.Stochastic","page":"Overview","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.isdeterministic","page":"Overview","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.isstochastic","page":"Overview","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/#ReactiveMP.sdtype","page":"Overview","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"plus_node = make_node(+)\n\nprintln(\"Is `+` node deterministic: \", isdeterministic(plus_node))\nprintln(\"Is `+` node stochastic: \", isstochastic(plus_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"bernoulli_node = make_node(Bernoulli)\n\nprintln(\"Is `Bernoulli` node deterministic: \", isdeterministic(bernoulli_node))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(bernoulli_node))","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"println(\"sdtype() of `+` node is \", sdtype(plus_node))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(bernoulli_node))\nnothing #hide","category":"page"},{"location":"lib/nodes/nodes/#lib-node-functional-dependencies-pipeline","page":"Overview","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Overview","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis pipeline translates directly to enforcing a variational message passing scheme. In order to compute a message out of some edge, this pipeline requires messages from edges within the same edge-cluster and marginals over other edge-clusters.\n\nSee also: ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require inbound messages\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial inbound messages for edges in indices\n\nNote: start_with uses setmessage! mechanism, hence, it can be visible by other listeners on the same edge. Explicit call to setmessage! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMessage(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nDeprecation warning: RequireInboundFunctionalDependencies has been deprecated in favor of RequireMessageFunctionalDependencies.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(indices::Tuple, start_with::Tuple)\n\nSimilar to DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the posterior marginal on that edge.\n\nArguments\n\nindices::Tuple, tuple of integers, which indicates what edges should require their own marginals\nstart_with::Tuple, tuple of nothing or <:Distribution, which specifies the initial marginal for edges in indices\n\nNote: start_with uses the setmarginal! mechanism, hence it can be visible to other listeners on the same edge. Explicit calls to setmarginal! overwrites whatever has been passed in start_with.\n\n@model macro accepts a simplified construction of this pipeline:\n\n@model function some_model()\n # ...\n y ~ NormalMeanVariance(x, τ) where {\n pipeline = RequireMarginal(x = vague(NormalMeanPrecision), τ)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n }\n # ...\nend\n\nNote: The simplified construction in @model macro syntax is only available in GraphPPL.jl of version >2.2.0.\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Overview","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#lib-node-traits","page":"Overview","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"Each factor node has to define the ReactiveMP.as_node_functional_form trait function and to specify a ReactiveMP.ValidNodeFunctionalForm singleton as a return object. By default ReactiveMP.as_node_functional_form returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/nodes/","page":"Overview","title":"Overview","text":"ReactiveMP.ValidNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.as_node_functional_form","category":"page"},{"location":"lib/nodes/nodes/#ReactiveMP.ValidNodeFunctionalForm","page":"Overview","title":"ReactiveMP.ValidNodeFunctionalForm","text":"ValidNodeFunctionalForm\n\nTrait specification for an object that can be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Overview","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that can not be used in model specification as a factor node.\n\nSee also: ReactiveMP.as_node_functional_form, ReactiveMP.ValidNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/nodes/#ReactiveMP.as_node_functional_form","page":"Overview","title":"ReactiveMP.as_node_functional_form","text":"as_node_functional_form(object)\n\nDetermines object node functional form trait specification. Returns either ValidNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.ValidNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in ReactiveMP.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, as_variable, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions and interaction with the Julia ecosystem","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions and interaction with the Julia ecosystem","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions and interaction with the Julia ecosystem","title":"Extensions and interaction with the Julia ecosystem","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\nSee also: CompositeFormConstraint\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. Any functional form constraint that defines is_point_mass_form_constraint() = true may be used only as the last element of the composition.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\nSee also: FormConstraintCheckLast, default_form_check_strategy, constrain_form\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, default_form_check_strategy, is_point_mass_form_constraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Is-point-mass-form-constraint-(optional)","page":"Custom functional form","title":"Is point mass form constraint (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form may implement a new method for the is_point_mass_form_constraint function that returns either true or false. This is an utility function that simplifes computation of the Bethe Free Energy and is not strictly necessary.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"is_point_mass_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.is_point_mass_form_constraint","page":"Custom functional form","title":"ReactiveMP.is_point_mass_form_constraint","text":"is_point_mass_form_constraint(form_constraint)\n\nSpecifies whether form constraint always returns PointMass estimates or not. For a given form_constraint returns either true or false.\n\nSee also: FormConstraintCheckEach, FormConstraintCheckLast, constrain_form\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Compatibility-with-@constraints-macro-(optional)","page":"Custom functional form","title":"Compatibility with @constraints macro (optional)","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"To make custom functional form constraint compatible with the @constraints macro, it must implement a new method for the make_form_constraint function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"make_form_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.make_form_constraint","page":"Custom functional form","title":"ReactiveMP.make_form_constraint","text":"make_form_constraint(::Type, args...; kwargs...)\n\nCreates form constraint object based on passed type with given args and kwargs. Used to simplify form constraint specification.\n\nAs an example:\n\nmake_form_constraint(PointMass)\n\ncreates an instance of PointMassFormConstraint and \n\nmake_form_constraint(SampleList, 5000, LeftProposal())\n\nshould create an instance of SampleListFormConstraint.\n\nSee also: AbstractFormConstraint\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.is_point_mass_form_constraint(::MeanPrecisionFormConstraint) = false\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"lib/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"lib/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"lib/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/message.md\",\n \"lib/node.md\",\n \"lib/math.md\",\n \"extra/contributing.md\"\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/algebra/common/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/common/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/common/","page":"Algebra utils","title":"Algebra utils","text":"diageye","category":"page"},{"location":"lib/algebra/common/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v3.14.0/siteinfo.js b/v3.14.0/siteinfo.js
new file mode 100644
index 000000000..a1967a827
--- /dev/null
+++ b/v3.14.0/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v3.14.0";
diff --git a/v4 b/v4
new file mode 120000
index 000000000..1ddc0f604
--- /dev/null
+++ b/v4
@@ -0,0 +1 @@
+v4.3.0
\ No newline at end of file
diff --git a/v4.0 b/v4.0
new file mode 120000
index 000000000..f684230d6
--- /dev/null
+++ b/v4.0
@@ -0,0 +1 @@
+v4.0.0
\ No newline at end of file
diff --git a/v4.0.0/.documenter-siteinfo.json b/v4.0.0/.documenter-siteinfo.json
new file mode 100644
index 000000000..bd11d2e10
--- /dev/null
+++ b/v4.0.0/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-12T15:01:33","documenter_version":"1.3.0"}}
\ No newline at end of file
diff --git a/v4.0.0/assets/documenter.js b/v4.0.0/assets/documenter.js
new file mode 100644
index 000000000..c6562b558
--- /dev/null
+++ b/v4.0.0/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v4.0.0/assets/img/bp-message.svg b/v4.0.0/assets/img/bp-message.svg
new file mode 100644
index 000000000..259b70803
--- /dev/null
+++ b/v4.0.0/assets/img/bp-message.svg
@@ -0,0 +1 @@
+
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diff --git a/v4.0.0/assets/img/coin-flip.png b/v4.0.0/assets/img/coin-flip.png
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index 000000000..2ed0f04c0
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diff --git a/v4.0.0/assets/img/coin-flip.svg b/v4.0.0/assets/img/coin-flip.svg
new file mode 100644
index 000000000..a85960c12
--- /dev/null
+++ b/v4.0.0/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
diff --git a/v4.0.0/assets/img/vmp-message.svg b/v4.0.0/assets/img/vmp-message.svg
new file mode 100644
index 000000000..475cd7f49
--- /dev/null
+++ b/v4.0.0/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v4.0.0/assets/themes/documenter-dark.css b/v4.0.0/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..53889fb99
--- /dev/null
+++ b/v4.0.0/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter 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.pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark 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.subtitle:not(:last-child),html.theme--documenter-dark .table-container:not(:last-child),html.theme--documenter-dark .table:not(:last-child),html.theme--documenter-dark .progress:not(:last-child),html.theme--documenter-dark .notification:not(:last-child),html.theme--documenter-dark .content:not(:last-child),html.theme--documenter-dark .box:not(:last-child){margin-bottom:1.5rem}html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;-moz-appearance:none;-webkit-appearance:none;background-color:rgba(10,10,10,0.2);border:none;border-radius:9999px;cursor:pointer;pointer-events:auto;display:inline-block;flex-grow:0;flex-shrink:0;font-size:0;height:20px;max-height:20px;max-width:20px;min-height:20px;min-width:20px;outline:none;position:relative;vertical-align:top;width:20px}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark 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+ Theme: a11y-dark
+ Author: @ericwbailey
+ Maintainer: @ericwbailey
+
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.button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter 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diff --git a/v4.0.0/assets/themes/documenter-light.css b/v4.0.0/assets/themes/documenter-light.css
new file mode 100644
index 000000000..2f168c77b
--- /dev/null
+++ b/v4.0.0/assets/themes/documenter-light.css
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.0.0/assets/themeswap.js b/v4.0.0/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.0.0/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.0.0/assets/warner.js b/v4.0.0/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.0.0/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
+ document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+ maybeAddWarning();
+}
diff --git a/v4.0.0/custom/custom-addons/index.html b/v4.0.0/custom/custom-addons/index.html
new file mode 100644
index 000000000..942f92485
--- /dev/null
+++ b/v4.0.0/custom/custom-addons/index.html
@@ -0,0 +1,28 @@
+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
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diff --git a/v4.0.0/custom/custom-functional-form/index.html b/v4.0.0/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(form_constraint, distribution)
This function must approximate distribution
object in a form that satisfies form_constraint
.
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v4.0.0/extra/contributing/index.html b/v4.0.0/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.0.0/extra/extensions/index.html b/v4.0.0/extra/extensions/index.html
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+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.0.0/extra/methods/index.html b/v4.0.0/extra/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/v4.0.0/index.html b/v4.0.0/index.html
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.0.0/lib/marginal/index.html b/v4.0.0/lib/marginal/index.html
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+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
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+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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+Continuous transition · ReactiveMP.jl The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
. ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Friday 12 April 2024 . Using Julia version 1.10.2.
diff --git a/v4.0.0/lib/nodes/logical/index.html b/v4.0.0/lib/nodes/logical/index.html
new file mode 100644
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+
+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Friday 12 April 2024 . Using Julia version 1.10.2.
diff --git a/v4.0.0/lib/rules/index.html b/v4.0.0/lib/rules/index.html
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in2 μ(out) :: Any μ(in1) :: Any * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing HalfNormal out q(v) :: BayesBase.PointMass Nothing GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing BIFMHelper in μ(out) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.3.0 on Friday 12 April 2024 . Using Julia version 1.10.2.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a. ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v4.0.0/siteinfo.js b/v4.0.0/siteinfo.js
new file mode 100644
index 000000000..efe9ad680
--- /dev/null
+++ b/v4.0.0/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.0.0";
diff --git a/v4.1 b/v4.1
new file mode 120000
index 000000000..b572ab0bd
--- /dev/null
+++ b/v4.1
@@ -0,0 +1 @@
+v4.1.2
\ No newline at end of file
diff --git a/v4.1.0/.documenter-siteinfo.json b/v4.1.0/.documenter-siteinfo.json
new file mode 100644
index 000000000..482da5a21
--- /dev/null
+++ b/v4.1.0/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-23T10:36:34","documenter_version":"1.4.0"}}
\ No newline at end of file
diff --git a/v4.1.0/assets/documenter.js b/v4.1.0/assets/documenter.js
new file mode 100644
index 000000000..c6562b558
--- /dev/null
+++ b/v4.1.0/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v4.1.0/assets/img/bp-message.svg b/v4.1.0/assets/img/bp-message.svg
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+
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+++ b/v4.1.0/assets/img/coin-flip.svg
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
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+
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--- /dev/null
+++ b/v4.1.0/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v4.1.0/assets/themes/documenter-dark.css b/v4.1.0/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..53889fb99
--- /dev/null
+++ b/v4.1.0/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter 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.button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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new file mode 100644
index 000000000..2f168c77b
--- /dev/null
+++ b/v4.1.0/assets/themes/documenter-light.css
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.1.0/assets/themeswap.js b/v4.1.0/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.1.0/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.1.0/assets/warner.js b/v4.1.0/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.1.0/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
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diff --git a/v4.1.0/custom/custom-addons/index.html b/v4.1.0/custom/custom-addons/index.html
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+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
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diff --git a/v4.1.0/custom/custom-functional-form/index.html b/v4.1.0/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(form_constraint, distribution)
This function must approximate distribution
object in a form that satisfies form_constraint
.
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v4.1.0/extra/contributing/index.html b/v4.1.0/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.1.0/extra/extensions/index.html b/v4.1.0/extra/extensions/index.html
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+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.1.0/extra/methods/index.html b/v4.1.0/extra/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/v4.1.0/index.html b/v4.1.0/index.html
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/v4.1.0/lib/algebra/index.html b/v4.1.0/lib/algebra/index.html
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.1.0/lib/marginal/index.html b/v4.1.0/lib/marginal/index.html
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+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/v4.1.0/lib/message/index.html b/v4.1.0/lib/message/index.html
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+
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
+
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+
+
+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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diff --git a/v4.1.0/lib/nodes/ar/index.html b/v4.1.0/lib/nodes/ar/index.html
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/v4.1.0/lib/nodes/bifm/index.html b/v4.1.0/lib/nodes/bifm/index.html
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+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/v4.1.0/lib/nodes/ctransition/index.html b/v4.1.0/lib/nodes/ctransition/index.html
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+
+Continuous transition · ReactiveMP.jl The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
. ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/v4.1.0/lib/nodes/delta/index.html b/v4.1.0/lib/nodes/delta/index.html
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+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/v4.1.0/lib/nodes/equality/index.html b/v4.1.0/lib/nodes/equality/index.html
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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diff --git a/v4.1.0/lib/nodes/flow/index.html b/v4.1.0/lib/nodes/flow/index.html
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.4.0 on Tuesday 23 April 2024 . Using Julia version 1.10.2.
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Theme
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This document was generated with Documenter.jl version 1.4.0 on Tuesday 23 April 2024 . Using Julia version 1.10.2.
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+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.4.0 on Tuesday 23 April 2024 . Using Julia version 1.10.2.
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+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in2 μ(out) :: Any μ(in1) :: Any * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any HalfNormal out q(v) :: BayesBase.PointMass Nothing MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.4.0 on Tuesday 23 April 2024 . Using Julia version 1.10.2.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a. ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v4.1.0/siteinfo.js b/v4.1.0/siteinfo.js
new file mode 100644
index 000000000..e9c06d2c2
--- /dev/null
+++ b/v4.1.0/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.1.0";
diff --git a/v4.1.1/.documenter-siteinfo.json b/v4.1.1/.documenter-siteinfo.json
new file mode 100644
index 000000000..6a0d0d6bf
--- /dev/null
+++ b/v4.1.1/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-04-30T20:01:50","documenter_version":"1.4.0"}}
\ No newline at end of file
diff --git a/v4.1.1/assets/documenter.js b/v4.1.1/assets/documenter.js
new file mode 100644
index 000000000..c6562b558
--- /dev/null
+++ b/v4.1.1/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v4.1.1/assets/img/bp-message.svg b/v4.1.1/assets/img/bp-message.svg
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+++ b/v4.1.1/assets/img/bp-message.svg
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+
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diff --git a/v4.1.1/assets/img/coin-flip.png b/v4.1.1/assets/img/coin-flip.png
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+++ b/v4.1.1/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
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+
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diff --git a/v4.1.1/assets/img/vmp-message.svg b/v4.1.1/assets/img/vmp-message.svg
new file mode 100644
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--- /dev/null
+++ b/v4.1.1/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v4.1.1/assets/themes/documenter-dark.css b/v4.1.1/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..53889fb99
--- /dev/null
+++ b/v4.1.1/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark 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.pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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new file mode 100644
index 000000000..2f168c77b
--- /dev/null
+++ b/v4.1.1/assets/themes/documenter-light.css
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span.sgr42{background-color:#066f00}.ansi span.sgr43{background-color:#856b00}.ansi span.sgr44{background-color:#2149b0}.ansi span.sgr45{background-color:#7d4498}.ansi span.sgr46{background-color:#007989}.ansi span.sgr47{background-color:gray}.ansi span.sgr90{color:#616161}.ansi span.sgr91{color:#cb3c33}.ansi span.sgr92{color:#0e8300}.ansi span.sgr93{color:#a98800}.ansi span.sgr94{color:#3c5dcd}.ansi span.sgr95{color:#9256af}.ansi span.sgr96{color:#008fa3}.ansi span.sgr97{color:#f5f5f5}.ansi span.sgr100{background-color:#616161}.ansi span.sgr101{background-color:#cb3c33}.ansi span.sgr102{background-color:#0e8300}.ansi span.sgr103{background-color:#a98800}.ansi span.sgr104{background-color:#3c5dcd}.ansi span.sgr105{background-color:#9256af}.ansi span.sgr106{background-color:#008fa3}.ansi span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*!
+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.1.1/assets/themeswap.js b/v4.1.1/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.1.1/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.1.1/assets/warner.js b/v4.1.1/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.1.1/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
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diff --git a/v4.1.1/custom/custom-addons/index.html b/v4.1.1/custom/custom-addons/index.html
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+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
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diff --git a/v4.1.1/custom/custom-functional-form/index.html b/v4.1.1/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(form_constraint, distribution)
This function must approximate distribution
object in a form that satisfies form_constraint
.
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v4.1.1/extra/contributing/index.html b/v4.1.1/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.1.1/extra/extensions/index.html b/v4.1.1/extra/extensions/index.html
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+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.1.1/extra/methods/index.html b/v4.1.1/extra/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/v4.1.1/index.html b/v4.1.1/index.html
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/v4.1.1/lib/algebra/index.html b/v4.1.1/lib/algebra/index.html
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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diff --git a/v4.1.1/lib/helpers/index.html b/v4.1.1/lib/helpers/index.html
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.1.1/lib/marginal/index.html b/v4.1.1/lib/marginal/index.html
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+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/v4.1.1/lib/message/index.html b/v4.1.1/lib/message/index.html
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+
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
+
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+
+
+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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diff --git a/v4.1.1/lib/nodes/ar/index.html b/v4.1.1/lib/nodes/ar/index.html
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/v4.1.1/lib/nodes/bifm/index.html b/v4.1.1/lib/nodes/bifm/index.html
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+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/v4.1.1/lib/nodes/ctransition/index.html b/v4.1.1/lib/nodes/ctransition/index.html
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+
+Continuous transition · ReactiveMP.jl The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
. ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/v4.1.1/lib/nodes/delta/index.html b/v4.1.1/lib/nodes/delta/index.html
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+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/v4.1.1/lib/nodes/equality/index.html b/v4.1.1/lib/nodes/equality/index.html
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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diff --git a/v4.1.1/lib/nodes/flow/index.html b/v4.1.1/lib/nodes/flow/index.html
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
Theme
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This document was generated with Documenter.jl version 1.4.0 on Tuesday 30 April 2024 . Using Julia version 1.10.3.
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Theme
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+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
Theme
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This document was generated with Documenter.jl version 1.4.0 on Tuesday 30 April 2024 . Using Julia version 1.10.3.
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+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in2 μ(out) :: Any μ(in1) :: Any dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass HalfNormal out q(v) :: BayesBase.PointMass Nothing Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.4.0 on Tuesday 30 April 2024 . Using Julia version 1.10.3.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a. ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v4.1.1/siteinfo.js b/v4.1.1/siteinfo.js
new file mode 100644
index 000000000..61d5aca15
--- /dev/null
+++ b/v4.1.1/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.1.1";
diff --git a/v4.1.2/.documenter-siteinfo.json b/v4.1.2/.documenter-siteinfo.json
new file mode 100644
index 000000000..e01004a84
--- /dev/null
+++ b/v4.1.2/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-17T09:43:17","documenter_version":"1.4.1"}}
\ No newline at end of file
diff --git a/v4.1.2/assets/documenter.js b/v4.1.2/assets/documenter.js
new file mode 100644
index 000000000..c6562b558
--- /dev/null
+++ b/v4.1.2/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v4.1.2/assets/img/bp-message.svg b/v4.1.2/assets/img/bp-message.svg
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+++ b/v4.1.2/assets/img/bp-message.svg
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+
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diff --git a/v4.1.2/assets/img/coin-flip.png b/v4.1.2/assets/img/coin-flip.png
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+++ b/v4.1.2/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
+
+
+
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+
+
+
diff --git a/v4.1.2/assets/img/vmp-message.svg b/v4.1.2/assets/img/vmp-message.svg
new file mode 100644
index 000000000..475cd7f49
--- /dev/null
+++ b/v4.1.2/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v4.1.2/assets/themes/documenter-dark.css b/v4.1.2/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..1d7170158
--- /dev/null
+++ b/v4.1.2/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark 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.pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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diff --git a/v4.1.2/assets/themes/documenter-light.css b/v4.1.2/assets/themes/documenter-light.css
new file mode 100644
index 000000000..07f9d0883
--- /dev/null
+++ b/v4.1.2/assets/themes/documenter-light.css
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.1.2/assets/themeswap.js b/v4.1.2/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.1.2/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.1.2/assets/warner.js b/v4.1.2/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.1.2/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
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diff --git a/v4.1.2/custom/custom-addons/index.html b/v4.1.2/custom/custom-addons/index.html
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+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
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diff --git a/v4.1.2/custom/custom-functional-form/index.html b/v4.1.2/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(form_constraint, distribution)
This function must approximate distribution
object in a form that satisfies form_constraint
.
source In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision
distribution, but we still need to define our custom functional form constraint:
using ReactiveMP, BayesBase
+
+# First we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
Next we define the behaviour of our functional form constraint:
ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined
+ # However this quantities might be approximated with some other external method, e.g. Laplace approximation
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # ProductOf is the special case, read about this type more in the corresponding documentation section
+ # of the `BayesBase` package
+ # ...
+end
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diff --git a/v4.1.2/extra/contributing/index.html b/v4.1.2/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.1.2/extra/extensions/index.html b/v4.1.2/extra/extensions/index.html
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+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.1.2/extra/methods/index.html b/v4.1.2/extra/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/v4.1.2/index.html b/v4.1.2/index.html
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/v4.1.2/lib/algebra/index.html b/v4.1.2/lib/algebra/index.html
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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diff --git a/v4.1.2/lib/helpers/index.html b/v4.1.2/lib/helpers/index.html
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.1.2/lib/marginal/index.html b/v4.1.2/lib/marginal/index.html
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+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/v4.1.2/lib/message/index.html b/v4.1.2/lib/message/index.html
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+
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
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+
+
+
+
+
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+
+
+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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diff --git a/v4.1.2/lib/nodes/ar/index.html b/v4.1.2/lib/nodes/ar/index.html
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/v4.1.2/lib/nodes/bifm/index.html b/v4.1.2/lib/nodes/bifm/index.html
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+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/v4.1.2/lib/nodes/ctransition/index.html b/v4.1.2/lib/nodes/ctransition/index.html
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+
+Continuous transition · ReactiveMP.jl The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
. ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/v4.1.2/lib/nodes/delta/index.html b/v4.1.2/lib/nodes/delta/index.html
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+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/v4.1.2/lib/nodes/equality/index.html b/v4.1.2/lib/nodes/equality/index.html
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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diff --git a/v4.1.2/lib/nodes/flow/index.html b/v4.1.2/lib/nodes/flow/index.html
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
Theme
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This document was generated with Documenter.jl version 1.4.1 on Monday 17 June 2024 . Using Julia version 1.10.4.
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
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+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
Theme
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This document was generated with Documenter.jl version 1.4.1 on Monday 17 June 2024 . Using Julia version 1.10.4.
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+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper out q(in) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real HalfNormal out q(v) :: BayesBase.PointMass Nothing MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.4.1 on Monday 17 June 2024 . Using Julia version 1.10.4.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a. ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(form_constraint, distribution)\n\nThis function must approximate distribution object in a form that satisfies form_constraint.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. We show a relatively simple use-case, which might not be very useful in practice, but serves as a simple step-by-step guide. Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parametrisation, for example mean-precision. We can use built-in NormalMeanPrecision distribution, but we still need to define our custom functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, BayesBase\n\n# First we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Next we define the behaviour of our functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This is quite a naive assumption, that a given `dsitribution` object has `mean` and `precision` defined\n # However this quantities might be approximated with some other external method, e.g. Laplace approximation\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # ProductOf is the special case, read about this type more in the corresponding documentation section\n # of the `BayesBase` package\n # ... \nend","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v4.1.2/siteinfo.js b/v4.1.2/siteinfo.js
new file mode 100644
index 000000000..43ebccb14
--- /dev/null
+++ b/v4.1.2/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.1.2";
diff --git a/v4.2 b/v4.2
new file mode 120000
index 000000000..6f3e563d0
--- /dev/null
+++ b/v4.2
@@ -0,0 +1 @@
+v4.2.1
\ No newline at end of file
diff --git a/v4.2.0/.documenter-siteinfo.json b/v4.2.0/.documenter-siteinfo.json
new file mode 100644
index 000000000..541e80edb
--- /dev/null
+++ b/v4.2.0/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-17T13:55:08","documenter_version":"1.4.1"}}
\ No newline at end of file
diff --git a/v4.2.0/assets/documenter.js b/v4.2.0/assets/documenter.js
new file mode 100644
index 000000000..c6562b558
--- /dev/null
+++ b/v4.2.0/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+
+ let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v4.2.0/assets/img/bp-message.svg b/v4.2.0/assets/img/bp-message.svg
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+
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+++ b/v4.2.0/assets/img/coin-flip.svg
@@ -0,0 +1,794 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
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diff --git a/v4.2.0/assets/img/vmp-message.svg b/v4.2.0/assets/img/vmp-message.svg
new file mode 100644
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--- /dev/null
+++ b/v4.2.0/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
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diff --git a/v4.2.0/assets/themes/documenter-dark.css b/v4.2.0/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..1d7170158
--- /dev/null
+++ b/v4.2.0/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark 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.pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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diff --git a/v4.2.0/assets/themes/documenter-light.css b/v4.2.0/assets/themes/documenter-light.css
new file mode 100644
index 000000000..07f9d0883
--- /dev/null
+++ b/v4.2.0/assets/themes/documenter-light.css
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.2.0/assets/themeswap.js b/v4.2.0/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.2.0/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.2.0/assets/warner.js b/v4.2.0/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.2.0/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
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+
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+ return;
+ }
+
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+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
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+ document.body.removeChild(div);
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+ div.innerHTML =
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+ div.appendChild(closer);
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diff --git a/v4.2.0/custom/custom-addons/index.html b/v4.2.0/custom/custom-addons/index.html
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+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
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diff --git a/v4.2.0/custom/custom-functional-form/index.html b/v4.2.0/custom/custom-functional-form/index.html
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source preprocess_form_constraints(constraints)
This function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint
object. Wraps unknown form constraints into a WrappedFormConstraint
object.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(constraint, something)
This function applies a given form constraint to a given object.
source In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional form constraint implementation is the prod
function in the BayesBase
package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.
Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint
functional form constraint:
using ReactiveMP, ExponentialFamily, Distributions, BayesBase
+
+# First, we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
+
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This assumes that the given `distribution` object has `mean` and `precision` defined.
+ # These quantities might be approximated using other methods, such as Laplace approximation.
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # `ProductOf` is a special case. Read more about this type in the corresponding
+ # documentation section of the `BayesBase` package.
+ # ...
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())
+
+constrain_form(constraint, NormalMeanVariance(0, 2))
ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=0.5)
Some constraint objects might not be subtypes of AbstractFormConstraint
. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP
expects users to pass a WrappedFormConstraint
object, which wraps the original object and makes it compatible with the ReactiveMP
inference backend. Note that the ReactiveMP.preprocess_form_constraints
function automatically wraps all objects that are not subtypes of AbstractFormConstraint
.
Additionally, objects wrapped by WrappedFormConstraints
may implement the ReactiveMP.prepare_context
function. This function's output will be stored in the WrappedFormConstraints
along with the original object. If prepare_context
is implemented, the constrain_form
function will take three arguments: the original constraint, the context, and the object that needs to be constrained.
WrappedFormConstraint(constraint, context)
This is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form
function. By default all objects that are not sub-typed from AbstractFormConstraint
are wrapped into this object. Use ReactiveMP.prepare_context
to provide an extra context for a given form constraint, that can be reused between multiple constrain_form
calls.
source prepare_context(constraint)
This function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext
if no context is needed (the default behaviour).
source constrain_form(wrapped::WrappedFormConstraint, something)
This function unwraps the wrapped
object and calls constrain_form
function with the provided context. If the context is not provided, simply calls constrain_form
with the wrapped constraint. Otherwise passes the context to the constrain_form
function as the second argument.
source using ReactiveMP, Distributions, BayesBase, Random
+
+# First, we define our custom form constraint that creates a set of samples
+# Note that this is not a subtype of `AbstractFormConstraint`
+struct MyCustomSampleListFormConstraint end
+
+# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions
+# which are necessary for the `ReactiveMP` inference backend
+ReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()
+
+# We implement the `prepare_context` function, which returns a random number generator
+function ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)
+ return Random.default_rng()
+end
+
+# We implement the `constrain_form` function, which returns a set of samples
+function ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)
+ return rand(context, distribution, 10)
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())
+
+constrain_form(constraint, Normal(0, 10))
10-element Vector{Float64}:
+ -10.81883805738703
+ -11.448384469487106
+ 4.549932493015364
+ 0.09603115905814513
+ 5.895065521960378
+ -23.042956349675755
+ 7.666453778406911
+ -8.673244629455843
+ -2.798396583188306
+ 15.499910583766221
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diff --git a/v4.2.0/extra/contributing/index.html b/v4.2.0/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.2.0/extra/extensions/index.html b/v4.2.0/extra/extensions/index.html
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+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.2.0/extra/methods/index.html b/v4.2.0/extra/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/v4.2.0/index.html b/v4.2.0/index.html
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/v4.2.0/lib/algebra/index.html b/v4.2.0/lib/algebra/index.html
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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diff --git a/v4.2.0/lib/helpers/index.html b/v4.2.0/lib/helpers/index.html
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.2.0/lib/marginal/index.html b/v4.2.0/lib/marginal/index.html
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+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/v4.2.0/lib/message/index.html b/v4.2.0/lib/message/index.html
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+
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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diff --git a/v4.2.0/lib/nodes/ar/index.html b/v4.2.0/lib/nodes/ar/index.html
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/v4.2.0/lib/nodes/bifm/index.html b/v4.2.0/lib/nodes/bifm/index.html
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+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/v4.2.0/lib/nodes/ctransition/index.html b/v4.2.0/lib/nodes/ctransition/index.html
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+
+Continuous transition · ReactiveMP.jl The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
. ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/v4.2.0/lib/nodes/delta/index.html b/v4.2.0/lib/nodes/delta/index.html
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+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/v4.2.0/lib/nodes/equality/index.html b/v4.2.0/lib/nodes/equality/index.html
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
Theme
Automatic (OS) documenter-light documenter-dark
This document was generated with Documenter.jl version 1.4.1 on Monday 17 June 2024 . Using Julia version 1.10.4.
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+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
Theme
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
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+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
Theme
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper out q(in) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Distributions.Gamma Nothing q(β) :: Distributions.Gamma ExponentialFamily.GammaShapeRate out q(α) :: BayesBase.PointMass Nothing q(β) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real HalfNormal out q(v) :: BayesBase.PointMass Nothing DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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This document was generated with Documenter.jl version 1.4.1 on Monday 17 June 2024 . Using Julia version 1.10.4.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a. ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint\nReactiveMP.preprocess_form_constraints","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.preprocess_form_constraints","page":"Custom functional form","title":"ReactiveMP.preprocess_form_constraints","text":"preprocess_form_constraints(constraints)\n\nThis function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint object. Wraps unknown form constraints into a WrappedFormConstraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(constraint, something)\n\nThis function applies a given form constraint to a given object. \n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional form constraint implementation is the prod function in the BayesBase package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, ExponentialFamily, Distributions, BayesBase\n\n# First, we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end\n\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This assumes that the given `distribution` object has `mean` and `precision` defined.\n # These quantities might be approximated using other methods, such as Laplace approximation.\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # `ProductOf` is a special case. Read more about this type in the corresponding \n # documentation section of the `BayesBase` package.\n # ... \nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())\n\nconstrain_form(constraint, NormalMeanVariance(0, 2))","category":"page"},{"location":"custom/custom-functional-form/#Wrapped-Form-Constraints","page":"Custom functional form","title":"Wrapped Form Constraints","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Some constraint objects might not be subtypes of AbstractFormConstraint. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP expects users to pass a WrappedFormConstraint object, which wraps the original object and makes it compatible with the ReactiveMP inference backend. Note that the ReactiveMP.preprocess_form_constraints function automatically wraps all objects that are not subtypes of AbstractFormConstraint.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Additionally, objects wrapped by WrappedFormConstraints may implement the ReactiveMP.prepare_context function. This function's output will be stored in the WrappedFormConstraints along with the original object. If prepare_context is implemented, the constrain_form function will take three arguments: the original constraint, the context, and the object that needs to be constrained.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.WrappedFormConstraint\nReactiveMP.prepare_context\nReactiveMP.constrain_form(::ReactiveMP.WrappedFormConstraint, something)","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.WrappedFormConstraint","page":"Custom functional form","title":"ReactiveMP.WrappedFormConstraint","text":"WrappedFormConstraint(constraint, context)\n\nThis is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form function. By default all objects that are not sub-typed from AbstractFormConstraint are wrapped into this object. Use ReactiveMP.prepare_context to provide an extra context for a given form constraint, that can be reused between multiple constrain_form calls.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.prepare_context","page":"Custom functional form","title":"ReactiveMP.prepare_context","text":"prepare_context(constraint)\n\nThis function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext if no context is needed (the default behaviour).\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form-Tuple{ReactiveMP.WrappedFormConstraint, Any}","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(wrapped::WrappedFormConstraint, something)\n\nThis function unwraps the wrapped object and calls constrain_form function with the provided context. If the context is not provided, simply calls constrain_form with the wrapped constraint. Otherwise passes the context to the constrain_form function as the second argument.\n\n\n\n\n\n","category":"method"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, Distributions, BayesBase, Random\n\n# First, we define our custom form constraint that creates a set of samples\n# Note that this is not a subtype of `AbstractFormConstraint`\nstruct MyCustomSampleListFormConstraint end\n\n# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions\n# which are necessary for the `ReactiveMP` inference backend\nReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()\n\n# We implement the `prepare_context` function, which returns a random number generator\nfunction ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)\n return Random.default_rng()\nend\n\n# We implement the `constrain_form` function, which returns a set of samples\nfunction ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)\n return rand(context, distribution, 10)\nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())\n\nconstrain_form(constraint, Normal(0, 10))","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v4.2.0/siteinfo.js b/v4.2.0/siteinfo.js
new file mode 100644
index 000000000..caf2f959b
--- /dev/null
+++ b/v4.2.0/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.2.0";
diff --git a/v4.2.1/.documenter-siteinfo.json b/v4.2.1/.documenter-siteinfo.json
new file mode 100644
index 000000000..bbf4a93da
--- /dev/null
+++ b/v4.2.1/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-27T09:59:36","documenter_version":"1.5.0"}}
\ No newline at end of file
diff --git a/v4.2.1/assets/documenter.js b/v4.2.1/assets/documenter.js
new file mode 100644
index 000000000..b2bdd43ee
--- /dev/null
+++ b/v4.2.1/assets/documenter.js
@@ -0,0 +1,1059 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * RegX escape function from MDN
+ * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+ function escapeRegExp(string) {
+ return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+ searchstring = escapeRegExp(querystring);
+ let textindex = new RegExp(`${searchstring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ combineWith: "AND",
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
diff --git a/v4.2.1/assets/img/bp-message.svg b/v4.2.1/assets/img/bp-message.svg
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+
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+++ b/v4.2.1/assets/img/coin-flip.svg
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+
+
+
+
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+
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+
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+
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+
+
+
+
+
+
+
+
+
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+
+
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+
+
+
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--- /dev/null
+++ b/v4.2.1/assets/img/vmp-message.svg
@@ -0,0 +1 @@
+
\ No newline at end of file
diff --git a/v4.2.1/assets/themes/catppuccin-frappe.css b/v4.2.1/assets/themes/catppuccin-frappe.css
new file mode 100644
index 000000000..54a5b77ea
--- /dev/null
+++ b/v4.2.1/assets/themes/catppuccin-frappe.css
@@ -0,0 +1 @@
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kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe 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html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:hover,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:focus,html.theme--catppuccin-frappe 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!important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe 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.button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe 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.button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe 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.docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-frappe .image.is-2by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-frappe .image.is-3by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-frappe .image.is-9by16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-frappe .image.is-1by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-frappe .image.is-1by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-frappe .image.is-16x16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-frappe .image.is-24x24,html.theme--catppuccin-frappe #documenter 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diff --git a/v4.2.1/assets/themes/catppuccin-latte.css b/v4.2.1/assets/themes/catppuccin-latte.css
new file mode 100644
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+++ b/v4.2.1/assets/themes/catppuccin-latte.css
@@ -0,0 +1 @@
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!important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-link.is-light{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:hover,html.theme--catppuccin-latte .button.is-link.is-light.is-hovered{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:active,html.theme--catppuccin-latte .button.is-link.is-light.is-active{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:hover,html.theme--catppuccin-latte .button.is-info.is-hovered{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus,html.theme--catppuccin-latte .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus:not(:active),html.theme--catppuccin-latte .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(23,146,153,0.25)}html.theme--catppuccin-latte .button.is-info:active,html.theme--catppuccin-latte .button.is-info.is-active{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:#179299;box-shadow:none}html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;color:#179299}html.theme--catppuccin-latte .button.is-info.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-outlined.is-focused{background-color:#179299;border-color:#179299;color:#fff}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte .content.is-normal{font-size:1rem}html.theme--catppuccin-latte .content.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .content.is-large{font-size:1.5rem}html.theme--catppuccin-latte .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-latte .icon.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-latte .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-latte .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-latte .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-latte .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-latte .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-latte div.icon-text{display:flex}html.theme--catppuccin-latte .image,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-latte .image img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-latte .image img.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-latte .image.is-fullwidth,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-latte .image.is-square img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-latte .image.is-square .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-latte .image.is-1by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-latte .image.is-1by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-latte .image.is-5by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-latte .image.is-5by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-latte .image.is-4by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-latte .image.is-4by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-latte .image.is-3by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-latte .image.is-5by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-latte .image.is-5by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-latte .image.is-16by9 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-latte .image.is-16by9 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-latte .image.is-2by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-latte .image.is-2by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-latte .image.is-3by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-latte .image.is-3by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-latte .image.is-4by5 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-latte .image.is-4by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-latte .image.is-3by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-latte .image.is-3by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-latte .image.is-2by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-latte .image.is-2by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by5 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-latte .image.is-3by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-latte .image.is-9by16 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-latte .image.is-9by16 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-latte .image.is-1by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-latte .image.is-1by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-latte .image.is-1by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-latte .image.is-1by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-latte .image.is-square,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-latte .image.is-1by1,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-latte .image.is-5by4,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-latte .image.is-4by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-latte .image.is-3by2,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-latte .image.is-5by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-latte .image.is-16by9,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-latte .image.is-2by1,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-latte .image.is-3by1,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-latte .image.is-4by5,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-latte .image.is-3by4,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-latte .image.is-2by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-latte .image.is-3by5,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-latte .image.is-9by16,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-latte .image.is-1by2,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-latte .image.is-1by3,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-latte .image.is-16x16,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-latte .image.is-24x24,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-24x24{height:24px;width:24px}html.theme--catppuccin-latte .image.is-32x32,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-32x32{height:32px;width:32px}html.theme--catppuccin-latte .image.is-48x48,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-48x48{height:48px;width:48px}html.theme--catppuccin-latte .image.is-64x64,html.theme--catppuccin-latte 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.navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte 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a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte 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.pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte 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diff --git a/v4.2.1/assets/themes/catppuccin-macchiato.css b/v4.2.1/assets/themes/catppuccin-macchiato.css
new file mode 100644
index 000000000..6ed16f8eb
--- /dev/null
+++ b/v4.2.1/assets/themes/catppuccin-macchiato.css
@@ -0,0 +1 @@
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.button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:hover,html.theme--catppuccin-macchiato .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus,html.theme--catppuccin-macchiato .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus:not(:active),html.theme--catppuccin-macchiato .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-macchiato .button.is-light:active,html.theme--catppuccin-macchiato .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-dark,html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:hover,html.theme--catppuccin-macchiato .content kbd.button:hover,html.theme--catppuccin-macchiato .button.is-dark.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-hovered{background-color:#313447;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus,html.theme--catppuccin-macchiato .content kbd.button:focus,html.theme--catppuccin-macchiato .button.is-dark.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus:not(:active),html.theme--catppuccin-macchiato .content kbd.button:focus:not(:active),html.theme--catppuccin-macchiato .button.is-dark.is-focused:not(:active),html.theme--catppuccin-macchiato .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,58,79,0.25)}html.theme--catppuccin-macchiato .button.is-dark:active,html.theme--catppuccin-macchiato .content kbd.button:active,html.theme--catppuccin-macchiato .button.is-dark.is-active,html.theme--catppuccin-macchiato .content kbd.button.is-active{background-color:#2c2f40;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark[disabled],html.theme--catppuccin-macchiato .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:#363a4f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-dark.is-inverted,html.theme--catppuccin-macchiato .content kbd.button.is-inverted{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted:hover,html.theme--catppuccin-macchiato 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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-primary,html.theme--catppuccin-macchiato .docstring>section>a.button.docs-sourcelink{background-color:#8aadf4;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-primary:hover,html.theme--catppuccin-macchiato .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-macchiato .button.is-primary.is-hovered,html.theme--catppuccin-macchiato .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#7ea5f3;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato 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.button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato 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diff --git a/v4.2.1/assets/themes/catppuccin-mocha.css b/v4.2.1/assets/themes/catppuccin-mocha.css
new file mode 100644
index 000000000..6f27b4c5f
--- /dev/null
+++ b/v4.2.1/assets/themes/catppuccin-mocha.css
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.button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-outlined:hover,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-white.is-outlined:focus,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black:hover,html.theme--catppuccin-mocha .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black:focus,html.theme--catppuccin-mocha .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black:focus:not(:active),html.theme--catppuccin-mocha .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-mocha .button.is-black:active,html.theme--catppuccin-mocha .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-mocha .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted:hover,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-outlined:hover,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-black.is-outlined:focus,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha 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.button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted:hover,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-outlined:hover,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-light.is-outlined:focus,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-dark,html.theme--catppuccin-mocha .content kbd.button{background-color:#313244;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:hover,html.theme--catppuccin-mocha .content kbd.button:hover,html.theme--catppuccin-mocha .button.is-dark.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-hovered{background-color:#2c2d3d;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus,html.theme--catppuccin-mocha .content kbd.button:focus,html.theme--catppuccin-mocha .button.is-dark.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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kbd.button.is-inverted{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-dark.is-inverted[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-focused{background-color:#313244;border-color:#313244;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha 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.button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha 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diff --git a/v4.2.1/assets/themes/documenter-dark.css b/v4.2.1/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..2892b385e
--- /dev/null
+++ b/v4.2.1/assets/themes/documenter-dark.css
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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark 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.navbar-link .icon:only-child{margin-left:-0.25rem;margin-right:-0.25rem}html.theme--documenter-dark a.navbar-item,html.theme--documenter-dark .navbar-link{cursor:pointer}html.theme--documenter-dark a.navbar-item:focus,html.theme--documenter-dark a.navbar-item:focus-within,html.theme--documenter-dark a.navbar-item:hover,html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link:focus,html.theme--documenter-dark .navbar-link:focus-within,html.theme--documenter-dark .navbar-link:hover,html.theme--documenter-dark .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#1abc9c}html.theme--documenter-dark .navbar-item{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .navbar-item img{max-height:1.75rem}html.theme--documenter-dark .navbar-item.has-dropdown{padding:0}html.theme--documenter-dark .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .navbar-item.is-tab{border-bottom:1px solid 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link.is-active{color:#1abc9c}html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark 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diff --git a/v4.2.1/assets/themes/documenter-light.css b/v4.2.1/assets/themes/documenter-light.css
new file mode 100644
index 000000000..a435b3b63
--- /dev/null
+++ b/v4.2.1/assets/themes/documenter-light.css
@@ -0,0 +1,9 @@
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.2.1/assets/themeswap.js b/v4.2.1/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.2.1/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.2.1/assets/warner.js b/v4.2.1/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.2.1/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
+ document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+ maybeAddWarning();
+}
diff --git a/v4.2.1/custom/custom-addons/index.html b/v4.2.1/custom/custom-addons/index.html
new file mode 100644
index 000000000..bded8ff7c
--- /dev/null
+++ b/v4.2.1/custom/custom-addons/index.html
@@ -0,0 +1,28 @@
+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
Theme
Automatic (OS) documenter-light documenter-dark catppuccin-latte catppuccin-frappe catppuccin-macchiato catppuccin-mocha
This document was generated with Documenter.jl version 1.5.0 on Thursday 27 June 2024 . Using Julia version 1.10.4.
diff --git a/v4.2.1/custom/custom-functional-form/index.html b/v4.2.1/custom/custom-functional-form/index.html
new file mode 100644
index 000000000..2c9ce4dc0
--- /dev/null
+++ b/v4.2.1/custom/custom-functional-form/index.html
@@ -0,0 +1,59 @@
+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source preprocess_form_constraints(constraints)
This function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint
object. Wraps unknown form constraints into a WrappedFormConstraint
object.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(constraint, something)
This function applies a given form constraint to a given object.
source In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional form constraint implementation is the prod
function in the BayesBase
package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.
Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint
functional form constraint:
using ReactiveMP, ExponentialFamily, Distributions, BayesBase
+
+# First, we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
+
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This assumes that the given `distribution` object has `mean` and `precision` defined.
+ # These quantities might be approximated using other methods, such as Laplace approximation.
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # `ProductOf` is a special case. Read more about this type in the corresponding
+ # documentation section of the `BayesBase` package.
+ # ...
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())
+
+constrain_form(constraint, NormalMeanVariance(0, 2))
ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=0.5)
Some constraint objects might not be subtypes of AbstractFormConstraint
. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP
expects users to pass a WrappedFormConstraint
object, which wraps the original object and makes it compatible with the ReactiveMP
inference backend. Note that the ReactiveMP.preprocess_form_constraints
function automatically wraps all objects that are not subtypes of AbstractFormConstraint
.
Additionally, objects wrapped by WrappedFormConstraints
may implement the ReactiveMP.prepare_context
function. This function's output will be stored in the WrappedFormConstraints
along with the original object. If prepare_context
is implemented, the constrain_form
function will take three arguments: the original constraint, the context, and the object that needs to be constrained.
WrappedFormConstraint(constraint, context)
This is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form
function. By default all objects that are not sub-typed from AbstractFormConstraint
are wrapped into this object. Use ReactiveMP.prepare_context
to provide an extra context for a given form constraint, that can be reused between multiple constrain_form
calls.
source prepare_context(constraint)
This function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext
if no context is needed (the default behaviour).
source constrain_form(wrapped::WrappedFormConstraint, something)
This function unwraps the wrapped
object and calls constrain_form
function with the provided context. If the context is not provided, simply calls constrain_form
with the wrapped constraint. Otherwise passes the context to the constrain_form
function as the second argument.
source using ReactiveMP, Distributions, BayesBase, Random
+
+# First, we define our custom form constraint that creates a set of samples
+# Note that this is not a subtype of `AbstractFormConstraint`
+struct MyCustomSampleListFormConstraint end
+
+# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions
+# which are necessary for the `ReactiveMP` inference backend
+ReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()
+
+# We implement the `prepare_context` function, which returns a random number generator
+function ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)
+ return Random.default_rng()
+end
+
+# We implement the `constrain_form` function, which returns a set of samples
+function ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)
+ return rand(context, distribution, 10)
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())
+
+constrain_form(constraint, Normal(0, 10))
10-element Vector{Float64}:
+ -13.199166986826656
+ -11.563172721282598
+ 5.632646435571828
+ 3.211306733961604
+ -7.953212038818901
+ 8.83310659687043
+ -9.051694445786913
+ -2.0996570885192654
+ 8.067134139428596
+ 0.29388173363463854
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diff --git a/v4.2.1/extra/contributing/index.html b/v4.2.1/extra/contributing/index.html
new file mode 100644
index 000000000..9a057402b
--- /dev/null
+++ b/v4.2.1/extra/contributing/index.html
@@ -0,0 +1,2 @@
+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.2.1/extra/extensions/index.html b/v4.2.1/extra/extensions/index.html
new file mode 100644
index 000000000..53dfb728d
--- /dev/null
+++ b/v4.2.1/extra/extensions/index.html
@@ -0,0 +1,2 @@
+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.2.1/extra/methods/index.html b/v4.2.1/extra/methods/index.html
new file mode 100644
index 000000000..829757a38
--- /dev/null
+++ b/v4.2.1/extra/methods/index.html
@@ -0,0 +1,177 @@
+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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diff --git a/v4.2.1/index.html b/v4.2.1/index.html
new file mode 100644
index 000000000..e17c468a3
--- /dev/null
+++ b/v4.2.1/index.html
@@ -0,0 +1,2 @@
+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/v4.2.1/lib/algebra/index.html b/v4.2.1/lib/algebra/index.html
new file mode 100644
index 000000000..3a4845b7b
--- /dev/null
+++ b/v4.2.1/lib/algebra/index.html
@@ -0,0 +1,5 @@
+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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diff --git a/v4.2.1/lib/helpers/index.html b/v4.2.1/lib/helpers/index.html
new file mode 100644
index 000000000..e4f3d1245
--- /dev/null
+++ b/v4.2.1/lib/helpers/index.html
@@ -0,0 +1,14 @@
+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.2.1/lib/marginal/index.html b/v4.2.1/lib/marginal/index.html
new file mode 100644
index 000000000..bc6a1bc22
--- /dev/null
+++ b/v4.2.1/lib/marginal/index.html
@@ -0,0 +1,21 @@
+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/v4.2.1/lib/message/index.html b/v4.2.1/lib/message/index.html
new file mode 100644
index 000000000..4a647bdf6
--- /dev/null
+++ b/v4.2.1/lib/message/index.html
@@ -0,0 +1,76 @@
+
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/v4.2.1/lib/nodes/bifm/index.html b/v4.2.1/lib/nodes/bifm/index.html
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+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/v4.2.1/lib/nodes/ctransition/index.html b/v4.2.1/lib/nodes/ctransition/index.html
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+
+Continuous transition · ReactiveMP.jl The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
. ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/v4.2.1/lib/nodes/delta/index.html b/v4.2.1/lib/nodes/delta/index.html
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+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/v4.2.1/lib/nodes/equality/index.html b/v4.2.1/lib/nodes/equality/index.html
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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diff --git a/v4.2.1/lib/nodes/flow/index.html b/v4.2.1/lib/nodes/flow/index.html
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+
+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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diff --git a/v4.2.1/lib/nodes/index.html b/v4.2.1/lib/nodes/index.html
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+
+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Theme
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This document was generated with Documenter.jl version 1.5.0 on Thursday 27 June 2024 . Using Julia version 1.10.4.
diff --git a/v4.2.1/lib/nodes/logical/index.html b/v4.2.1/lib/nodes/logical/index.html
new file mode 100644
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+
+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
Theme
Automatic (OS) documenter-light documenter-dark catppuccin-latte catppuccin-frappe catppuccin-macchiato catppuccin-mocha
This document was generated with Documenter.jl version 1.5.0 on Thursday 27 June 2024 . Using Julia version 1.10.4.
diff --git a/v4.2.1/lib/rules/index.html b/v4.2.1/lib/rules/index.html
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
See also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing SoftDot γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(θ) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot x μ(y) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(θ) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y μ(x) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli BIFMHelper out q(in) :: Any Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} NOT in μ(out) :: Distributions.Bernoulli Nothing ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.GammaShapeRate β q(out) :: Any Nothing q(α) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Any Nothing q(β) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.GammaShapeRate out q(α) :: Any Nothing q(β) :: Any ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing HalfNormal out q(v) :: BayesBase.PointMass Nothing ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
Theme
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This document was generated with Documenter.jl version 1.5.0 on Thursday 27 June 2024 . Using Julia version 1.10.4.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The ContinuousTransition node transforms an m-dimensional (dx) vector x into an n-dimensional (dy) vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a. ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint\nReactiveMP.preprocess_form_constraints","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.preprocess_form_constraints","page":"Custom functional form","title":"ReactiveMP.preprocess_form_constraints","text":"preprocess_form_constraints(constraints)\n\nThis function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint object. Wraps unknown form constraints into a WrappedFormConstraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(constraint, something)\n\nThis function applies a given form constraint to a given object. \n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional form constraint implementation is the prod function in the BayesBase package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, ExponentialFamily, Distributions, BayesBase\n\n# First, we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end\n\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This assumes that the given `distribution` object has `mean` and `precision` defined.\n # These quantities might be approximated using other methods, such as Laplace approximation.\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # `ProductOf` is a special case. Read more about this type in the corresponding \n # documentation section of the `BayesBase` package.\n # ... \nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())\n\nconstrain_form(constraint, NormalMeanVariance(0, 2))","category":"page"},{"location":"custom/custom-functional-form/#Wrapped-Form-Constraints","page":"Custom functional form","title":"Wrapped Form Constraints","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Some constraint objects might not be subtypes of AbstractFormConstraint. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP expects users to pass a WrappedFormConstraint object, which wraps the original object and makes it compatible with the ReactiveMP inference backend. Note that the ReactiveMP.preprocess_form_constraints function automatically wraps all objects that are not subtypes of AbstractFormConstraint.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Additionally, objects wrapped by WrappedFormConstraints may implement the ReactiveMP.prepare_context function. This function's output will be stored in the WrappedFormConstraints along with the original object. If prepare_context is implemented, the constrain_form function will take three arguments: the original constraint, the context, and the object that needs to be constrained.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.WrappedFormConstraint\nReactiveMP.prepare_context\nReactiveMP.constrain_form(::ReactiveMP.WrappedFormConstraint, something)","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.WrappedFormConstraint","page":"Custom functional form","title":"ReactiveMP.WrappedFormConstraint","text":"WrappedFormConstraint(constraint, context)\n\nThis is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form function. By default all objects that are not sub-typed from AbstractFormConstraint are wrapped into this object. Use ReactiveMP.prepare_context to provide an extra context for a given form constraint, that can be reused between multiple constrain_form calls.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.prepare_context","page":"Custom functional form","title":"ReactiveMP.prepare_context","text":"prepare_context(constraint)\n\nThis function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext if no context is needed (the default behaviour).\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form-Tuple{ReactiveMP.WrappedFormConstraint, Any}","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(wrapped::WrappedFormConstraint, something)\n\nThis function unwraps the wrapped object and calls constrain_form function with the provided context. If the context is not provided, simply calls constrain_form with the wrapped constraint. Otherwise passes the context to the constrain_form function as the second argument.\n\n\n\n\n\n","category":"method"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, Distributions, BayesBase, Random\n\n# First, we define our custom form constraint that creates a set of samples\n# Note that this is not a subtype of `AbstractFormConstraint`\nstruct MyCustomSampleListFormConstraint end\n\n# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions\n# which are necessary for the `ReactiveMP` inference backend\nReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()\n\n# We implement the `prepare_context` function, which returns a random number generator\nfunction ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)\n return Random.default_rng()\nend\n\n# We implement the `constrain_form` function, which returns a set of samples\nfunction ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)\n return rand(context, distribution, 10)\nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())\n\nconstrain_form(constraint, Normal(0, 10))","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
diff --git a/v4.2.1/siteinfo.js b/v4.2.1/siteinfo.js
new file mode 100644
index 000000000..70dde09f4
--- /dev/null
+++ b/v4.2.1/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.2.1";
diff --git a/v4.3 b/v4.3
new file mode 120000
index 000000000..1ddc0f604
--- /dev/null
+++ b/v4.3
@@ -0,0 +1 @@
+v4.3.0
\ No newline at end of file
diff --git a/v4.3.0/.documenter-siteinfo.json b/v4.3.0/.documenter-siteinfo.json
new file mode 100644
index 000000000..91a34fa82
--- /dev/null
+++ b/v4.3.0/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-19T12:39:36","documenter_version":"1.5.0"}}
\ No newline at end of file
diff --git a/v4.3.0/assets/documenter.js b/v4.3.0/assets/documenter.js
new file mode 100644
index 000000000..b2bdd43ee
--- /dev/null
+++ b/v4.3.0/assets/documenter.js
@@ -0,0 +1,1059 @@
+// Generated by Documenter.jl
+requirejs.config({
+ paths: {
+ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+ 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+ 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+ 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+ 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+ 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+ 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+ 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+ 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+ },
+ shim: {
+ "highlight-julia": {
+ "deps": [
+ "highlight"
+ ]
+ },
+ "katex-auto-render": {
+ "deps": [
+ "katex"
+ ]
+ },
+ "headroom-jquery": {
+ "deps": [
+ "jquery",
+ "headroom"
+ ]
+ },
+ "highlight-julia-repl": {
+ "deps": [
+ "highlight"
+ ]
+ }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+ renderMathInElement(
+ document.body,
+ {
+ "delimiters": [
+ {
+ "left": "$",
+ "right": "$",
+ "display": false
+ },
+ {
+ "left": "$$",
+ "right": "$$",
+ "display": true
+ },
+ {
+ "left": "\\[",
+ "right": "\\]",
+ "display": true
+ }
+ ]
+}
+
+ );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+ hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+ let articleToggleTitle = "Expand docstring";
+
+ debounce(() => {
+ if ($(this).siblings("section").is(":visible")) {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+ } else {
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ articleToggleTitle = "Collapse docstring";
+ }
+
+ $(this)
+ .find(".docstring-article-toggle-button")
+ .prop("title", articleToggleTitle);
+ $(this).siblings("section").slideToggle();
+ });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+ let articleToggleTitle = "Expand docstring";
+ let navArticleToggleTitle = "Expand all docstrings";
+ let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+ debounce(() => {
+ if (isExpanded) {
+ $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-down")
+ .addClass("fa-chevron-right");
+
+ isExpanded = false;
+
+ $(".docstring section").slideUp(animationSpeed);
+ } else {
+ $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+ $(".docstring-article-toggle-button")
+ .removeClass("fa-chevron-right")
+ .addClass("fa-chevron-down");
+
+ isExpanded = true;
+ articleToggleTitle = "Collapse docstring";
+ navArticleToggleTitle = "Collapse all docstrings";
+
+ $(".docstring section").slideDown(animationSpeed);
+ }
+
+ $(this).prop("title", navArticleToggleTitle);
+ $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+ });
+});
+
+function debounce(callback, timeout = 300) {
+ if (Date.now() - timer > timeout) {
+ callback();
+ }
+
+ clearTimeout(timer);
+
+ timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+ for (const el of document.getElementsByTagName("pre")) {
+ const button = document.createElement("button");
+ button.classList.add("copy-button", "fa-solid", "fa-copy");
+ button.setAttribute("aria-label", "Copy this code block");
+ button.setAttribute("title", "Copy");
+
+ el.appendChild(button);
+
+ const success = function () {
+ button.classList.add("success", "fa-check");
+ button.classList.remove("fa-copy");
+ };
+
+ const failure = function () {
+ button.classList.add("error", "fa-xmark");
+ button.classList.remove("fa-copy");
+ };
+
+ button.addEventListener("click", function () {
+ copyToClipboard(el.innerText).then(success, failure);
+
+ setTimeout(function () {
+ button.classList.add("fa-copy");
+ button.classList.remove("success", "fa-check", "fa-xmark");
+ }, 5000);
+ });
+ }
+}
+
+function copyToClipboard(text) {
+ // clipboard API is only available in secure contexts
+ if (window.navigator && window.navigator.clipboard) {
+ return window.navigator.clipboard.writeText(text);
+ } else {
+ return new Promise(function (resolve, reject) {
+ try {
+ const el = document.createElement("textarea");
+ el.textContent = text;
+ el.style.position = "fixed";
+ el.style.opacity = 0;
+ document.body.appendChild(el);
+ el.select();
+ document.execCommand("copy");
+
+ resolve();
+ } catch (err) {
+ reject(err);
+ } finally {
+ document.body.removeChild(el);
+ }
+ });
+ }
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+ addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+ $("#documenter .docs-navbar").headroom({
+ tolerance: { up: 10, down: 10 },
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let meta = $("div[data-docstringscollapsed]").data();
+
+ if (meta?.docstringscollapsed) {
+ $("#documenter-article-toggle-button").trigger({
+ type: "click",
+ noToggleAnimation: true,
+ });
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+ run search
+ find the first 200 unique results from each category, and compute their divs for display
+ note that this is necessary and sufficient information for the main thread to find the
+ first 200 unique results from any given filter set
+ post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results)
+
+On text update
+ if worker is not running, launch_search()
+
+launch_search
+ set worker_is_running to true, set last_search_text to the search text
+ post the search query to worker
+
+on message from worker
+ if last_search_text is not the same as the text in the search field,
+ the latest search result is not reflective of the latest search query, so update again
+ launch_search()
+ otherwise
+ set worker_is_running to false
+
+ regardless, display the new search results to the user
+ save the unfiltered_results as a global
+ update_search()
+
+on filter click
+ adjust the filter selection
+ update_search()
+
+update_search
+ apply search filters by looping through the unfiltered_results and finding the first 200
+ unique results that match the filters
+
+ Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+ importScripts(
+ "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+ );
+
+ let data = documenterSearchIndex.map((x, key) => {
+ x["id"] = key; // minisearch requires a unique for each object
+ return x;
+ });
+
+ // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+ // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+ // ideally we'd just filter the original list but it's not available as a variable
+ const stopWords = new Set([
+ "a",
+ "able",
+ "about",
+ "across",
+ "after",
+ "almost",
+ "also",
+ "am",
+ "among",
+ "an",
+ "and",
+ "are",
+ "as",
+ "at",
+ "be",
+ "because",
+ "been",
+ "but",
+ "by",
+ "can",
+ "cannot",
+ "could",
+ "dear",
+ "did",
+ "does",
+ "either",
+ "ever",
+ "every",
+ "from",
+ "got",
+ "had",
+ "has",
+ "have",
+ "he",
+ "her",
+ "hers",
+ "him",
+ "his",
+ "how",
+ "however",
+ "i",
+ "if",
+ "into",
+ "it",
+ "its",
+ "just",
+ "least",
+ "like",
+ "likely",
+ "may",
+ "me",
+ "might",
+ "most",
+ "must",
+ "my",
+ "neither",
+ "no",
+ "nor",
+ "not",
+ "of",
+ "off",
+ "often",
+ "on",
+ "or",
+ "other",
+ "our",
+ "own",
+ "rather",
+ "said",
+ "say",
+ "says",
+ "she",
+ "should",
+ "since",
+ "so",
+ "some",
+ "than",
+ "that",
+ "the",
+ "their",
+ "them",
+ "then",
+ "there",
+ "these",
+ "they",
+ "this",
+ "tis",
+ "to",
+ "too",
+ "twas",
+ "us",
+ "wants",
+ "was",
+ "we",
+ "were",
+ "what",
+ "when",
+ "who",
+ "whom",
+ "why",
+ "will",
+ "would",
+ "yet",
+ "you",
+ "your",
+ ]);
+
+ let index = new MiniSearch({
+ fields: ["title", "text"], // fields to index for full-text search
+ storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+ processTerm: (term) => {
+ let word = stopWords.has(term) ? null : term;
+ if (word) {
+ // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+ word = word
+ .replace(/^[^a-zA-Z0-9@!]+/, "")
+ .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+ word = word.toLowerCase();
+ }
+
+ return word ?? null;
+ },
+ // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+ // find anything if searching for "add!", only for the entire qualification
+ tokenize: (string) => string.split(/[\s\-\.]+/),
+ // options which will be applied during the search
+ searchOptions: {
+ prefix: true,
+ boost: { title: 100 },
+ fuzzy: 2,
+ },
+ });
+
+ index.addAll(data);
+
+ /**
+ * Used to map characters to HTML entities.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const htmlEscapes = {
+ "&": "&",
+ "<": "<",
+ ">": ">",
+ '"': """,
+ "'": "'",
+ };
+
+ /**
+ * Used to match HTML entities and HTML characters.
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ const reUnescapedHtml = /[&<>"']/g;
+ const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+ /**
+ * Escape function from lodash
+ * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+ */
+ function escape(string) {
+ return string && reHasUnescapedHtml.test(string)
+ ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+ : string || "";
+ }
+
+ /**
+ * RegX escape function from MDN
+ * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+ function escapeRegExp(string) {
+ return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+ }
+
+ /**
+ * Make the result component given a minisearch result data object and the value
+ * of the search input as queryString. To view the result object structure, refer:
+ * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+ *
+ * @param {object} result
+ * @param {string} querystring
+ * @returns string
+ */
+ function make_search_result(result, querystring) {
+ let search_divider = `
`;
+ let display_link =
+ result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+ (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+ if (result.page !== "") {
+ display_link += ` (${result.page})`;
+ }
+ searchstring = escapeRegExp(querystring);
+ let textindex = new RegExp(`${searchstring}`, "i").exec(result.text);
+ let text =
+ textindex !== null
+ ? result.text.slice(
+ Math.max(textindex.index - 100, 0),
+ Math.min(
+ textindex.index + querystring.length + 100,
+ result.text.length
+ )
+ )
+ : ""; // cut-off text before and after from the match
+
+ text = text.length ? escape(text) : "";
+
+ let display_result = text.length
+ ? "..." +
+ text.replace(
+ new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence
+ '$& '
+ ) +
+ "..."
+ : ""; // highlights the match
+
+ let in_code = false;
+ if (!["page", "section"].includes(result.category.toLowerCase())) {
+ in_code = true;
+ }
+
+ // We encode the full url to escape some special characters which can lead to broken links
+ let result_div = `
+
+
+
${escape(result.title)}
+
${result.category}
+
+
+ ${display_result}
+
+
+ ${display_link}
+
+
+ ${search_divider}
+ `;
+
+ return result_div;
+ }
+
+ self.onmessage = function (e) {
+ let query = e.data;
+ let results = index.search(query, {
+ filter: (result) => {
+ // Only return relevant results
+ return result.score >= 1;
+ },
+ combineWith: "AND",
+ });
+
+ // Pre-filter to deduplicate and limit to 200 per category to the extent
+ // possible without knowing what the filters are.
+ let filtered_results = [];
+ let counts = {};
+ for (let filter of filters) {
+ counts[filter] = 0;
+ }
+ let present = {};
+
+ for (let result of results) {
+ cat = result.category;
+ cnt = counts[cat];
+ if (cnt < 200) {
+ id = cat + "---" + result.location;
+ if (present[id]) {
+ continue;
+ }
+ present[id] = true;
+ filtered_results.push({
+ location: result.location,
+ category: cat,
+ div: make_search_result(result, query),
+ });
+ }
+ }
+
+ postMessage(filtered_results);
+ };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+ ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+ "(" +
+ worker_function.toString() +
+ ")(" +
+ JSON.stringify(documenterSearchIndex["docs"]) +
+ "," +
+ JSON.stringify(documenterBaseURL) +
+ "," +
+ JSON.stringify(filters) +
+ ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+ if (!worker_is_running) {
+ launch_search();
+ }
+});
+
+function launch_search() {
+ worker_is_running = true;
+ last_search_text = $(".documenter-search-input").val();
+ worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+ if (last_search_text !== $(".documenter-search-input").val()) {
+ launch_search();
+ } else {
+ worker_is_running = false;
+ }
+
+ unfiltered_results = e.data;
+ update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+ if ($(this).hasClass("search-filter-selected")) {
+ selected_filter = "";
+ } else {
+ selected_filter = $(this).text().toLowerCase();
+ }
+
+ // This updates search results and toggles classes for UI:
+ update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+ let querystring = $(".documenter-search-input").val();
+
+ if (querystring.trim()) {
+ if (selected_filter == "") {
+ results = unfiltered_results;
+ } else {
+ results = unfiltered_results.filter((result) => {
+ return selected_filter == result.category.toLowerCase();
+ });
+ }
+
+ let search_result_container = ``;
+ let modal_filters = make_modal_body_filters();
+ let search_divider = `
`;
+
+ if (results.length) {
+ let links = [];
+ let count = 0;
+ let search_results = "";
+
+ for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+ let result = results[i];
+ if (result.location && !links.includes(result.location)) {
+ search_results += result.div;
+ count++;
+ links.push(result.location);
+ }
+ }
+
+ if (count == 1) {
+ count_str = "1 result";
+ } else if (count == 200) {
+ count_str = "200+ results";
+ } else {
+ count_str = count + " results";
+ }
+ let result_count = `${count_str}
`;
+
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+ ${result_count}
+
+ ${search_results}
+
+
+ `;
+ } else {
+ search_result_container = `
+
+ ${modal_filters}
+ ${search_divider}
+
0 result(s)
+
+ No result found!
+ `;
+ }
+
+ if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").removeClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(search_result_container);
+ } else {
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".search-modal-card-body").html(`
+ Type something to get started!
+ `);
+ }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+ let str = filters
+ .map((val) => {
+ if (selected_filter == val.toLowerCase()) {
+ return `${val} `;
+ } else {
+ return `${val} `;
+ }
+ })
+ .join("");
+
+ return `
+
+ Filters:
+ ${str}
+
`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function () {
+ var settings = $("#documenter-settings");
+ $("#documenter-settings-button").click(function () {
+ settings.toggleClass("is-active");
+ });
+ // Close the dialog if X is clicked
+ $("#documenter-settings button.delete").click(function () {
+ settings.removeClass("is-active");
+ });
+ // Close dialog if ESC is pressed
+ $(document).keyup(function (e) {
+ if (e.keyCode == 27) settings.removeClass("is-active");
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+ let search_modal_header = `
+
+ `;
+
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ let search_modal_footer = `
+
+ `;
+
+ $(document.body).append(
+ `
+
+
+
+ ${search_modal_header}
+
+ ${initial_search_body}
+
+ ${search_modal_footer}
+
+
+ `
+ );
+
+ document.querySelector(".docs-search-query").addEventListener("click", () => {
+ openModal();
+ });
+
+ document
+ .querySelector(".close-search-modal")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+
+ $(document).on("click", ".search-result-link", function () {
+ closeModal();
+ });
+
+ document.addEventListener("keydown", (event) => {
+ if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+ openModal();
+ } else if (event.key === "Escape") {
+ closeModal();
+ }
+
+ return false;
+ });
+
+ // Functions to open and close a modal
+ function openModal() {
+ let searchModal = document.querySelector("#search-modal");
+
+ searchModal.classList.add("is-active");
+ document.querySelector(".documenter-search-input").focus();
+ }
+
+ function closeModal() {
+ let searchModal = document.querySelector("#search-modal");
+ let initial_search_body = `
+ Type something to get started!
+ `;
+
+ searchModal.classList.remove("is-active");
+ document.querySelector(".documenter-search-input").blur();
+
+ if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+ $(".search-modal-card-body").addClass("is-justify-content-center");
+ }
+
+ $(".documenter-search-input").val("");
+ $(".search-modal-card-body").html(initial_search_body);
+ }
+
+ document
+ .querySelector("#search-modal .modal-background")
+ .addEventListener("click", () => {
+ closeModal();
+ });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+ var sidebar = $("#documenter > .docs-sidebar");
+ var sidebar_button = $("#documenter-sidebar-button");
+ sidebar_button.click(function (ev) {
+ ev.preventDefault();
+ sidebar.toggleClass("visible");
+ if (sidebar.hasClass("visible")) {
+ // Makes sure that the current menu item is visible in the sidebar.
+ $("#documenter .docs-menu a.is-active").focus();
+ }
+ });
+ $("#documenter > .docs-main").bind("click", function (ev) {
+ if ($(ev.target).is(sidebar_button)) {
+ return;
+ }
+ if (sidebar.hasClass("visible")) {
+ sidebar.removeClass("visible");
+ }
+ });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+ e = $("#documenter .docs-autofit");
+ function resize() {
+ var L = parseInt(e.css("max-width"), 10);
+ var L0 = e.width();
+ if (L0 > L) {
+ var h0 = parseInt(e.css("font-size"), 10);
+ e.css("font-size", (L * h0) / L0);
+ // TODO: make sure it survives resizes?
+ }
+ }
+ // call once and then register events
+ resize();
+ $(window).resize(resize);
+ $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+ var sidebar = $("#documenter .docs-menu").get(0);
+ var active = $("#documenter .docs-menu .is-active").get(0);
+ if (typeof active !== "undefined") {
+ sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+ // onchange callback
+ $("#documenter-themepicker").change(function themepick_callback(ev) {
+ var themename = $("#documenter-themepicker option:selected").attr("value");
+ if (themename === "auto") {
+ // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+ window.localStorage.removeItem("documenter-theme");
+ } else {
+ // set_theme(themename);
+ window.localStorage.setItem("documenter-theme", themename);
+ }
+ // We re-use the global function from themeswap.js to actually do the swapping.
+ set_theme_from_local_storage();
+ });
+
+ // Make sure that the themepicker displays the correct theme when the theme is retrieved
+ // from localStorage
+ if (typeof window.localStorage !== "undefined") {
+ var theme = window.localStorage.getItem("documenter-theme");
+ if (theme !== null) {
+ $("#documenter-themepicker option").each(function (i, e) {
+ e.selected = e.value === theme;
+ });
+ }
+ }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+ // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+ // siteinfo.js file, we just return immediately and not display the version selector.
+ if (
+ typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+ DOCUMENTER_VERSION_SELECTOR_DISABLED
+ ) {
+ return;
+ }
+
+ var version_selector = $("#documenter .docs-version-selector");
+ var version_selector_select = $("#documenter .docs-version-selector select");
+
+ version_selector_select.change(function (x) {
+ target_href = version_selector_select
+ .children("option:selected")
+ .get(0).value;
+ window.location.href = target_href;
+ });
+
+ // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+ if (
+ typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+ $("#version-selector > option").length == 0
+ ) {
+ var option = $(
+ "" +
+ DOCUMENTER_CURRENT_VERSION +
+ " "
+ );
+ version_selector_select.append(option);
+ }
+
+ if (typeof DOC_VERSIONS !== "undefined") {
+ var existing_versions = version_selector_select.children("option");
+ var existing_versions_texts = existing_versions.map(function (i, x) {
+ return x.text;
+ });
+ DOC_VERSIONS.forEach(function (each) {
+ var version_url = documenterBaseURL + "/../" + each + "/";
+ var existing_id = $.inArray(each, existing_versions_texts);
+ // if not already in the version selector, add it as a new option,
+ // otherwise update the old option with the URL and enable it
+ if (existing_id == -1) {
+ var option = $(
+ "" + each + " "
+ );
+ version_selector_select.append(option);
+ } else {
+ var option = existing_versions[existing_id];
+ option.value = version_url;
+ option.disabled = false;
+ }
+ });
+ }
+
+ // only show the version selector if the selector has been populated
+ if (version_selector_select.children("option").length > 0) {
+ version_selector.toggleClass("visible");
+ }
+});
+
+})
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+
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+
+
+
+
+
+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
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+
+
+
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+++ b/v4.3.0/assets/img/vmp-message.svg
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+
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diff --git a/v4.3.0/assets/themes/catppuccin-frappe.css b/v4.3.0/assets/themes/catppuccin-frappe.css
new file mode 100644
index 000000000..54a5b77ea
--- /dev/null
+++ b/v4.3.0/assets/themes/catppuccin-frappe.css
@@ -0,0 +1 @@
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.button.is-text[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-text{background-color:transparent;border-color:transparent;box-shadow:none}html.theme--catppuccin-frappe .button.is-ghost{background:none;border-color:rgba(0,0,0,0);color:#8caaee;text-decoration:none}html.theme--catppuccin-frappe .button.is-ghost:hover,html.theme--catppuccin-frappe .button.is-ghost.is-hovered{color:#8caaee;text-decoration:underline}html.theme--catppuccin-frappe .button.is-white{background-color:#fff;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white:hover,html.theme--catppuccin-frappe .button.is-white.is-hovered{background-color:#f9f9f9;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white:focus,html.theme--catppuccin-frappe .button.is-white.is-focused{border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white:focus:not(:active),html.theme--catppuccin-frappe .button.is-white.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-frappe .button.is-white:active,html.theme--catppuccin-frappe .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white{background-color:#fff;border-color:#fff;box-shadow:none}html.theme--catppuccin-frappe .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted:hover,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--catppuccin-frappe .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-outlined:hover,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-white.is-outlined:focus,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:hover,html.theme--catppuccin-frappe .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:focus,html.theme--catppuccin-frappe .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:focus:not(:active),html.theme--catppuccin-frappe .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-frappe .button.is-black:active,html.theme--catppuccin-frappe .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-frappe .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:hover,html.theme--catppuccin-frappe .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus,html.theme--catppuccin-frappe .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus:not(:active),html.theme--catppuccin-frappe .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-frappe .button.is-light:active,html.theme--catppuccin-frappe .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-dark,html.theme--catppuccin-frappe .content kbd.button{background-color:#414559;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:hover,html.theme--catppuccin-frappe .content kbd.button:hover,html.theme--catppuccin-frappe .button.is-dark.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-hovered{background-color:#3c3f52;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:focus,html.theme--catppuccin-frappe .content kbd.button:focus,html.theme--catppuccin-frappe .button.is-dark.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:focus:not(:active),html.theme--catppuccin-frappe .content kbd.button:focus:not(:active),html.theme--catppuccin-frappe .button.is-dark.is-focused:not(:active),html.theme--catppuccin-frappe .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(65,69,89,0.25)}html.theme--catppuccin-frappe .button.is-dark:active,html.theme--catppuccin-frappe .content kbd.button:active,html.theme--catppuccin-frappe .button.is-dark.is-active,html.theme--catppuccin-frappe .content kbd.button.is-active{background-color:#363a4a;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark[disabled],html.theme--catppuccin-frappe .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button{background-color:#414559;border-color:#414559;box-shadow:none}html.theme--catppuccin-frappe .button.is-dark.is-inverted,html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-focused{background-color:#414559;border-color:#414559;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content 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!important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe .image.is-3by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-frappe .image.is-5by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-frappe .image.is-16by9,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-frappe .image.is-2by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-frappe .image.is-3by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-frappe .image.is-4by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-frappe .image.is-3by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-frappe .image.is-2by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-frappe .image.is-3by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-frappe .image.is-9by16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-frappe .image.is-1by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-frappe .image.is-1by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-frappe .image.is-16x16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-frappe .image.is-24x24,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-24x24{height:24px;width:24px}html.theme--catppuccin-frappe .image.is-32x32,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-32x32{height:32px;width:32px}html.theme--catppuccin-frappe .image.is-48x48,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-48x48{height:48px;width:48px}html.theme--catppuccin-frappe .image.is-64x64,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-64x64{height:64px;width:64px}html.theme--catppuccin-frappe .image.is-96x96,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-96x96{height:96px;width:96px}html.theme--catppuccin-frappe .image.is-128x128,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-128x128{height:128px;width:128px}html.theme--catppuccin-frappe .notification{background-color:#292c3c;border-radius:.4em;position:relative;padding:1.25rem 2.5rem 1.25rem 1.5rem}html.theme--catppuccin-frappe .notification 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diff --git a/v4.3.0/assets/themes/catppuccin-latte.css b/v4.3.0/assets/themes/catppuccin-latte.css
new file mode 100644
index 000000000..ca172b630
--- /dev/null
+++ b/v4.3.0/assets/themes/catppuccin-latte.css
@@ -0,0 +1 @@
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.button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte 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.button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--catppuccin-latte .button.is-primary.is-focused:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(30,102,245,0.25)}html.theme--catppuccin-latte .button.is-primary:active,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-active,html.theme--catppuccin-latte 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.button.is-primary.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte .button.is-primary.is-outlined:focus,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-primary.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#1e66f5;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte 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.file.is-link.is-active .file-cta{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info .file-cta{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:hover .file-cta,html.theme--catppuccin-latte .file.is-info.is-hovered .file-cta{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:focus .file-cta,html.theme--catppuccin-latte .file.is-info.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(23,146,153,0.25);color:#fff}html.theme--catppuccin-latte .file.is-info:active .file-cta,html.theme--catppuccin-latte .file.is-info.is-active .file-cta{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success .file-cta{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:hover .file-cta,html.theme--catppuccin-latte .file.is-success.is-hovered .file-cta{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:focus .file-cta,html.theme--catppuccin-latte .file.is-success.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(64,160,43,0.25);color:#fff}html.theme--catppuccin-latte .file.is-success:active .file-cta,html.theme--catppuccin-latte .file.is-success.is-active .file-cta{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning .file-cta{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:hover .file-cta,html.theme--catppuccin-latte .file.is-warning.is-hovered .file-cta{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:focus .file-cta,html.theme--catppuccin-latte .file.is-warning.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(223,142,29,0.25);color:#fff}html.theme--catppuccin-latte .file.is-warning:active .file-cta,html.theme--catppuccin-latte .file.is-warning.is-active .file-cta{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger .file-cta{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:hover .file-cta,html.theme--catppuccin-latte .file.is-danger.is-hovered .file-cta{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:focus .file-cta,html.theme--catppuccin-latte .file.is-danger.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(210,15,57,0.25);color:#fff}html.theme--catppuccin-latte .file.is-danger:active .file-cta,html.theme--catppuccin-latte .file.is-danger.is-active .file-cta{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte 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.icon:only-child,html.theme--catppuccin-latte .navbar-link .icon:only-child{margin-left:-0.25rem;margin-right:-0.25rem}html.theme--catppuccin-latte a.navbar-item,html.theme--catppuccin-latte .navbar-link{cursor:pointer}html.theme--catppuccin-latte a.navbar-item:focus,html.theme--catppuccin-latte a.navbar-item:focus-within,html.theme--catppuccin-latte a.navbar-item:hover,html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link:focus,html.theme--catppuccin-latte .navbar-link:focus-within,html.theme--catppuccin-latte .navbar-link:hover,html.theme--catppuccin-latte .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}html.theme--catppuccin-latte .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .navbar-item img{max-height:1.75rem}html.theme--catppuccin-latte .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-latte .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-touch{top:0}html.theme--catppuccin-latte .navbar.is-fixed-top .navbar-menu,html.theme--catppuccin-latte .navbar.is-fixed-top-touch .navbar-menu{-webkit-overflow-scrolling:touch;max-height:calc(100vh - 4rem);overflow:auto}html.theme--catppuccin-latte html.has-navbar-fixed-top-touch,html.theme--catppuccin-latte body.has-navbar-fixed-top-touch{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-touch,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-touch{padding-bottom:4rem}}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .navbar,html.theme--catppuccin-latte .navbar-menu,html.theme--catppuccin-latte .navbar-start,html.theme--catppuccin-latte .navbar-end{align-items:stretch;display:flex}html.theme--catppuccin-latte .navbar{min-height:4rem}html.theme--catppuccin-latte .navbar.is-spaced{padding:1rem 2rem}html.theme--catppuccin-latte .navbar.is-spaced .navbar-start,html.theme--catppuccin-latte .navbar.is-spaced .navbar-end{align-items:center}html.theme--catppuccin-latte .navbar.is-spaced a.navbar-item,html.theme--catppuccin-latte .navbar.is-spaced .navbar-link{border-radius:.4em}html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link.is-active{background-color:transparent !important}html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within 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.navbar-dropdown.is-boxed,.navbar.is-spaced html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown,html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed{opacity:1;pointer-events:auto;transform:translateY(0)}html.theme--catppuccin-latte .navbar-menu{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .navbar-start{justify-content:flex-start;margin-right:auto}html.theme--catppuccin-latte .navbar-end{justify-content:flex-end;margin-left:auto}html.theme--catppuccin-latte .navbar-dropdown{background-color:#1e66f5;border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid rgba(0,0,0,0.2);box-shadow:0 8px 8px rgba(10,10,10,0.1);display:none;font-size:0.875rem;left:0;min-width:100%;position:absolute;top:100%;z-index:20}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding:0.375rem 1rem;white-space:nowrap}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte .pagination.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-latte .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-latte .pagination.is-rounded .pagination-previous,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-latte .pagination.is-rounded .pagination-next,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-latte .pagination.is-rounded .pagination-link,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-latte .pagination,html.theme--catppuccin-latte .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte .pagination-previous:active,html.theme--catppuccin-latte .pagination-next:active,html.theme--catppuccin-latte .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--catppuccin-latte .pagination-previous[disabled],html.theme--catppuccin-latte .pagination-previous.is-disabled,html.theme--catppuccin-latte .pagination-next[disabled],html.theme--catppuccin-latte .pagination-next.is-disabled,html.theme--catppuccin-latte .pagination-link[disabled],html.theme--catppuccin-latte .pagination-link.is-disabled{background-color:#acb0be;border-color:#acb0be;box-shadow:none;color:#616587;opacity:0.5}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{padding-left:.75em;padding-right:.75em;white-space:nowrap}html.theme--catppuccin-latte .pagination-link.is-current{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .pagination-ellipsis{color:#9ca0b0;pointer-events:none}html.theme--catppuccin-latte .pagination-list{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-list li{list-style:none}@media screen and (max-width: 768px){html.theme--catppuccin-latte .pagination{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination-previous{order:2}html.theme--catppuccin-latte .pagination-next{order:3}html.theme--catppuccin-latte .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-centered .pagination-list{justify-content:center;order:2}html.theme--catppuccin-latte .pagination.is-centered .pagination-next{order:3}html.theme--catppuccin-latte .pagination.is-right .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-right .pagination-next{order:2}html.theme--catppuccin-latte .pagination.is-right .pagination-list{justify-content:flex-end;order:3}}html.theme--catppuccin-latte .panel{border-radius:8px;box-shadow:#171717;font-size:1rem}html.theme--catppuccin-latte .panel:not(:last-child){margin-bottom:1.5rem}html.theme--catppuccin-latte .panel.is-white .panel-heading{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .panel.is-white .panel-tabs a.is-active{border-bottom-color:#fff}html.theme--catppuccin-latte .panel.is-white .panel-block.is-active .panel-icon{color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-heading{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-tabs a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-latte .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-latte .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-latte .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-latte .panel.is-dark .panel-heading,html.theme--catppuccin-latte .content kbd.panel .panel-heading{background-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-latte .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#ccd0da}html.theme--catppuccin-latte .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .content kbd.panel .panel-block.is-active .panel-icon{color:#ccd0da}html.theme--catppuccin-latte .panel.is-primary .panel-heading,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-primary .panel-tabs a.is-active,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-primary .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-link .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-info 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diff --git a/v4.3.0/assets/themes/catppuccin-macchiato.css b/v4.3.0/assets/themes/catppuccin-macchiato.css
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+++ b/v4.3.0/assets/themes/catppuccin-macchiato.css
@@ -0,0 +1 @@
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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato 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.button.is-link[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link{background-color:#8aadf4;border-color:#8aadf4;box-shadow:none}html.theme--catppuccin-macchiato .button.is-link.is-inverted{background-color:#fff;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined{background-color:transparent;border-color:#8aadf4;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-outlined:hover,html.theme--catppuccin-macchiato 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.button.is-link.is-outlined{background-color:transparent;border-color:#8aadf4;box-shadow:none;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-light{background-color:#ecf2fd;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:hover,html.theme--catppuccin-macchiato .button.is-link.is-light.is-hovered{background-color:#e1eafc;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:active,html.theme--catppuccin-macchiato .button.is-link.is-light.is-active{background-color:#d5e2fb;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-info{background-color:#8bd5ca;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info:hover,html.theme--catppuccin-macchiato .button.is-info.is-hovered{background-color:#82d2c6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info:focus,html.theme--catppuccin-macchiato .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info:focus:not(:active),html.theme--catppuccin-macchiato .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(139,213,202,0.25)}html.theme--catppuccin-macchiato .button.is-info:active,html.theme--catppuccin-macchiato .button.is-info.is-active{background-color:#78cec1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info{background-color:#8bd5ca;border-color:#8bd5ca;box-shadow:none}html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content h6{color:#cad3f5;font-weight:600;line-height:1.125}html.theme--catppuccin-macchiato .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-macchiato .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-macchiato .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-macchiato .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-macchiato .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-macchiato .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-macchiato .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-macchiato .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-macchiato .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-macchiato .content blockquote{background-color:#1e2030;border-left:5px solid #5b6078;padding:1.25em 1.5em}html.theme--catppuccin-macchiato .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-macchiato .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-macchiato .content figure img{display:inline-block}html.theme--catppuccin-macchiato .content figure figcaption{font-style:italic}html.theme--catppuccin-macchiato .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-macchiato .content sup,html.theme--catppuccin-macchiato .content sub{font-size:75%}html.theme--catppuccin-macchiato .content table{width:100%}html.theme--catppuccin-macchiato .content table td,html.theme--catppuccin-macchiato .content table th{border:1px solid #5b6078;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-macchiato .content table th{color:#b5c1f1}html.theme--catppuccin-macchiato .content table th:not([align]){text-align:inherit}html.theme--catppuccin-macchiato .content table thead td,html.theme--catppuccin-macchiato .content table thead th{border-width:0 0 2px;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tfoot td,html.theme--catppuccin-macchiato .content table tfoot th{border-width:2px 0 0;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tbody tr:last-child td,html.theme--catppuccin-macchiato .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-macchiato .content .tabs li+li{margin-top:0}html.theme--catppuccin-macchiato .content.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-macchiato .content.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .content.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .content.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-macchiato .icon.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-macchiato .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-macchiato .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-macchiato .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-macchiato .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-macchiato .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-macchiato .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-macchiato div.icon-text{display:flex}html.theme--catppuccin-macchiato .image,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-macchiato .image img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-macchiato .image img.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-macchiato .image.is-fullwidth,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-macchiato .image.is-square img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-macchiato .image.is-square .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-macchiato .image.is-1by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-macchiato .image.is-1by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by4 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-macchiato .image.is-5by4 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-macchiato .image.is-4by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-macchiato .image.is-4by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by2 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-macchiato .image.is-3by2 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-macchiato 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.has-ratio,html.theme--catppuccin-macchiato .image.is-4by5 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-macchiato .image.is-4by5 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by4 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-macchiato .image.is-3by4 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-macchiato .image.is-2by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-macchiato .image.is-2by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by5 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar 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form.docs-search>input[disabled]:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-ms-input-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .textarea,html.theme--catppuccin-macchiato .input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input{box-shadow:inset 0 0.0625em 0.125em rgba(10,10,10,0.05);max-width:100%;width:100%}html.theme--catppuccin-macchiato .textarea[readonly],html.theme--catppuccin-macchiato .input[readonly],html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[readonly]{box-shadow:none}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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diff --git a/v4.3.0/assets/themes/catppuccin-mocha.css b/v4.3.0/assets/themes/catppuccin-mocha.css
new file mode 100644
index 000000000..6f27b4c5f
--- /dev/null
+++ b/v4.3.0/assets/themes/catppuccin-mocha.css
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kbd.button.is-inverted{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-dark.is-inverted[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-focused{background-color:#313244;border-color:#313244;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha 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kbd.button.is-outlined{background-color:transparent;border-color:#313244;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha 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.button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #89b4fa #89b4fa !important}html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table td,html.theme--catppuccin-mocha .content table th{border:1px solid #585b70;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-mocha .content table th{color:#b8c5ef}html.theme--catppuccin-mocha .content table th:not([align]){text-align:inherit}html.theme--catppuccin-mocha .content table thead td,html.theme--catppuccin-mocha .content table thead th{border-width:0 0 2px;color:#b8c5ef}html.theme--catppuccin-mocha .content table tfoot td,html.theme--catppuccin-mocha .content table tfoot th{border-width:2px 0 0;color:#b8c5ef}html.theme--catppuccin-mocha .content table tbody tr:last-child td,html.theme--catppuccin-mocha .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-mocha .content .tabs li+li{margin-top:0}html.theme--catppuccin-mocha .content.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-mocha .content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-mocha .image.is-square,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-mocha .image.is-1by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-mocha .image.is-5by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-mocha .image.is-4by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-mocha .image.is-3by2,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-mocha .image.is-5by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-mocha .image.is-16by9,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-mocha .image.is-2by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-mocha .image.is-3by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-mocha .image.is-4by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-mocha .image.is-3by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-mocha .image.is-2by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-mocha .image.is-3by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-mocha .image.is-9by16,html.theme--catppuccin-mocha #documenter 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diff --git a/v4.3.0/assets/themes/documenter-dark.css b/v4.3.0/assets/themes/documenter-dark.css
new file mode 100644
index 000000000..2892b385e
--- /dev/null
+++ b/v4.3.0/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
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+ Theme: a11y-dark
+ Author: @ericwbailey
+ Maintainer: @ericwbailey
+
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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark 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.button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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diff --git a/v4.3.0/assets/themes/documenter-light.css b/v4.3.0/assets/themes/documenter-light.css
new file mode 100644
index 000000000..a435b3b63
--- /dev/null
+++ b/v4.3.0/assets/themes/documenter-light.css
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+ Theme: Default
+ Description: Original highlight.js style
+ Author: (c) Ivan Sagalaev
+ Maintainer: @highlightjs/core-team
+ Website: https://highlightjs.org/
+ License: see project LICENSE
+ Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v4.3.0/assets/themeswap.js b/v4.3.0/assets/themeswap.js
new file mode 100644
index 000000000..9f5eebe6a
--- /dev/null
+++ b/v4.3.0/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the tag..
+function set_theme_from_local_storage() {
+ // Initialize the theme to null, which means default
+ var theme = null;
+ // If the browser supports the localstorage and is not disabled then try to get the
+ // documenter theme
+ if (window.localStorage != null) {
+ // Get the user-picked theme from localStorage. May be `null`, which means the default
+ // theme.
+ theme = window.localStorage.getItem("documenter-theme");
+ }
+ // Check if the users preference is for dark color scheme
+ var darkPreference =
+ window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+ // Initialize a few variables for the loop:
+ //
+ // - active: will contain the index of the theme that should be active. Note that there
+ // is no guarantee that localStorage contains sane values. If `active` stays `null`
+ // we either could not find the theme or it is the default (primary) theme anyway.
+ // Either way, we then need to stick to the primary theme.
+ //
+ // - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+ // that are not the currently active theme)
+ var active = null;
+ var disabled = [];
+ var primaryLightTheme = null;
+ var primaryDarkTheme = null;
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+ // attribute set.
+ if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+ primaryLightTheme = themename;
+ }
+ // Check if the theme is primary dark theme so that we could store its name in darkTheme
+ if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+ primaryDarkTheme = themename;
+ }
+ // If we find a matching theme (and it's not the default), we'll set active to non-null
+ if (themename === theme) active = i;
+ // Store the style sheets of inactive themes so that we could disable them
+ if (themename !== theme) disabled.push(ss);
+ }
+ var activeTheme = null;
+ if (active !== null) {
+ // If we did find an active theme, we'll (1) add the theme--$(theme) class to
+ document.getElementsByTagName("html")[0].className = "theme--" + theme;
+ activeTheme = theme;
+ } else {
+ // If we did _not_ find an active theme, then we need to fall back to the primary theme
+ // which can either be dark or light, depending on the user's OS preference.
+ var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+ // In case it somehow happens that the relevant primary theme was not found in the
+ // preceding loop, we abort without doing anything.
+ if (activeTheme === null) {
+ console.error("Unable to determine primary theme.");
+ return;
+ }
+ // When switching to the primary light theme, then we must not have a class name
+ // for the tag. That's only for non-primary or the primary dark theme.
+ if (darkPreference) {
+ document.getElementsByTagName("html")[0].className =
+ "theme--" + activeTheme;
+ } else {
+ document.getElementsByTagName("html")[0].className = "";
+ }
+ }
+ for (var i = 0; i < document.styleSheets.length; i++) {
+ var ss = document.styleSheets[i];
+ // The tag of each style sheet is expected to have a data-theme-name attribute
+ // which must contain the name of the theme. The names in localStorage much match this.
+ var themename = ss.ownerNode.getAttribute("data-theme-name");
+ // attribute not set => non-theme stylesheet => ignore
+ if (themename === null) continue;
+ // we'll disable all the stylesheets, except for the active one
+ ss.disabled = !(themename == activeTheme);
+ }
+}
+set_theme_from_local_storage();
diff --git a/v4.3.0/assets/warner.js b/v4.3.0/assets/warner.js
new file mode 100644
index 000000000..3f6f5d008
--- /dev/null
+++ b/v4.3.0/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+ // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+ // in siteinfo.js.
+ // If either of these are undefined something went horribly wrong, so we abort.
+ if (
+ window.DOCUMENTER_NEWEST === undefined ||
+ window.DOCUMENTER_CURRENT_VERSION === undefined ||
+ window.DOCUMENTER_STABLE === undefined
+ ) {
+ return;
+ }
+
+ // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+ if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+ return;
+ }
+
+ // Current version is newest version, so no need to add a warning.
+ if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+ return;
+ }
+
+ // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+ if (document.body.querySelector('meta[name="robots"]') === null) {
+ const meta = document.createElement("meta");
+ meta.name = "robots";
+ meta.content = "noindex";
+
+ document.getElementsByTagName("head")[0].appendChild(meta);
+ }
+
+ const div = document.createElement("div");
+ div.classList.add("outdated-warning-overlay");
+ const closer = document.createElement("button");
+ closer.classList.add("outdated-warning-closer", "delete");
+ closer.addEventListener("click", function () {
+ document.body.removeChild(div);
+ });
+ const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+ div.innerHTML =
+ 'This documentation is not for the latest stable release, but for either the development version or an older release.Click here to go to the documentation for the latest stable release. ';
+ div.appendChild(closer);
+ document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+ document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+ maybeAddWarning();
+}
diff --git a/v4.3.0/custom/custom-addons/index.html b/v4.3.0/custom/custom-addons/index.html
new file mode 100644
index 000000000..9ec225f2d
--- /dev/null
+++ b/v4.3.0/custom/custom-addons/index.html
@@ -0,0 +1,28 @@
+
+Custom addons · ReactiveMP.jl Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.
Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal)
function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.
Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl
and by including it in the ReactiveMP.jl
file.
Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon
. In our example this becomes:
struct AddonCount{T} <: AbstractAddon
+ count :: T
+end
You can add additional fields or functions for improved handling, such as get_count()
or show()
functions.
As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon()
function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.
In our example we could write
# This specification assumes that the default value for addon is `AddonCount(nothing)`
+function message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)
+
+ # get number of operations of messages
+ message_count = 0
+ for message in messages
+ message_count += getcount(message)
+ end
+
+ # get number of operations of marginals
+ marginal_count = 0
+ for marginal in marginals
+ marginal_count += getcount(marginal)
+ end
+
+ # extend addons with AddonCount() structure
+ return AddonCount(message_count + marginal_count + 1)
+end
+
The goal is to update the AddonCount
structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons
and accepts 5 arguments. In our example this becomes
function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)
+ return AddonCount(left_addon.count + right_addon.count + 1)
+end
here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon
and right_addon
argument specify the addoncount
objects that are being multiplied. corresponding to these addons, there are the distributions left_dist
and right_dist
, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist
is also passed along for potentially reusing the result of earlier computations.
For more advanced information check the implementation of the log-scale or memory addons.
AddonDebug(f :: Function)
This addon calls the function f
over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals.
Example
checkfornans(x) = isnan(x)
+checkfornans(x::AbstractArray) = any(checkfornans.(x))
+checkfornans(x::Tuple) = any(checkfornans.(x))
+
+addons = (AddonDebug(dist -> checkfornans(params(dist))),)
source
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diff --git a/v4.3.0/custom/custom-functional-form/index.html b/v4.3.0/custom/custom-functional-form/index.html
new file mode 100644
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+
+Custom functional form · ReactiveMP.jl In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod
function in the BayesBase
package. For example, if we refer to our CustomFunctionalForm
as to f
we can see the whole functional form constraints pipeline as:
\[q(x) = f\left(\frac{\overrightarrow{\mu}(x)\overleftarrow{\mu}(x)}{\int \overrightarrow{\mu}(x)\overleftarrow{\mu}(x) \mathrm{d}x}\right)\]
ReactiveMP.jl
, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.
AbstractFormConstraint
Every functional form constraint is a subtype of AbstractFormConstraint
abstract type.
Note: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint
.
source UnspecifiedFormConstraint
One of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct
to be a valid functional form in the inference backend.
source CompositeFormConstraint
Creates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy
.
source preprocess_form_constraints(constraints)
This function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint
object. Wraps unknown form constraints into a WrappedFormConstraint
object.
source Every custom functional form must implement a new method for the default_form_check_strategy
function that returns either FormConstraintCheckEach
or FormConstraintCheckLast
.
FormConstraintCheckLast
: q(x) = f(μ1(x) * μ2(x) * μ3(x))
FormConstraintCheckEach
: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))
default_form_check_strategy(form_constraint)
Returns a default check strategy (e.g. FormConstraintCheckEach
or FormConstraintCheckEach
) for a given form constraint object.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed after each subsequent prod
function.
source FormConstraintCheckEach
This form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod
to obtain a posterior marginal. With this form check strategy constrain_form
function will be executed only once after all subsequenct prod
functions have been executed.
source FormConstraintCheckPickDefault
This form constraint check strategy simply fallbacks to a default check strategy for a given form constraint.
source Every custom functional form must implement a new method for the default_prod_constraint
function that returns a proper prod_constraint
object.
default_prod_constraint(form_constraint)
Returns a default prod constraint needed to apply a given form_constraint
. For most form constraints this function returns ProdGeneric
.
source The main function that a custom functional form must implement, which we referred to as f
in the beginning of this section, is the constrain_form
function.
constrain_form(constraint, something)
This function applies a given form constraint to a given object.
source In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl
inference backend. An important part of the functional form constraint implementation is the prod
function in the BayesBase
package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.
Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint
functional form constraint:
using ReactiveMP, ExponentialFamily, Distributions, BayesBase
+
+# First, we define our functional form structure with no fields
+struct MeanPrecisionFormConstraint <: AbstractFormConstraint end
+
+ReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution)
+ # This assumes that the given `distribution` object has `mean` and `precision` defined.
+ # These quantities might be approximated using other methods, such as Laplace approximation.
+ m = mean(distribution) # or approximate with some other method
+ p = precision(distribution) # or approximate with some other method
+ return NormalMeanPrecision(m, p)
+end
+
+function ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)
+ # `ProductOf` is a special case. Read more about this type in the corresponding
+ # documentation section of the `BayesBase` package.
+ # ...
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())
+
+constrain_form(constraint, NormalMeanVariance(0, 2))
ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=0.5)
Some constraint objects might not be subtypes of AbstractFormConstraint
. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP
expects users to pass a WrappedFormConstraint
object, which wraps the original object and makes it compatible with the ReactiveMP
inference backend. Note that the ReactiveMP.preprocess_form_constraints
function automatically wraps all objects that are not subtypes of AbstractFormConstraint
.
Additionally, objects wrapped by WrappedFormConstraints
may implement the ReactiveMP.prepare_context
function. This function's output will be stored in the WrappedFormConstraints
along with the original object. If prepare_context
is implemented, the constrain_form
function will take three arguments: the original constraint, the context, and the object that needs to be constrained.
WrappedFormConstraint(constraint, context)
This is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form
function. By default all objects that are not sub-typed from AbstractFormConstraint
are wrapped into this object. Use ReactiveMP.prepare_context
to provide an extra context for a given form constraint, that can be reused between multiple constrain_form
calls.
source prepare_context(constraint)
This function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext
if no context is needed (the default behaviour).
source constrain_form(wrapped::WrappedFormConstraint, something)
This function unwraps the wrapped
object and calls constrain_form
function with the provided context. If the context is not provided, simply calls constrain_form
with the wrapped constraint. Otherwise passes the context to the constrain_form
function as the second argument.
source using ReactiveMP, Distributions, BayesBase, Random
+
+# First, we define our custom form constraint that creates a set of samples
+# Note that this is not a subtype of `AbstractFormConstraint`
+struct MyCustomSampleListFormConstraint end
+
+# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions
+# which are necessary for the `ReactiveMP` inference backend
+ReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()
+ReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()
+
+# We implement the `prepare_context` function, which returns a random number generator
+function ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)
+ return Random.default_rng()
+end
+
+# We implement the `constrain_form` function, which returns a set of samples
+function ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)
+ return rand(context, distribution, 10)
+end
+
+constraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())
+
+constrain_form(constraint, Normal(0, 10))
10-element Vector{Float64}:
+ -11.421409245522918
+ -0.23631795427240188
+ 8.584791714456655
+ -2.989534881034304
+ 9.399991408278956
+ 9.04758933973381
+ -3.3019063647069884
+ -2.1125378875925223
+ 15.16202965285666
+ 3.9213643721553684
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diff --git a/v4.3.0/extra/contributing/index.html b/v4.3.0/extra/contributing/index.html
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+
+Contributing · ReactiveMP.jl We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.
We track bugs using GitHub issues . We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP
for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.
We welcome new feature proposals. However, before submitting a feature request, consider a few things:
Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions. If you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on. We suggest that you use the dev
command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev
command, for example:
] dev git@github.com:your_username/ReactiveMP.jl.git
The dev
command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP
. All local changes to ReactiveMP code will be reflected in imported code.
It is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.
We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master
branch of the ReactiveMP.jl repository.
Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/
directory) and benchmarks (can be found in /benchmark/
directory) have to run without errors as well.
ReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format
command to fix code style. This command overwrites files.
We use default Julia style guide . We list here a few important points and our modifications to the Julia style guide:
Use 4 spaces for indentation Type names use UpperCamelCase
. For example: AbstractFactorNode
, RandomVariable
, etc.. Function names are lowercase
with underscores, when necessary. For example: activate!
, randomvar
, etc.. Variable names and function arguments use snake_case
The name of a method that modifies its argument(s) must end in !
We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.
All unit tests are located in the /test/
directory. The /test/
directory follows the structure of the /src/
directory. Each test file should have following filename format: test_*.jl
. Some tests are also present in jldoctest
docs annotations directly in the source code. See Julia's documentation about doctests.
The tests can be evaluated by running following command in the Julia REPL:
] test ReactiveMP
In addition tests can be evaluated by running following command in the ReactiveMP root directory:
make test
If a bug has been discovered in an external dependencies of the ReactiveMP.jl
it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl
file for hot-fixes before a new release of the broken dependecy is available.
ReactiveMP.jl
uses Makefile
for most common operations:
make help
: Shows help snippetmake test
: Run tests, supports extra argumentsmake test test_args="distributions:normal_mean_variance"
would run tests only from distributions/test_normal_mean_variance.jl
make test test_args="distributions:normal_mean_variance models:lgssm"
would run tests both from distributions/test_normal_mean_variance.jl
and models/test_lgssm.jl
make docs
: Compile documentationmake benchmark
: Run simple benchmarkmake lint
: Check codestylemake format
: Check and fix codestyle
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diff --git a/v4.3.0/extra/extensions/index.html b/v4.3.0/extra/extensions/index.html
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+
+Extensions · ReactiveMP.jl ReactiveMP.jl
exports extra functionality if other Julia packages are loaded in the same environment.
The Optimizers.jl
package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl
are compatible with the CVI approximation method.
The DiffResults.jl
provides the DiffResult
type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad
option in the CVI approximation method (in the Gaussian
case).
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diff --git a/v4.3.0/extra/methods/index.html b/v4.3.0/extra/methods/index.html
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+
+Exported methods · ReactiveMP.jl In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:
using ReactiveMP
A nice explanation about how modules/packages work in Julia can be found in the official documentation .
In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:
import ReactiveMP: mean
One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:
import ReactiveMP: mean as mean_from_reactivemp
+import Distributions: mean as mean_from_distributions
+import BayesBase: mean as mean_from_bayes_base
mean_from_reactivemp === mean_from_distributions
true
mean_from_reactivemp === mean_from_bayes_base
true
Even though we import mean
function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import
them specifically. Read more about this in the section of the Julia's documentation .
# It is easier to let Julia resolve names automatically
+# Julia will not overwrite `mean` that is coming from both packages
+using ReactiveMP, Distributions, BayesBase, ExponentialFamily
mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`
0.0
mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`
0.0
Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP.
prefix, e.g ReactiveMP.mean
.
Some exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.
foreach(println, names(ReactiveMP))
@average_energy
+@call_marginalrule
+@call_rule
+@logscale
+@marginalrule
+@node
+@rule
+AND
+AR
+ARMeta
+ARsafe
+ARunsafe
+AbstractApproximationMethod
+AbstractFormConstraint
+AbstractMessage
+AbstractPipelineStage
+AbstractVariable
+Adam
+AdditiveCouplingLayer
+AddonDebug
+AddonLogScale
+AddonMemory
+AsyncPipelineStage
+Autoregressive
+AverageEnergy
+BIFM
+BIFMHelper
+BIFMMeta
+CTMeta
+CTransition
+CVI
+CVIProjection
+CompanionMatrix
+CompanionMatrixTransposed
+CompiledFlowModel
+CompositeFormConstraint
+CompositePipelineStage
+ConstVariable
+ContinuousTransition
+ContinuousTransitionMeta
+CustomProdStrategy
+DataVariable
+DataVariableActivationOptions
+DefaultFunctionalDependencies
+DefferedMessage
+DeltaFn
+DeltaFnNode
+DeltaMeta
+Deterministic
+DifferentialEntropy
+DiscontinuePipelineStage
+EmptyPipelineStage
+FactorBoundFreeEnergy
+FactorNode
+Flow
+FlowMeta
+FlowModel
+FoldLeftProdStrategy
+FoldRightProdStrategy
+FormConstraintCheckEach
+FormConstraintCheckLast
+FormConstraintCheckPickDefault
+ForwardDiffGrad
+GCV
+GCVMetadata
+GammaMixture
+GammaMixtureNode
+GaussHermiteCubature
+GaussLaguerreQuadrature
+GaussianMixture
+GaussianMixtureNode
+HalfNormal
+IMPLY
+ImportanceSamplingApproximation
+IncludeAll
+InputLayer
+InverseWishart
+LaplaceApproximation
+Linearization
+LoggerPipelineStage
+Marginal
+Marginalisation
+Message
+Mixture
+MixtureNode
+MomentMatching
+MvNormalMeanScalePrecision
+NOT
+NodeFunctionRuleFallback
+NormalMixture
+NormalMixtureNode
+OR
+PermutationLayer
+PermutationMatrix
+PlanarFlow
+Poisson
+Probit
+ProbitMeta
+ProdCVI
+RadialFlow
+RandomVariable
+RandomVariableActivationOptions
+ReactiveMP
+RequireEverythingFunctionalDependencies
+RequireMarginalFunctionalDependencies
+RequireMessageFunctionalDependencies
+ScheduleOnPipelineStage
+SkipClamped
+SkipClampedAndInitial
+SkipInitial
+SoftDot
+StandardBasisVector
+Stochastic
+Transition
+UT
+Uninformative
+Unscented
+UnscentedTransform
+UnspecifiedFormConstraint
+VariableBoundEntropy
+apply_pipeline_stage
+approximation_name
+approximation_short_name
+as_marginal
+as_message
+compile
+constrain_form
+constvar
+datavar
+default_form_check_strategy
+default_prod_constraint
+degree
+diageye
+dot
+factorisation
+factornode
+functional_dependencies
+functionalform
+getapproximation
+getdata
+getinterfaces
+getlayers
+getlogscale
+getmarginal
+getmarginals
+getmemory
+getmodel
+getprediction
+getpredictions
+ghcubature
+huge
+is_clamped
+is_initial
+isdeterministic
+isstochastic
+laplace
+localmarginalnames
+localmarginals
+marginalrule
+nr_params
+randomvar
+rule
+schedule_updates
+score
+sdtype
+setmarginal!
+setmarginals!
+setmessage!
+setmessages!
+skipindex
+softdot
+srcubature
+tiny
+update!
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+
+Introduction · ReactiveMP.jl Julia package for reactive message passing Bayesian inference engine on a factor graph.
This package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl
package and its documentation .
ReactiveMP.jl
is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2 , link3 ).
The ReactiveMP.jl
package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation .
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diff --git a/v4.3.0/lib/algebra/index.html b/v4.3.0/lib/algebra/index.html
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+
+Algebra utils · ReactiveMP.jl diageye(::Type{T}, n::Int)
An alias for the Matrix{T}(I, n, n)
. Returns a matrix of size n x n
with ones (of type T
) on the diagonal and zeros everywhere else.
source diageye(n::Int)
An alias for the Matrix{Float64}(I, n, n)
. Returns a matrix of size n x n
with ones (of type Float64
) on the diagonal and zeros everywhere else.
source CompanionMatrix
Represents a matrix of the following structure:
θ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0
source PermutationMatrix(ind::Array{T})
creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind)
.
A permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:
\[ A_{ij} = \{0, 1\}\\
+ ∑_{i} A_{ij} = 1\\
+ ∑_{j} A_{ij} = 1\]
An example is the 3-dimensional permutation matrix
\[A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}\]
source StandardBasisVector{T, len, ind}(scale::T)
StandardBasisVector
creates a standard Cartesian basis vector of zeros of length len
with a single element scale
at index ind
.
An example is the 3-dimensional standard basis vector for the first dimension
\[e = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}\]
Which can be constructed by calling e = StandardBasisVector(3, 1, 1)
source ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))
source ImportanceSamplingApproximation
This structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations
Fields
rng
: random number generator objectsnsamples
: number of samples generated by defaultsource mul_inplace!(alpha, A)
Returns alpha * A
, modifying and reusing A
storage if possible.
See also: negate_inplace!
source negate_inplace!(A)
Returns -A
, modifying and reusing A
storage if possible.
See also: mul_inplace!
source mul_trace(A, B)
Computes tr(A * B) without allocating A * B.
source rank1update(A, x)
+rank1update(A, x, y)
Helper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation
source v_a_vT(v, a)
Computes va v^T efficiently.
source powerset(iterator)
Computes the set of all possible sets of the iterator
.
source Modified-bessel function of second kind
mx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient
source
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diff --git a/v4.3.0/lib/helpers/index.html b/v4.3.0/lib/helpers/index.html
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+
+Helper utils · ReactiveMP.jl ReactiveMP
implements various structures/functions/methods as "helper" structures that might be useful in various contexts.
SkipIndexIterator
A special type of iterator that simply iterates over internal iterator
, but skips index skip
.
Arguments
iterator
: internal iteratorskip
: index to skip (integer)See also: skipindex
source skipindex(iterator, skip)
Creation operator for SkipIndexIterator
.
julia> s = ReactiveMP.skipindex(1:3, 2)
+2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:
+ 1
+ 3
+
+julia> collect(s)
+2-element Vector{Int64}:
+ 1
+ 3
See also: SkipIndexIterator
source proxy_type(proxy, type)
Returns a type wrapped with a proxy type in a form of ProxyType{ <: Type }
.
Arguments
proxy
: Proxy type used to wrap type
type
: Type to be wrappedsource ensure_symbol(input)
This function ensures that the given argument has a Symbol type
source @proxy_methods(proxy_type, proxy_getter, proxy_methods)
Generates proxy methods for a specified proxy_type
using proxy_getter
. For example:
@proxy_methods Message getdata [
+ Distributions.mean,
+ Distributions.var
+]
generates:
Distributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))
+Distributions.var(proxy::Message) = Distributions.mean(getdata(proxy))
source upper_type(type)
This function returns Type{ <: T }
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be extendedsource bottom_type(type)
This function returns T
expression for the following input expressions:
typeof(T) Type{ <: T } Type{ T } T Arguments
type
: Type expression to be loweredsource
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diff --git a/v4.3.0/lib/marginal/index.html b/v4.3.0/lib/marginal/index.html
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+
+Marginals · ReactiveMP.jl All marginals are encoded with the type Marginal
.
Marginal(data, is_clamped, is_initial, addons)
An implementation of a marginal in variational message passing framework.
Arguments
data::D
: marginal always holds some data object associated with it, which is usually a probability distributionis_clamped::Bool
, specifies if this marginal was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this marginal was used for initializationaddons::A
, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Marginal(distribution, false, true, nothing)
+Marginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
source From an implementation point a view the Marginal
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch.
getdata(marginal::Marginal)
Returns data
associated with the marginal
.
source is_clamped(marginal::Marginal)
Checks if marginal
is clamped or not.
See also: is_initial
source is_initial(marginal::Marginal)
Checks if marginal
is initial or not.
See also: is_clamped
source getaddons(marginal::Marginal)
Returns addons
associated with the marginal
.
source as_marginal(any)
A function that converts any
to an instance of Marginal
.
source to_marginal(any)
Transforms an input to a proper marginal distribution. Called inside as_marginal
. Some nodes do not use Distributions.jl
, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal
is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl
). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart
and InverseWishart
).
Note: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+marginal = Marginal(distribution, false, true, nothing)
Marginal(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(marginal), precision(marginal)
(0.0, 1.0)
logpdf(marginal, 1.0)
-1.4189385332046727
is_clamped(marginal), is_initial(marginal)
(false, true)
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diff --git a/v4.3.0/lib/message/index.html b/v4.3.0/lib/message/index.html
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+
+Messages · ReactiveMP.jl In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.
Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function . The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.
using StatsPlots, Distributions
+
+plot(Normal(0.0, 1.0), label = "Univariate Gaussian distribution", fillalpha = 0.4, fill = 0)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation . However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference . The ReactiveMP.jl
package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.
Belief propagation message
Variational message with structured factorisation q(x, y)q(z) assumption
All messages are encoded with the type Message
.
An abstract supertype for all concrete message types.
source Message(data, is_clamped, is_initial, addons)
An implementation of a message in variational message passing framework.
Arguments
data::D
: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary functionis_clamped::Bool
, specifies if this message was the result of constant computations (e.g. clamped constants)is_initial::Bool
, specifies if this message was used for initializationaddons::A
, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.Example
julia> distribution = Gamma(10.0, 2.0)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> message = Message(distribution, false, true, nothing)
+Message(Distributions.Gamma{Float64}(α=10.0, θ=2.0))
+
+julia> mean(message)
+20.0
+
+julia> getdata(message)
+Distributions.Gamma{Float64}(α=10.0, θ=2.0)
+
+julia> is_clamped(message)
+false
+
+julia> is_initial(message)
+true
+
source From an implementation point a view the Message
structure does nothing but hold some data
object and redirects most of the statistical related functions to that data
object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial
and is_clamped
fields to determine if product of two messages results in is_initial
or is_clamped
posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.
getdata(message::Message)
Returns data
associated with the message
.
source is_clamped(message::Message)
Checks if message
is clamped or not.
source is_initial(message::Message)
Checks if message
is initial or not.
source getaddons(message::Message)
Returns addons
associated with the message
.
source as_message(::AbstractMessage)
A function that converts an abstract message to an instance of Message
.
source using ReactiveMP, BayesBase, ExponentialFamily
+
+distribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)
+message = Message(distribution, false, true, nothing)
Message(ExponentialFamily.NormalMeanPrecision{Float64}(μ=0.0, w=1.0))
mean(message), precision(message)
(0.0, 1.0)
logpdf(message, 1.0)
-1.4189385332046727
is_clamped(message), is_initial(message)
(false, true)
In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl
uses the multiply_messages
function, which internally uses the prod
function defined in BayesBase.jl
with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl
package for more information.
multiply_messages(prod_strategy, left::Message, right::Message)
Multiplies two messages left
and right
using a given product strategy prod_strategy
. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.
source messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)
Returns a suitable prod computation function for a given strategy and constraints
source A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message
method.
source
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diff --git a/v4.3.0/lib/nodes/ar/index.html b/v4.3.0/lib/nodes/ar/index.html
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+
+Autoregressive · ReactiveMP.jl ar_unit(::T, order)
Returns [ 1.0, 0.0 ... 0.0 ]
with length equal to order in case if T is Multivariate, and 1.0
in case if T is Univariate
source ar_slice(::T, array, ranges...)
Returns array[ranges...]
in case if T is Multivariate, and first(array[ranges...])
in case if T is Univariate
source
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diff --git a/v4.3.0/lib/nodes/bifm/index.html b/v4.3.0/lib/nodes/bifm/index.html
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index 000000000..688a6b503
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+
+BIFM · ReactiveMP.jl See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl
.
The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.
out ~ BIFM(in, zprev, znext)
Interfaces:
out - latent output (observation) of the BIFM node in - latent input of the BIFM node zprev - previous latent state of the BIFM node znext - next latent state of the BIFM node Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
Example
# set priors
+z_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))
+z_tmp ~ BIFMHelper(z_prior)
+
+# update last/previous hidden state
+z_prev = z_tmp
+
+# loop through observations
+for i in 1:nr_samples
+
+ # specify input as random variable
+ u[i] ~ MvNormalMeanPrecision(μu, Wu)
+
+ # specify observation
+ xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }
+ x[i] ~ MvNormalMeanPrecision(xt[i], Wx)
+
+ # update last/previous hidden state
+ z_prev = z[i]
+
+end
source The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.
source The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.
out ~ BIFMHelper(in)
Interfaces:
out - output of the BIFMHelper node, should be connected to the state space model. in - input of the BIFMHelper node, should be connected to the prior for the latent state. Note: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.
source
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diff --git a/v4.3.0/lib/nodes/ctransition/index.html b/v4.3.0/lib/nodes/ctransition/index.html
new file mode 100644
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+
+Continuous transition · ReactiveMP.jl The functional form of the ContinuousTransition node is given by: y ~ Normal(K(a) * x, W⁻¹)
This node transforms an m-dimensional vector x into an n-dimensional vector y via a linear (or nonlinear) transformation with a n×m
-dimensional matrix A
that is constructed from a vector a
via a transformation K(a). ContinuousTransition node is primarily used in two regimes:
When no structure on A is specified:
transformation = a -> reshape(a, 2, 2)
+...
+a ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
When some structure if A is known:
transformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]
+...
+a ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))
+y ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}
+...
To construct the matrix A
, the elements of a
are reshaped into A
according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1
, e.g.
a ~ MvNormalMeanCovariance([0.0], [1.;])`.
Check ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.
y ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}
Interfaces:
y - n-dimensional output of the ContinuousTransition node. x - m-dimensional input of the ContinuousTransition node. a - any-dimensional vector that casts into the matrix A
. W - n×n
-dimensional precision matrix used to soften the transition and perform variational message passing. Note that you can set W to a fixed value or put a prior on it to control the amount of jitter.
The ContinuousTransition node support two factorizations:
Mean-field factorization: @constraints begin
+ q(y, x, a, W) = q(y)q(x)q(a)q(W)
+end
Structured factorization: @constraints begin
+ q(y, x, a, W) = q(y, x)q(a)q(W)
+end
source ContinuousTransitionMeta
is used as a metadata flag in ContinuousTransition
to define the transformation function for constructing the matrix A
from vector a
.
ContinuousTransitionMeta
requires a transformation function and the length of vector a
, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.
Constructors:
ContinuousTransitionMeta(transformation::Function, â::Vector{<:Real})
: Constructs a ContinuousTransitionMeta
struct with the transformation function and allocated basis vectors.Fields:
f
: Represents the transformation function that transforms vector a
into matrix A
The ContinuousTransitionMeta
struct plays a pivotal role in defining how the vector a
is transformed into the matrix A
, thus influencing the behavior of the ContinuousTransition
node.
source `ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.
source
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diff --git a/v4.3.0/lib/nodes/delta/index.html b/v4.3.0/lib/nodes/delta/index.html
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+
+Delta · ReactiveMP.jl DeltaMeta(method = ..., [ inverse = ... ])
DeltaMeta
structure specifies the approximation method for the outbound messages in the DeltaFn
node.
Arguments
method
: required, the approximation method, currently supported methods are Linearization
, Unscented
and CVI
.inverse
: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)Is is also possible to pass the AbstractApproximationMethod
to the meta of the delta node directly. In this case inverse
is set to nothing
.
source Some nodes use IndexedInterface
, ManyOf
structure reflects a collection of marginals from the collection of IndexedInterface
s. @rule
macro also treats ManyOf
specially.
source The Linearization
structure defines the approximation method of the Delta
and Flow
factor nodes. This method performs a local linearization of f around expansion point x.
The Linearization
structure with default parameters can be constructed as Linearization()
.
The Linearization
structure is used inside the DeltaMeta
or FlowMeta
structures and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }
source local_linearization(g, x)
Returns linear components (a, b)
for the function g
at the point x
.
source RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)
source The Unscented
structure defines the approximation method of the Delta
and Flow
factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.
Arguments
α
: Spread parameter for unscented transform #1β
: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node inputκ
: Spread parameter for unscented transform #2e
: Internal cacheThe Unscented
structure with default parameters can be constructed as Unscented()
.
The Unscented
structure is used inside the DeltaMeta
or FlowMeta
structure and can be included as:
y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }
+ # or
+ y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }
source Return the sigma points and weights for a Gaussian distribution
source CVIApproximationDeltaFnRuleLayout
Custom rule layout for the Delta node in case of the CVI approximation method:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses the joint over the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
source This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp
source ForwardDiffGrad(chunk_size::Int)
The auto-differentiation backend for the CVI procedure. Uses the ForwardDiff
library to compute gradients/derivatives. If chunk_size
is not specified then uses the heuristic from ForwardDiff
, which is type-unstable.
The ForwardDiff.jl
must be added to the current Julia environment.
source ProdCVI
The ProdCVI
structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist)
. This method performs an approximation of the product of the dist
and logp
with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing
).
ProdCVI
is deprecated in favor of CVIProjection
.
Arguments
rng
: random number generatorn_samples
: number of samples to use for statistics approximationn_iterations
: number of iteration for the natural parameters gradient optimizationopt
: optimizer, which will be used to perform the natural parameters gradient optimization stepgrad
: optional, defaults to ForwardDiffGrad()
, structure to select how the gradient and the hessian will be computedn_gradpoints
: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)enforce_proper_messages
: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)
warn
: optional, defaults to true, enables or disables warnings related to the optimization stepsn_gradpoints
option is ignored in the Gaussian case
Adding the Optimisers.jl
in your Julia environment enables additional optimizers from the Optimisers.jl
for the CVI approximation method. Adding the DiffResults
in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian
type.
source CVIProjection(; parameters...)
A structure representing the parameters for the Conjugate Variational Inference (CVI) projection method. This structure is a subtype of AbstractApproximationMethod
and is used to configure the settings for CVI.
The CVIProjection
method requires ExponentialFamilyProjection
package installed in the current environment.
Parameters
rng::R
: The random number generator used for sampling. Default is Random.MersenneTwister(42)
.marginalsamples::S
: The number of samples used for approximating marginal distributions. Default is 10
.outsamples::S
: The number of samples used for approximating output message distributions. Default is 100
.prjparams::P
: Parameters for the exponential family projection. Default is nothing
, in which case it will use ExponentialFamilyProjection.DefaultProjectionParameters()
.The CVIProjection
method is an experimental enhancement of the now-deprecated CVI
, offering better stability and improved accuracy. Note that the parameters of this structure, as well as their defaults, are subject to change during the experimentation phase.
source cvi_setup!(opt, λ)
Initialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.
source cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)
Uses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the new λ.
source DeltaFnDefaultRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edgeq_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edgesm_out
: uses all inbound messages on the ins
edgesm_in_k
: uses the inbound message on the in_k
edge and q_ins
See also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout
source DeltaFnDefaultKnownInverseRuleLayout
Default rule layout for the Delta node:
Layout
In order to compute:
q_out
: mirrors the posterior marginal on the out
edge (same as the DeltaFnDefaultRuleLayout
)q_ins
: uses inbound message on the out
edge and all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_out
: uses all inbound messages on the ins
edges (same as the DeltaFnDefaultRuleLayout
)m_in_k
: uses inbound message on the out
edge and inbound messages on the ins
edges except k
source
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diff --git a/v4.3.0/lib/nodes/equality/index.html b/v4.3.0/lib/nodes/equality/index.html
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+
+Equality node · ReactiveMP.jl EqualityNode
Generic idea of an equality node is to keep track of intermediate left
and right
messages in a convenient manner so they can be reused during prod
for random variables with large degree
.
<- left –––- right -> ––- | = | ––– –––- | | outbound
Attributes:
left
: An observable that indicates that left
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.right
: An observable that indicates that right
message can be computed, always sends missing
since we are not interested in actual value. Can be treated as notification.cache_left
: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.cache_right
: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain
.See also: EqualityChain
source
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+Flow · ReactiveMP.jl See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl
.
The PlanarFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + {\bf{u}} \tanh({\bf{w}}^\top {\bf{x}} + b)\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{u}}\in \mathbb{R}^D$ , ${\bf{w}}\in \mathbb{R}^D$ and $b\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The RadialFlow function is defined as
\[f({\bf{x}}) = {\bf{x}} + \frac{\beta({bf{z}} - {\bf{z}}_0)}{\alpha + |{\bf{z}} - {\bf{z}}_0|}\]
with input and output dimension $D$ . Here ${\bf{x}}\in \mathbb{R}^D$ represents the input of the function. Furthermore ${\bf{z}}_0\in \mathbb{R}^D$ , $\alpha\in \mathbb{R}$ and $\beta\in\mathbb{R}$ represent the parameters of the function. The function contracts and expands the input space.
This function has been introduced in:
Rezende, Danilo, and Shakir Mohamed. "Variational inference with normalizing flows." International conference on machine learning. PMLR, 2015.
source The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) )
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel)
. This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector)
.
Note: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.
source compile()
compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source compile(model::FlowModel, params::Vector)
lets you initialize a model model
with a vector of parameters params
.
Input arguments
model::FlowModel
- a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.params::Vector
- a vector of parameters with which the model should be compiled.Return arguments
::CompiledFlowModel
- a compiled model with set parameters, such that it can be used for processing data.source The additive coupling layer specifies an invertible function ${\bf{y}} = g({\bf{x}})$ following the specific structure (for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ ):
\[ \begin{align}
+ y_1 &= x_1 \\
+ y_2 &= x_2 + f(x_1)
+ \end{align}\]
where $f(\cdot)$ denotes an arbitrary function with mapping $f: \mathbb{R} \rightarrow \mathbb{R}$ . This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as
\[ \begin{align}
+ x_1 &= y_1 \\
+ x_2 &= y_2 - f(y_1)
+ \end{align}\]
The current implementation only allows for the mapping $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ , although this layer can be generalized for arbitrary input dimensions.
AdditiveCouplingLayer(f <: AbstractCouplingFlow)
creates the layer structure with function f
.
Example
f = PlanarFlow()
+layer = AdditiveCouplingLayer(f)
This layer structure has been introduced in:
Dinh, Laurent, David Krueger, and Yoshua Bengio. "Nice: Non-linear independent components estimation." arXiv preprint arXiv:1410.8516 (2014).
source The input layer specifies the input dimension to a flow model.
layer = InputLayer(3)
source The permutation layer specifies an invertible mapping ${\bf{y}} = g({\bf{x}}) = P{\bf{x}}$ where $P$ is a permutation matrix.
source The FlowMeta
structure contains the meta data of the Flow
factor node. More specifically, it contains the model of the Flow
factor node. The FlowMeta
structure can be constructed as FlowMeta(model)
. Make sure that the flow model has been compiled.
The FlowMeta
structure is required for the Flow
factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }
source
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+Factor nodes · ReactiveMP.jl In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.
@node(fformtype, sdtype, interfaces_list)
@node
macro creates a node for a fformtype
type object. To obtain a list of predefined nodes use ?is_predefined_node
.
Arguments
fformtype
: Either an existing type identifier, e.g. Normal
or a function type identifier, e.g. typeof(+)
sdtype
: Either Stochastic
or Deterministic
. Defines the type of the functional relationshipinterfaces_list
: Defines a fixed list of edges of a factor node, by convention the first element should be out
. Example: [ out, mean, variance ]
Note: interfaces_list
must not include names that contain _
symbol in them, as it is reserved to identify joint posteriors around the node object.
Examples
+struct MyNormalDistribution
+ mean :: Float64
+ var :: Float64
+end
+
+@node MyNormalDistribution Stochastic [ out, mean, var ]
+@node typeof(+) Deterministic [ out, in1, in2 ]
List of available nodes
See ?is_predefined_node
.
source GenericFactorNode(functionalform, interfaces)
Generic factor node object that represents a factor node with a given functionalform
and interfaces
.
source FactorNodeLocalMarginal
This object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.
source NodeInterface
NodeInterface
object represents a single node-variable connection.
source IndexedNodeInterface
IndexedNodeInterface
object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.
source messagein(interface)
Returns an inbound messages stream from the given interface.
source messageout(interface)
Returns an outbound messages stream from the given interface.
source tag(interface)
Returns a tag of the interface in the form of Val{ name(interface) }
. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.
source name(interface)
Returns a name of the interface.
source interfaces(fform)
Returns a Val
object with a tuple of interface names for a given factor node type. Returns nothing
for unknown functional form.
source getvariable(interface)
Returns a variable connected to the given interface.
source inputinterfaces(fform)
Similar to interfaces
, but returns a Val
object with a tuple of input interface names for a given factor node type. Returns nothing
for unknown functional form.
source alias_interface(factor_type, index, name)
Converts the given name
to a correct interface name for a given factor node type and index.
source collect_factorisation(nodetype, factorisation)
This function converts given factorisation to a correct internal factorisation representation for a given node.
source collect_pipeline(nodetype, pipeline)
This function converts given pipeline to a correct internal pipeline representation for a factor given node.
source collect_meta(nodetype, meta)
This function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta
in case if meta is nothing
.
See also: default_meta
, FactorNode
source as_node_symbol(type)
Returns a symbol associated with a node type
.
source ReactiveMP.jl
exports the @node
macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:
struct MyNewCustomNode end
+
+@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]
+# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^
+# Node's tag/name Node's type A fixed set of edges
+# Another possible The very first edge (in this example `x`) is considered
+# value is to be the output of the node
+# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`
This expression registers a new node that can be used with the inference engine. Note, however, that the @node
macro does not generate any message passing update rules. These must be defined using the @rule
macro.
We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic
or Stochastic
functional form type.
For example the +
node has the Deterministic
type:
println("Is `+` node deterministic: ", isdeterministic(sdtype(+)))
+println("Is `+` node stochastic: ", isstochastic(sdtype(+)))
Is `+` node deterministic: true
+Is `+` node stochastic: false
On the other hand, the Bernoulli
node has the Stochastic
type:
println("Is `Bernoulli` node deterministic: ", isdeterministic(sdtype(Bernoulli)))
+println("Is `Bernoulli` node stochastic: ", isstochastic(sdtype(Bernoulli)))
Is `Bernoulli` node deterministic: false
+Is `Bernoulli` node stochastic: true
To get an actual instance of the type object we use sdtype
function:
println("sdtype() of `+` node is ", sdtype(+))
+println("sdtype() of `Bernoulli` node is ", sdtype(Bernoulli))
sdtype() of `+` node is Deterministic()
+sdtype() of `Bernoulli` node is Stochastic()
The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node $f$ with three edges: $x$ , $y$ and $z$ :
\[\mu(x) = \int \mu(y) \mu(z) f(x, y, z) \mathrm{d}y \mathrm{d}z\]
Here we see that in the standard setting for the belief-propagation message out of edge $x$ , we need only messages from the edges $y$ and $z$ . In contrast, consider the variational message update rule equation with mean-field assumption:
\[\mu(x) = \exp \int q(y) q(z) \log f(x, y, z) \mathrm{d}y \mathrm{d}z\]
We see that in this setting, we do not need messages $\mu(y)$ and $\mu(z)$ , but only the marginals $q(y)$ and $q(z)$ . The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl
uses so-called DefaultFunctionalDependencies
that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:
DefaultFunctionalDependencies
This functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.
source RequireMessageFunctionalDependencies(specifications::NamedTuple)
+RequireMessageFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the inbound message on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing
is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'inbound' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMarginalFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source RequireMarginalFunctionalDependencies(specifications::NamedTuple)
+RequireMarginalFunctionalDependencies(; specifications...)
The same as DefaultFunctionalDependencies
, but in order to compute a message out of some edge also requires the marginal on the this edge.
The specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing
is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple
directly.
RequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)
+ # ^^^ ^^^
+ # request 'marginal' for 'x' we may do the same for 'τ',
+ # and initialise with `vague(...)` but here we skip initialisation
See also: ReactiveMP.DefaultFunctionalDependencies
, ReactiveMP.RequireMessageFunctionalDependencies
, ReactiveMP.RequireEverythingFunctionalDependencies
source Each factor node has to define the ReactiveMP.is_predefined_node
trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm
singleton as a return object. By default ReactiveMP.is_predefined_node
returns ReactiveMP.UndefinedNodeFunctionalForm
. Objects that do not specify this property correctly cannot be used in model specification.
@node
macro does that automatically
UndefinedNodeFunctionalForm
Trait specification for an object that has not been marked as a factor node with the @node
macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.
See also: ReactiveMP.is_predefined_node
, ReactiveMP.PredefinedNodeFunctionalForm
source AbstractPipelineStage
An abstract type for all custom pipelines stages
source apply_pipeline_stage(stage, factornode, tag, stream)
Applies a given pipeline stage to the stream
argument given factornode
and tag
of an edge.
source EmptyPipelineStage <: AbstractPipelineStage
Dummy empty pipeline stage that does not modify the original pipeline.
source CompositePipelineStage{T} <: AbstractPipelineStage
Composite pipeline stage that consists of multiple inner pipeline stages
source LoggerPipelineStage <: AbstractPipelineStage
Logs all updates from stream
into output
Arguments
output
: (optional), an output stream used to print log statementssource DiscontinuePipelineStage <: AbstractPipelineStage
Applies the discontinue()
operator from Rocket.jl
library to the given pipeline
source AsyncPipelineStage <: AbstractPipelineStage
Applies the async()
operator from Rocket.jl
library to the given pipeline
source ScheduleOnPipelineStage{S} <: AbstractPipelineStage
Applies the schedule_on()
operator from Rocket.jl
library to the given pipeline with a provided scheduler
Arguments
scheduler
: scheduler to schedule updates on. Must be compatible with Rocket.jl
library and schedule_on()
operator.source schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))
Schedules posterior marginal updates for given variables using stage
. By default creates ScheduleOnPipelineStage
with PendingScheduler()
from Rocket.jl
library. Returns a scheduler with release!
method available to release all scheduled updates.
source To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node
or Base.doc(ReactiveMP.is_predefined_node)
.
?ReactiveMP.is_predefined_node
is_predefined_node(object)
Determines if the object
has been marked as a factor node with the @node
macro. Returns either PredefinedNodeFunctionalForm()
or UndefinedNodeFunctionalForm()
.
See also: ReactiveMP.PredefinedNodeFunctionalForm
, ReactiveMP.UndefinedNodeFunctionalForm
Type{<:Uninformative} : Stochastic : out
The Uninformative
has been marked as a valid Stochastic
factor node with the @node
macro with [ out ]
interfaces.
Type{<:Uniform} : Stochastic : out, a (or α, left), b (or β, right)
The Uniform
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α, left), b (or β, right) ]
interfaces.
Type{<:NormalMeanVariance} : Stochastic : out, μ (or mean), v (or var)
The NormalMeanVariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), v (or var) ]
interfaces.
Type{<:NormalMeanPrecision} : Stochastic : out, μ (or mean), τ (or invcov, precision)
The NormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), τ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanCovariance} : Stochastic : out, μ (or mean), Σ (or cov)
The MvNormalMeanCovariance
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Σ (or cov) ]
interfaces.
Type{<:MvNormalMeanPrecision} : Stochastic : out, μ (or mean), Λ (or invcov, precision)
The MvNormalMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), Λ (or invcov, precision) ]
interfaces.
Type{<:MvNormalMeanScalePrecision} : Stochastic : out, μ (or mean), γ (or precision)
The MvNormalMeanScalePrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, μ (or mean), γ (or precision) ]
interfaces.
Type{<:MvNormalWeightedMeanPrecision} : Stochastic : out, ξ (or xi, weightedmean), Λ (or invcov, precision)
The MvNormalWeightedMeanPrecision
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ξ (or xi, weightedmean), Λ (or invcov, precision) ]
interfaces.
Type{<:Gamma} : Stochastic : out, α (or shape), θ (or scale)
The Gamma
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaInverse} : Stochastic : out, α (or shape), θ (or scale)
The GammaInverse
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or shape), θ (or scale) ]
interfaces.
Type{<:GammaShapeRate} : Stochastic : out, α (or a, shape), β (or b, rate)
The GammaShapeRate
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, α (or a, shape), β (or b, rate) ]
interfaces.
Type{<:Beta} : Stochastic : out, a (or α), b (or β)
The Beta
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a (or α), b (or β) ]
interfaces.
Type{<:Categorical} : Stochastic : out, p
The Categorical
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p ]
interfaces.
Type{<:MatrixDirichlet} : Stochastic : out, a
The MatrixDirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Dirichlet} : Stochastic : out, a
The Dirichlet
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, a ]
interfaces.
Type{<:Bernoulli} : Stochastic : out, p (or θ)
The Bernoulli
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, p (or θ) ]
interfaces.
Type{<:GCV} : Stochastic : y, x, z, κ, ω
The GCV
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, z, κ, ω ]
interfaces.
Type{<:Wishart} : Stochastic : out, ν (or df), S (or scale)
The Wishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale) ]
interfaces.
Type{<:InverseWishart} : Stochastic : out, ν (or df), S (or scale, Ψ)
The InverseWishart
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, ν (or df), S (or scale, Ψ) ]
interfaces.
typeof(dot) : Deterministic : out, in1, in2
The typeof(dot)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:softdot} : Stochastic : y, θ (or theta), x, γ (or gamma)
The softdot
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, θ (or theta), x, γ (or gamma) ]
interfaces.
Type{<:Transition} : Stochastic : out, in, a
The Transition
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in, a ]
interfaces.
Type{<:AR} : Stochastic : y (or out), x, θ, γ
The AR
has been marked as a valid Stochastic
factor node with the @node
macro with [ y (or out), x, θ, γ ]
interfaces.
Type{<:BIFM} : Deterministic : out, in, zprev, znext
The BIFM
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in, zprev, znext ]
interfaces.
Type{<:BIFMHelper} : Stochastic : out, in
The BIFMHelper
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Probit} : Stochastic : out, in
The Probit
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:Poisson} : Stochastic : out, l (or λ)
The Poisson
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, l (or λ) ]
interfaces.
Type{<:ContinuousTransition} : Stochastic : y, x, a, W
The ContinuousTransition
has been marked as a valid Stochastic
factor node with the @node
macro with [ y, x, a, W ]
interfaces.
Type{<:HalfNormal} : Stochastic : out, v (or var, σ²)
The HalfNormal
has been marked as a valid Stochastic
factor node with the @node
macro with [ out, v (or var, σ²) ]
interfaces.
Type{<:Flow} : Deterministic : out, in
The Flow
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
typeof(+) : Deterministic : out, in1, in2
The typeof(+)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(-) : Deterministic : out, in1, in2
The typeof(-)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
typeof(*) : Deterministic : out, A, in
The typeof(*)
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, A, in ]
interfaces.
Type{<:AND} : Deterministic : out, in1, in2
The AND
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:OR} : Deterministic : out, in1, in2
The OR
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
Type{<:NOT} : Deterministic : out, in
The NOT
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in ]
interfaces.
Type{<:IMPLY} : Deterministic : out, in1, in2
The IMPLY
has been marked as a valid Deterministic
factor node with the @node
macro with [ out, in1, in2 ]
interfaces.
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+Logical · ReactiveMP.jl AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |
source OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |
source IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |
source NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |
source
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+
+Message update rules · ReactiveMP.jl rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute an outbound message for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out}
or ::Val{:μ}
vconstraint
: Variable constraints for an outbound interface, e.g. Marginalisation
or MomentMatching
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta informationaddons
: Extra addons information__node
: Node referenceFor all available rules, see ReactiveMP.print_rules_table()
.
See also: @rule
, marginalrule
, @marginalrule
source @rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @rule
macro help to define new methods for the rule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Edge
: edge label, usually edge labels are defined with the @node
macroConstrain
: DEPRECATED, please just use the Marginalisation
labelArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.Here are various examples of the @rule
macro usage:
Belief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance
node toward the :μ
edge with the Marginalisation
constraint. Input arguments are m_out
and m_v
, which are the messages from the corresponding edges out
and v
and have the type PointMass
. @rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))
Mean-field message update rule for the NormalMeanVariance
node towards the :μ
edge with the Marginalisation
constraint. Input arguments are q_out
and q_v
, which are the marginals on the corresponding edges out
and v
of type Any
. @rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))
Structured Variational message update rule for the NormalMeanVariance
node towards the :out
edge with the Marginalisation
constraint. Input arguments are m_μ
, which is a message from the μ
edge of type UnivariateNormalDistributionsFamily
, and q_v
, which is a marginal on the v
edge of type Any
. @rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin
+ m_μ_mean, m_μ_cov = mean_cov(m_μ)
+ return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))
+end
See also: rule
, marginalrule
, [@marginalrule
], @call_rule
source @call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The @call_rule
macro helps to call the rule
method with an easier syntax. The structure of the macro is almost the same as in the @rule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
The @call_rule
accepts optional list of options before the functional form specification, for example:
@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])
The list of available options is:
return_addons
- forces the @call_rule
to return the tuple of (result, addons)
fallback
- specifies the fallback rule to use in case the rule is not defined for the given NodeType
and specified argumentsSee also: @rule
, rule
, @call_marginalrule
source call_rule_create_node(::Type{ NodeType }, fformtype)
Creates a node object that will be used inside @call_rule
macro.
source call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message and marginal calling rules specification.
@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values
See also: @rule
source call_rule_is_node_required(fformtype)
Returns either CallRuleNodeRequired()
or CallRuleNodeNotRequired()
depending on if a specific fformtype
requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired()
for all known functional forms by default and CallRuleNodeRequired()
for all unknown functional forms.
source rule_macro_parse_on_tag(expression)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an on
tag for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin
+ ^^^^
+ `on` tag
+ ...
+end
or
@rule NormalMixture((:m, k), Marginalisation) (...) = begin
+ ^^^^^^^
+ `on` tag
+ ...
+end
Accepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.
See also: @rule
source rule_macro_parse_fn_args(inputs; specname, prefix, proxy)
Do not use this function directly. This function is private and does not belong to the public API.
This function is used to parse an arguments
tuple for message rules and marginal rules specification.
@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ `arguments` vector
+ ...
+end
Accepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.
See also: @rule
source rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)
This function checks if all inputs
are either in the allowed_inputs
or have prefixes in the allowed_prefixes
.
See also: @rule
source marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)
This function is used to compute a local joint marginal for a given node
Arguments
fform
: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance }
or ::typeof(+)
on
: Local joint marginal tag , e.g. ::Val{ :mean_precision }
or ::Val{ :out_mean_precision }
mnames
: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }
messages
: Tuple of message of the same length as mnames
used to compute an outbound messageqnames
: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }
marginals
: Tuple of marginals of the same length as qnames
used to compute an outbound messagemeta
: Extra meta information__node
: Node referenceSee also: rule
, @rule
@marginalrule
source @marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin
+ # rule body
+ return ...
+end
The @marginalrule
macro help to define new methods for the marginalrule
function. It works particularly well in combination with the @node
macro. It has a specific structure, which must specify:
NodeType
: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +
), use typeof(+)
Cluster
: edge cluster that contains joined edge labels with the _
symbol. Usually edge labels are defined with the @node
macroArguments
: defines a list of the input arguments for the rulem_*
prefix indicates that the argument is of type Message
from the edge *
q_*
prefix indicates that the argument is of type Marginal
on the edge *
Meta::MetaType
- optionally, a user can specify a Meta
object of type MetaType
. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing
.The @marginalrule
can return a NamedTuple
in the return
statement. This would indicate some variables in the joint marginal for the Cluster
are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y)
it is possible to return (x = ..., y = ...)
as the result of the computation to indicate that q(x, y) = q(x)q(y)
.
Here are various examples of the @marginalrule
macro usage:
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
.
@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ xi_out, W_out = weightedmean_precision(m_out)
+ xi_μ, W_μ = weightedmean_precision(m_μ)
+
+ W_bar = mean(q_τ)
+
+ W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]
+ xi = [xi_out; xi_μ]
+
+ return MvNormalWeightedMeanPrecision(xi, W)
+end
Marginal computation rule around the NormalMeanPrecision
node for the q(out, μ)
. The rule accepts arguments m_out
and m_μ
, which are the messages from the out
and μ
edges respectively, and q_τ
which is the marginal on the edge τ
. In this example the result of the computation is a NamedTuple
@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin
+ return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))
+end
source @call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])
The @call_marginalrule
macro helps to call the marginalrule
method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule
macro, but there is no begin ... end
block, but instead each argument must have a specified value with the =
operator.
See also: @marginalrule
, marginalrule
, @call_rule
source @test_rules [options] rule [ test_entries... ]
The @test_rules
macro generates test cases for message update rules for probabilistic programming models that follow the "message passing" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP
.
Note: The Test
module must be imported explicitly. The @test_rules
macro tries to use the @test
macro, which must be defined globally.
Arguments
The macro takes three arguments:
options
: An optional argument that specifies the options for the test generation process. See below for details.rule
: A rule specification in the same format as the @rule
macro, e.g. Beta(:out, Marginalisation)
or NormalMeanVariance(:μ, Marginalisation)
.test_entries
: An array of named tuples (input = ..., output = ...)
. The input
entry has the same format as the input for the @rule
macro. The output
entry specifies the expected output.Options
The following options are available:
check_type_promotion
: By default, this option is set to false
. If set to true
, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32
, then the expected output should also be of type Float32
. See the paramfloattype
and convert_paramfloattype
functions for details.atol
: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox
function from ReactiveMP
to check if outputs are approximately the same. This argument can be either a single number or an array of key => value
pairs.extra_float_types
: A set of extra float types to be used in the check_type_promotion
tests. This argument has no effect if check_type_promotion
is set to false
.The default values for the atol
option are:
Float32
: 1e-4
Float64
: 1e-6
BigFloat
: 1e-8
Examples
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
+
+@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [
+ (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),
+ (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),
+ (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))
+]
See also: ReactiveMP.@test_marginalrules
source @test_marginalrules [options] rule [ test_entries... ]
Effectively the same as @test_rules
, but for marginal computation rules. See the documentation for @test_rules
for more info.
See also: ReactiveMP.@test_rules
source NodeFunctionRuleFallback(extractfn = mean)
A fallback rule for Stochastic
nodes that uses a specified function (default: mean) to transform messages and marginals into a value. It calls the nodefunction
method to create the message.
When a node is defined with the @node
macro:
1. The nodefunction
typically calls logpdf
associated with the node's distribution. 2. The first edge in the @node
specification is used to evaluate logpdf
at. 3. Other edges are used to instantiate the associated distribution object.
julia> using ReactiveMP, BayesBase, Distributions
+
+julia> struct MyBeta{A, B} <: ContinuousUnivariateDistribution
+ a::A
+ b::B
+ end
+
+julia> BayesBase.logpdf(d::MyBeta, x) = logpdf(Beta(d.a, d.b), x)
+
+julia> BayesBase.insupport(d::MyBeta, x::Real) = true
+
+julia> @node MyBeta Stochastic [out, a, b]
+
+julia> message = @call_rule [fallback = NodeFunctionRuleFallback()] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2));
+
+julia> logpdf(message, 0.5)
+-0.5017644952110732
+
+julia> message = @call_rule [fallback = NodeFunctionRuleFallback(mode)] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2)); # evaluate at `mode`
+
+julia> logpdf(message, 0.5)
+-0.5954237415153454
source nodefunction(::Type{T}) where {T}
Returns a function that represents a node of type T
. The function typically takes arguments that represent the node's input and output variables in the same order as defined in the @node
macro.
source The list below has been automatically generated with the ReactiveMP.print_rules_table()
function.
Node Output Inputs Meta dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot in2 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in1) :: BayesBase.PointMass dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T dot out μ(in1) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + out μ(in1) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + out μ(in1) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + out μ(in1) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + out μ(in1) :: Distributions.Distribution Nothing μ(in2) :: Distributions.Distribution + in2 μ(out) :: Any μ(in1) :: Any - in2 μ(out) :: Any μ(in1) :: Any - in1 μ(out) :: Any μ(in2) :: Any - out μ(in1) :: Any μ(in2) :: Any + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T1, M, P} where {M<:AbstractVector{T1}, P<:AbstractMatrix{T1}} Nothing μ(in2) :: ExponentialFamily.MvNormalWeightedMeanPrecision{T2, M, P} where {M<:AbstractVector{T2}, P<:AbstractMatrix{T2}} + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: ExponentialFamily.MvNormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.MvNormalMeanPrecision + in1 μ(out) :: ExponentialFamily.NormalMeanPrecision Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: ExponentialFamily.NormalMeanPrecision + in1 μ(out) :: BayesBase.PointMass Nothing μ(in2) :: BayesBase.PointMass + in1 μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T + in1 μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(in2) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Distributions.UnivariateDistribution * in μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * in μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass * in μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:Real} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractMatrix} * in μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(A) :: BayesBase.PointMass{<:AbstractVector} * in μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * in μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: BayesBase.PointMass{<:Real} * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanPrecision * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: ExponentialFamily.MvNormalMeanCovariance * in μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass{<:LinearAlgebra.UniformScaling} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanPrecision * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.MvNormalMeanCovariance * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * out μ(A) :: BayesBase.PointMass{<:Real} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: ExponentialFamily.GammaDistributionsFamily * out μ(A) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * out μ(A) :: BayesBase.PointMass{<:AbstractMatrix} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: F * out μ(A) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * out μ(A) :: BayesBase.PointMass{<:AbstractVector} Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * out μ(A) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: Distributions.UnivariateDistribution Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Distributions.UnivariateDistribution * A μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T * A μ(out) :: BayesBase.PointMass Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass * A μ(out) :: ExponentialFamily.GammaDistributionsFamily Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} * A μ(out) :: F Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:Real} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractMatrix} * A μ(out) :: ExponentialFamily.MvNormalMeanCovariance Union{Nothing, MatrixCorrectionTools.AbstractCorrectionStrategy} μ(in) :: BayesBase.PointMass{<:AbstractVector} Transition in q(out) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition in q(out) :: Any Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real q(a) :: BayesBase.PointMass Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: ExponentialFamily.MatrixDirichlet Transition in μ(out) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.DiscreteNonParametric q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Distributions.Distribution{Distributions.Matrixvariate, Distributions.Continuous} Transition out q(in) :: Distributions.Categorical{P} where P<:Real Nothing q(a) :: Any Transition out q(in) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Transition out μ(in) :: Distributions.Categorical{P} where P<:Real Nothing μ(a) :: BayesBase.PointMass Transition a q(out_in) :: BayesBase.Contingency Nothing Transition a q(out) :: Any Nothing q(in) :: Distributions.Categorical{P} where P<:Real Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Beta out μ(a) :: BayesBase.PointMass Nothing μ(b) :: BayesBase.PointMass Distributions.Uniform out μ(b) :: BayesBase.PointMass Nothing q(a) :: BayesBase.PointMass Distributions.Uniform out μ(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Uniform out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Beta out q(a) :: BayesBase.PointMass Nothing q(b) :: BayesBase.PointMass Distributions.Dirichlet out q(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out q(a) :: BayesBase.PointMass Nothing Distributions.Dirichlet out μ(a) :: BayesBase.PointMass{<:AbstractVector} Nothing ExponentialFamily.MatrixDirichlet out μ(a) :: BayesBase.PointMass Nothing HalfNormal out q(v) :: BayesBase.PointMass Nothing ExponentialFamily.NormalMeanVariance v q(out_μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing ExponentialFamily.NormalMeanVariance v q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance v μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(μ) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance v μ(out) :: BayesBase.PointMass Nothing μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out q(μ) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out q(μ) :: Any Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance out μ(μ) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(v) :: Any ExponentialFamily.NormalMeanVariance μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: BayesBase.PointMass Nothing μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: BayesBase.PointMass Nothing q(v) :: BayesBase.PointMass ExponentialFamily.NormalMeanVariance μ q(out) :: Any Nothing q(v) :: Any ContinuousTransition W q(y) :: Any ContinuousTransitionMeta q(x) :: Any q(a) :: Any ContinuousTransition W q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransition a q(y) :: Any ContinuousTransitionMeta q(x) :: Any q(a) :: Any q(W) :: Any ContinuousTransition a q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition x q(y) :: Any ContinuousTransitionMeta q(a) :: Any q(W) :: Any ContinuousTransition x μ(y) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any ContinuousTransition y q(x) :: Any ContinuousTransitionMeta q(a) :: Any q(W) :: Any ContinuousTransition y μ(x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ContinuousTransitionMeta q(a) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T q(W) :: Any Mixture switch μ(out) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture out μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Nothing q(switch) :: BayesBase.PointMass Mixture out μ(switch) :: Any Nothing μ(inputs) :: ManyOf{<:Tuple{Vararg{Any, N}}} Mixture inputs μ(out) :: Any Nothing q(switch) :: BayesBase.PointMass Mixture inputs μ(out) :: Any Nothing μ(switch) :: Any NormalMixture{N} out q(switch) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} NormalMixture p q(out) :: Any Nothing q(switch) :: Any q(m) :: Any NormalMixture m q(out) :: Any Nothing q(switch) :: Any q(p) :: Any NormalMixture{N} switch q(out) :: Any Nothing q(m) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(p) :: ManyOf{<:Tuple{Vararg{Any, N}}} AND out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli AND in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli OR in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli AND in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli OR in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli Probit out μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} Probit out μ(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} NOT out μ(in) :: Distributions.Bernoulli Nothing Probit out q(in) :: BayesBase.PointMass Union{Nothing, ProbitMeta} BIFMHelper out q(in) :: Any Nothing Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Probit in μ(in) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Union{Nothing, ProbitMeta} q(out) :: BayesBase.PointMass Probit in μ(out) :: Union{BayesBase.PointMass, Distributions.Bernoulli} Union{Nothing, ProbitMeta} BIFMHelper in μ(out) :: Any Nothing NOT in μ(out) :: Distributions.Bernoulli Nothing Probit in q(out) :: BayesBase.PointMass Union{Nothing, ProbitMeta} ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out q(μ) :: Any Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision τ q(out_μ) :: Any Nothing ExponentialFamily.NormalMeanPrecision τ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic q(τ) :: Any ExponentialFamily.NormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ μ(out) :: ReactiveMP.ExponentialLinearQuadratic μ(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(τ) :: BayesBase.PointMass ExponentialFamily.NormalMeanPrecision μ q(out) :: Any Nothing q(τ) :: Any GCV ω q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(κ) :: Any GCV ω q(y_x) :: Any GCVMetadata q(z) :: Any q(κ) :: Any GCV x q(y) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV x μ(y) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y q(x) :: Any Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV y μ(x) :: Union{ReactiveMP.ExponentialLinearQuadratic, ExponentialFamily.UnivariateNormalDistributionsFamily, ExponentialFamily.UnivariateGaussianDistributionsFamily} Union{Nothing, GCVMetadata} q(z) :: Any q(κ) :: Any q(ω) :: Any GCV κ q(y) :: Any GCVMetadata q(x) :: Any q(z) :: Any q(ω) :: Any GCV κ q(y_x) :: Any GCVMetadata q(z) :: Any q(ω) :: Any GCV z q(y) :: Any GCVMetadata q(x) :: Any q(κ) :: Any q(ω) :: Any GCV z q(y_x) :: Any GCVMetadata q(κ) :: Any q(ω) :: Any ExponentialFamily.MvNormalMeanPrecision Λ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanPrecision Λ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out q(μ) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out q(μ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision out μ(μ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Distributions.Wishart ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ q(out) :: BayesBase.PointMass Nothing q(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ q(out) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Λ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanPrecision μ μ(out) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass Distributions.InverseGamma out q(α) :: Any Nothing q(θ) :: Any Distributions.Gamma out q(α) :: Any Nothing q(θ) :: Any Distributions.InverseGamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass Distributions.Gamma out μ(α) :: BayesBase.PointMass Nothing μ(θ) :: BayesBase.PointMass SoftDot γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(θ) :: Any SoftDot γ q(y) :: Any Nothing q(θ) :: Any q(x) :: Any SoftDot x μ(y) :: Union{ExponentialFamily.UnivariateNormalDistributionsFamily{T}, ExponentialFamily.UnivariateGaussianDistributionsFamily{T}} where T Nothing q(θ) :: Any q(γ) :: Any SoftDot x q(y) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y μ(x) :: Any Nothing q(θ) :: Any q(γ) :: Any SoftDot y q(θ) :: Any Nothing q(x) :: Any q(γ) :: Any SoftDot θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any SoftDot θ q(y) :: Any Nothing q(x) :: Any q(γ) :: Any MvNormalMeanScalePrecision γ q(out_μ) :: Any Nothing MvNormalMeanScalePrecision γ q(out) :: Any Nothing q(μ) :: Any MvNormalMeanScalePrecision μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision μ q(out) :: Any Nothing q(γ) :: Any MvNormalMeanScalePrecision out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(γ) :: Any MvNormalMeanScalePrecision out q(μ) :: Any Nothing q(γ) :: Any GammaMixture{N} out q(switch) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture b q(out) :: Any Nothing q(switch) :: Any q(a) :: Any GammaMixture a q(out) :: Any Nothing q(switch) :: Any q(b) :: ExponentialFamily.GammaDistributionsFamily GammaMixture{N} switch q(out) :: Any Nothing q(a) :: ManyOf{<:Tuple{Vararg{Any, N}}} q(b) :: ExponentialFamily.GammaDistributionsFamily Distributions.Wishart out q(ν) :: Any Nothing q(S) :: Any InverseWishart out q(ν) :: Any Nothing q(S) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any InverseWishart out μ(ν) :: BayesBase.PointMass Nothing q(S) :: Any Distributions.Wishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any InverseWishart out μ(S) :: BayesBase.PointMass Nothing q(ν) :: Any Distributions.Wishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass InverseWishart out μ(ν) :: BayesBase.PointMass Nothing μ(S) :: BayesBase.PointMass Distributions.Bernoulli out q(p) :: Any Nothing Distributions.Bernoulli out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out q(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli out μ(p) :: BayesBase.PointMass Nothing Distributions.Bernoulli out μ(p) :: Distributions.Beta Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real out μ(p) :: Distributions.Dirichlet Nothing Distributions.Bernoulli p q(out) :: Distributions.Categorical{P} where P<:Real Nothing Distributions.Bernoulli p q(out) :: Distributions.Bernoulli Nothing Distributions.Bernoulli p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: BayesBase.PointMass Nothing Distributions.Categorical{P} where P<:Real p q(out) :: Any Nothing Distributions.Bernoulli p μ(out) :: BayesBase.PointMass Nothing Poisson out q(l) :: ExponentialFamily.GammaDistributionsFamily Nothing Poisson out μ(l) :: BayesBase.PointMass Nothing Poisson l q(out) :: Any Nothing Poisson l μ(out) :: BayesBase.PointMass Nothing AR γ q(y) :: Any ARMeta q(x) :: Any q(θ) :: Any AR γ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T AR x q(y) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR x μ(y) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR y q(x) :: Any ARMeta q(θ) :: Any q(γ) :: Any AR y μ(x) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T ARMeta q(θ) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T q(γ) :: Any AR θ q(y) :: Any ARMeta q(x) :: Any q(γ) :: Any AR θ q(y_x) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ARMeta q(γ) :: Any ExponentialFamily.GammaShapeRate β q(out) :: Any Nothing q(α) :: Any ExponentialFamily.GammaShapeRate α q(out) :: Any Nothing q(β) :: ExponentialFamily.GammaDistributionsFamily ExponentialFamily.GammaShapeRate out q(α) :: Any Nothing q(β) :: Any ExponentialFamily.GammaShapeRate out μ(α) :: BayesBase.PointMass Nothing μ(β) :: BayesBase.PointMass DeltaFn in μ(in) :: Any DeltaMeta{M} q(ins) :: BayesBase.FactorizedJoint DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, Nothing} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(in) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} q(ins) :: ExponentialFamily.JointNormal DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Nothing DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn in μ(out) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M, I} μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaFn out q(ins) :: BayesBase.FactorizedJoint{P} DeltaMeta{M} DeltaFn out q(ins) :: BayesBase.FactorizedJoint DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} DeltaFn out μ(ins) :: Union{ExponentialFamily.NormalDistributionsFamily{T}, ExponentialFamily.GaussianDistributionsFamily{T}} where T DeltaMeta{M} BIFM zprev μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM znext μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} BIFM out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFM in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T BIFMMeta μ(zprev) :: BayesBase.TerminalProdArgument{<:Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T} μ(znext) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out q(μ) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out q(μ) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance out μ(μ) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance Σ q(out_μ) :: Any Nothing ExponentialFamily.MvNormalMeanCovariance Σ q(out) :: Any Nothing q(μ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ q(out) :: BayesBase.PointMass Nothing q(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ q(out) :: Any Nothing q(Σ) :: Any ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T Nothing μ(Σ) :: BayesBase.PointMass ExponentialFamily.MvNormalMeanCovariance μ μ(out) :: BayesBase.PointMass Nothing μ(Σ) :: BayesBase.PointMass Flow in μ(out) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow in μ(out) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow in μ(out) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} Flow out μ(in) :: Union{ExponentialFamily.MultivariateNormalDistributionsFamily{T}, ExponentialFamily.MultivariateGaussianDistributionsFamily{T}} where T FlowMeta{M, <:Unscented} Flow out μ(in) :: ExponentialFamily.MvNormalWeightedMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanPrecision FlowMeta{M, <:Linearization} Flow out μ(in) :: ExponentialFamily.MvNormalMeanCovariance FlowMeta{M, <:Linearization} ExponentialFamily.MvNormalWeightedMeanPrecision out q(ξ) :: Any Nothing q(Λ) :: Any ExponentialFamily.MvNormalWeightedMeanPrecision out μ(ξ) :: BayesBase.PointMass Nothing μ(Λ) :: BayesBase.PointMass out μ(in1) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli in2 μ(out) :: Distributions.Bernoulli Nothing μ(in1) :: Distributions.Bernoulli in1 μ(out) :: Distributions.Bernoulli Nothing μ(in2) :: Distributions.Bernoulli
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This document was generated with Documenter.jl version 1.5.0 on Friday 19 July 2024 . Using Julia version 1.10.4.
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+var documenterSearchIndex = {"docs":
+[{"location":"lib/message/#lib-message","page":"Messages","title":"Messages implementation","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In the message passing framework, one of the most important concepts is the message. Given a factor graph, messages are arbitrary functions that flow along the edges of the graph and hold information about the part of the graph from which they originate.","category":"page"},{"location":"lib/message/#lib-messages-as-distributions","page":"Messages","title":"Message as a distribution","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"Often, a message can be represented in the form of a probability distribution, as a probability distribution can be matched with its probability density function. The representation of messages as probability distributions is not only for convenience but also for performance reasons. For example, a univariate Gaussian distribution can be parameterized with two numbers, which significantly reduce the amount of information needed to pass along the edges of the graph.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using StatsPlots, Distributions\n\nplot(Normal(0.0, 1.0), label = \"Univariate Gaussian distribution\", fillalpha = 0.4, fill = 0)","category":"page"},{"location":"lib/message/#lib-message-vmp","page":"Messages","title":"Variational Message Passing","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"The message passing technique is useful for finding the posterior distribution over certain parameters in a model, originating from exact Bayesian inference, which is also known as Belief Propagation. However, the message passing technique can also be used to find approximate solutions to posteriors - a technique known as Variational inference. The ReactiveMP.jl package implements Variational Message Passing since it is a more general form than exact inference, and also because the exact solution can be framed as an approximate solution subject to no constraints. Here are visual schematics of the differences between messages in Belief propagation and Variational inference.","category":"page"},{"location":"lib/message/#lib-belief-propagation-message","page":"Messages","title":"Belief-Propagation (or Sum-Product) message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Belief propagation message","category":"page"},{"location":"lib/message/#lib-variational-message","page":"Messages","title":"Variational message","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"(Image: message) Variational message with structured factorisation q(x, y)q(z) assumption","category":"page"},{"location":"lib/message/#Message-type","page":"Messages","title":"Message type","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"All messages are encoded with the type Message. ","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"AbstractMessage\nMessage","category":"page"},{"location":"lib/message/#ReactiveMP.AbstractMessage","page":"Messages","title":"ReactiveMP.AbstractMessage","text":"An abstract supertype for all concrete message types.\n\n\n\n\n\n","category":"type"},{"location":"lib/message/#ReactiveMP.Message","page":"Messages","title":"ReactiveMP.Message","text":"Message(data, is_clamped, is_initial, addons)\n\nAn implementation of a message in variational message passing framework.\n\nArguments\n\ndata::D: message always holds some data object associated with it, which is usually a probability distribution, but can also be an arbitrary function\nis_clamped::Bool, specifies if this message was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this message was used for initialization\naddons::A, specifies the addons of the message, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Message(distribution, false, true, nothing)\nMessage(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n\n","category":"type"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"From an implementation point a view the Message structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. Our implementation also uses extra is_initial and is_clamped fields to determine if product of two messages results in is_initial or is_clamped posterior marginal. The final field contains the addons. These contain additional information on top of the functional form of the distribution, such as its scaling or computation history.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.getdata(message::Message)\nReactiveMP.is_clamped(message::Message)\nReactiveMP.is_initial(message::Message)\nReactiveMP.getaddons(message::Message)\nReactiveMP.as_message","category":"page"},{"location":"lib/message/#ReactiveMP.getdata-Tuple{Message}","page":"Messages","title":"ReactiveMP.getdata","text":"getdata(message::Message)\n\nReturns data associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_clamped-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_clamped","text":"is_clamped(message::Message)\n\nChecks if message is clamped or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.is_initial-Tuple{Message}","page":"Messages","title":"ReactiveMP.is_initial","text":"is_initial(message::Message)\n\nChecks if message is initial or not.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.getaddons-Tuple{Message}","page":"Messages","title":"ReactiveMP.getaddons","text":"getaddons(message::Message)\n\nReturns addons associated with the message.\n\n\n\n\n\n","category":"method"},{"location":"lib/message/#ReactiveMP.as_message","page":"Messages","title":"ReactiveMP.as_message","text":"as_message(::AbstractMessage)\n\nA function that converts an abstract message to an instance of Message.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmessage = Message(distribution, false, true, nothing)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"mean(message), precision(message)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"logpdf(message, 1.0)","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"is_clamped(message), is_initial(message)","category":"page"},{"location":"lib/message/#lib-messages-product","page":"Messages","title":"Product of messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"In message passing framework, in order to compute a posterior we must compute a normalized product of two messages. For this purpose the ReactiveMP.jl uses the multiply_messages function, which internally uses the prod function defined in BayesBase.jl with various product strategies. We refer an interested reader to the documentation of the BayesBase.jl package for more information.","category":"page"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.multiply_messages\nReactiveMP.messages_prod_fn","category":"page"},{"location":"lib/message/#ReactiveMP.multiply_messages","page":"Messages","title":"ReactiveMP.multiply_messages","text":"multiply_messages(prod_strategy, left::Message, right::Message)\n\nMultiplies two messages left and right using a given product strategy prod_strategy. Returns a new message with the result of the multiplication. Note that the resulting message is not necessarily normalized.\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#ReactiveMP.messages_prod_fn","page":"Messages","title":"ReactiveMP.messages_prod_fn","text":"messages_prod_fn(strategy, prod_constraint, form_constraint, form_check_strategy)\n\nReturns a suitable prod computation function for a given strategy and constraints\n\n\n\n\n\n","category":"function"},{"location":"lib/message/#lib-messages-deffered","page":"Messages","title":"Deffered messages","text":"","category":"section"},{"location":"lib/message/","page":"Messages","title":"Messages","text":"ReactiveMP.DefferedMessage","category":"page"},{"location":"lib/message/#ReactiveMP.DefferedMessage","page":"Messages","title":"ReactiveMP.DefferedMessage","text":"A special type of a message, for which the actual message is not computed immediately, but is computed later on demand (potentially never). To compute and get the actual message, one needs to call the as_message method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ar/#lib-nodes-ar","page":"Autoregressive","title":"Autoregressive node","text":"","category":"section"},{"location":"lib/nodes/ar/","page":"Autoregressive","title":"Autoregressive","text":"ReactiveMP.ar_unit\nReactiveMP.ar_slice","category":"page"},{"location":"lib/nodes/ar/#ReactiveMP.ar_unit","page":"Autoregressive","title":"ReactiveMP.ar_unit","text":"ar_unit(::T, order)\n\nReturns [ 1.0, 0.0 ... 0.0 ] with length equal to order in case if T is Multivariate, and 1.0 in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/ar/#ReactiveMP.ar_slice","page":"Autoregressive","title":"ReactiveMP.ar_slice","text":"ar_slice(::T, array, ranges...)\n\nReturns array[ranges...] in case if T is Multivariate, and first(array[ranges...]) in case if T is Univariate\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#lib-nodes-delta","page":"Delta","title":"Delta node","text":"","category":"section"},{"location":"lib/nodes/delta/","page":"Delta","title":"Delta","text":"ReactiveMP.DeltaMeta\nReactiveMP.ManyOf\nReactiveMP.Linearization\nReactiveMP.local_linearization\nReactiveMP.smoothRTS\nReactiveMP.Unscented\nReactiveMP.sigma_points_weights\nReactiveMP.CVIApproximationDeltaFnRuleLayout\nReactiveMP.log_approximate\nReactiveMP.ForwardDiffGrad\nReactiveMP.UT\nReactiveMP.UnscentedTransform\nReactiveMP.ProdCVI\nReactiveMP.CVI\nReactiveMP.CVIProjection\nReactiveMP.cvi_setup!\nReactiveMP.cvi_update!\nReactiveMP.DeltaFnDefaultRuleLayout\nReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","category":"page"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaMeta","page":"Delta","title":"ReactiveMP.DeltaMeta","text":"DeltaMeta(method = ..., [ inverse = ... ])\n\nDeltaMeta structure specifies the approximation method for the outbound messages in the DeltaFn node. \n\nArguments\n\nmethod: required, the approximation method, currently supported methods are Linearization, Unscented and CVI.\ninverse: optional, if no inverse provided, the backward rule will be computed based on RTS (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\nIs is also possible to pass the AbstractApproximationMethod to the meta of the delta node directly. In this case inverse is set to nothing.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ManyOf","page":"Delta","title":"ReactiveMP.ManyOf","text":"Some nodes use IndexedInterface, ManyOf structure reflects a collection of marginals from the collection of IndexedInterfaces. @rule macro also treats ManyOf specially.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.Linearization","page":"Delta","title":"ReactiveMP.Linearization","text":"The Linearization structure defines the approximation method of the Delta and Flow factor nodes. This method performs a local linearization of f around expansion point x.\n\nThe Linearization structure with default parameters can be constructed as Linearization().\n\nThe Linearization structure is used inside the DeltaMeta or FlowMeta structures and can be included as:\n\n y ~ f(x) where { meta = DeltaMeta(method = Linearization()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Linearization()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.local_linearization","page":"Delta","title":"ReactiveMP.local_linearization","text":"local_linearization(g, x)\n\nReturns linear components (a, b) for the function g at the point x.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.smoothRTS","page":"Delta","title":"ReactiveMP.smoothRTS","text":"RTS smoother update for inbound marginal; based on (Petersen et al. 2018; On Approximate Delta Gaussian Message Passing on Factor Graphs)\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.Unscented","page":"Delta","title":"ReactiveMP.Unscented","text":"The Unscented structure defines the approximation method of the Delta and Flow factor nodes. More specifically, it contains the hyperparameters used for sigma points computation.\n\nArguments\n\nα: Spread parameter for unscented transform #1\nβ: Algorithm parameter for incorporating prior information on the (non-Gaussian) distribution of Delta node input\nκ: Spread parameter for unscented transform #2\ne: Internal cache\n\nThe Unscented structure with default parameters can be constructed as Unscented().\n\nThe Unscented structure is used inside the DeltaMeta or FlowMeta structure and can be included as: \n\n y ~ f(x) where { meta = DeltaMeta(method = Unscented()) }\n # or\n y ~ Flow(x) where { meta = FlowMeta(flowmodel, Unscented()) }\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.sigma_points_weights","page":"Delta","title":"ReactiveMP.sigma_points_weights","text":"Return the sigma points and weights for a Gaussian distribution\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.CVIApproximationDeltaFnRuleLayout","page":"Delta","title":"ReactiveMP.CVIApproximationDeltaFnRuleLayout","text":"CVIApproximationDeltaFnRuleLayout\n\nCustom rule layout for the Delta node in case of the CVI approximation method:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses the joint over the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.log_approximate","page":"Delta","title":"ReactiveMP.log_approximate","text":"This function calculates the log of the Gauss-laguerre integral by making use of the log of the integrable function. ln ( ∫ exp(-x)f(x) dx ) ≈ ln ( ∑ wi * f(xi) ) = ln ( ∑ exp( ln(wi) + logf(xi) ) ) = ln ( ∑ exp( yi ) ) = max(yi) + ln ( ∑ exp( yi - max(yi) ) ) where we make use of the numerically stable log-sum-exp trick: https://en.wikipedia.org/wiki/LogSumExp\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.ForwardDiffGrad","page":"Delta","title":"ReactiveMP.ForwardDiffGrad","text":"ForwardDiffGrad(chunk_size::Int)\n\nThe auto-differentiation backend for the CVI procedure. Uses the ForwardDiff library to compute gradients/derivatives. If chunk_size is not specified then uses the heuristic from ForwardDiff, which is type-unstable.\n\nnote: Note\nThe ForwardDiff.jl must be added to the current Julia environment.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UT","page":"Delta","title":"ReactiveMP.UT","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.UnscentedTransform","page":"Delta","title":"ReactiveMP.UnscentedTransform","text":"An alias for the Unscented approximation method.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.ProdCVI","page":"Delta","title":"ReactiveMP.ProdCVI","text":"ProdCVI\n\nThe ProdCVI structure defines the approximation method hyperparameters of the prod(approximation::CVI, logp::F, dist). This method performs an approximation of the product of the dist and logp with Stochastic Variational message passing (SVMP-CVI) (See Probabilistic programming with stochastic variational message passing).\n\nnote: Note\nProdCVI is deprecated in favor of CVIProjection.\n\nArguments\n\nrng: random number generator\nn_samples: number of samples to use for statistics approximation\nn_iterations: number of iteration for the natural parameters gradient optimization\nopt: optimizer, which will be used to perform the natural parameters gradient optimization step\ngrad: optional, defaults to ForwardDiffGrad(), structure to select how the gradient and the hessian will be computed\nn_gradpoints: optional, defaults to 1, number of points to estimate gradient of the likelihood (dist*logp)\nenforce_proper_messages: optional, defaults to true, ensures that a message, computed towards the inbound edges, is a proper distribution, must be of type Val(true)/Val(false)\nwarn: optional, defaults to true, enables or disables warnings related to the optimization steps\n\nnote: Note\nn_gradpoints option is ignored in the Gaussian case\n\nnote: Note\nAdding the Optimisers.jl in your Julia environment enables additional optimizers from the Optimisers.jl for the CVI approximation method. Adding the DiffResults in your Julia environment enables faster gradient computations in case if all inputs are of the Gaussian type.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVI","page":"Delta","title":"ReactiveMP.CVI","text":"Alias for the ProdCVI method. See help for ProdCVI\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.CVIProjection","page":"Delta","title":"ReactiveMP.CVIProjection","text":"CVIProjection(; parameters...)\n\nA structure representing the parameters for the Conjugate Variational Inference (CVI) projection method. This structure is a subtype of AbstractApproximationMethod and is used to configure the settings for CVI.\n\nnote: Note\nThe CVIProjection method requires ExponentialFamilyProjection package installed in the current environment.\n\nParameters\n\nrng::R: The random number generator used for sampling. Default is Random.MersenneTwister(42).\nmarginalsamples::S: The number of samples used for approximating marginal distributions. Default is 10.\noutsamples::S: The number of samples used for approximating output message distributions. Default is 100.\nprjparams::P: Parameters for the exponential family projection. Default is nothing, in which case it will use ExponentialFamilyProjection.DefaultProjectionParameters().\n\nnote: Note\nThe CVIProjection method is an experimental enhancement of the now-deprecated CVI, offering better stability and improved accuracy. Note that the parameters of this structure, as well as their defaults, are subject to change during the experimentation phase.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_setup!","page":"Delta","title":"ReactiveMP.cvi_setup!","text":"cvi_setup!(opt, λ)\n\nInitialises the given optimiser for the CVI procedure given the structure of λ. Returns a tuple of the optimiser and the optimiser state.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.cvi_update!","page":"Delta","title":"ReactiveMP.cvi_update!","text":"cvi_update!(tuple_of_opt_and_state, new_λ, λ, ∇)\n\nUses the optimiser, its state and the gradient ∇ to change the trainable parameters in the λ. Modifies the optimiser state and and store the output in the newλ. Returns a tuple of the optimiser and the newλ.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultRuleLayout","text":"DeltaFnDefaultRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges\nm_out: uses all inbound messages on the ins edges\nm_in_k: uses the inbound message on the in_k edge and q_ins\n\nSee also: ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/delta/#ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","page":"Delta","title":"ReactiveMP.DeltaFnDefaultKnownInverseRuleLayout","text":"DeltaFnDefaultKnownInverseRuleLayout\n\nDefault rule layout for the Delta node:\n\nLayout\n\nIn order to compute:\n\nq_out: mirrors the posterior marginal on the out edge (same as the DeltaFnDefaultRuleLayout)\nq_ins: uses inbound message on the out edge and all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_out: uses all inbound messages on the ins edges (same as the DeltaFnDefaultRuleLayout)\nm_in_k: uses inbound message on the out edge and inbound messages on the ins edges except k\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node","page":"Factor nodes","title":"Nodes implementation","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"In the message passing framework, one of the most important concepts is a factor node. A factor node represents a local function in a factorised representation of a generative model.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"@node\nReactiveMP.FactorNode\nReactiveMP.FactorNodeLocalMarginal\nReactiveMP.NodeInterface\nReactiveMP.IndexedNodeInterface\nReactiveMP.messagein\nReactiveMP.messageout\nReactiveMP.tag\nReactiveMP.name\nReactiveMP.interfaces\nReactiveMP.getvariable\nReactiveMP.inputinterfaces\nReactiveMP.alias_interface\nReactiveMP.collect_factorisation\nReactiveMP.collect_pipeline\nReactiveMP.collect_meta\nReactiveMP.default_meta\nReactiveMP.as_node_symbol","category":"page"},{"location":"lib/nodes/#ReactiveMP.@node","page":"Factor nodes","title":"ReactiveMP.@node","text":"@node(fformtype, sdtype, interfaces_list)\n\n@node macro creates a node for a fformtype type object. To obtain a list of predefined nodes use ?is_predefined_node.\n\nArguments\n\nfformtype: Either an existing type identifier, e.g. Normal or a function type identifier, e.g. typeof(+)\nsdtype: Either Stochastic or Deterministic. Defines the type of the functional relationship\ninterfaces_list: Defines a fixed list of edges of a factor node, by convention the first element should be out. Example: [ out, mean, variance ]\n\nNote: interfaces_list must not include names that contain _ symbol in them, as it is reserved to identify joint posteriors around the node object.\n\nExamples\n\n\nstruct MyNormalDistribution\n mean :: Float64\n var :: Float64\nend\n\n@node MyNormalDistribution Stochastic [ out, mean, var ]\n\n\n@node typeof(+) Deterministic [ out, in1, in2 ]\n\nList of available nodes\n\nSee ?is_predefined_node.\n\n\n\n\n\n","category":"macro"},{"location":"lib/nodes/#ReactiveMP.FactorNode","page":"Factor nodes","title":"ReactiveMP.FactorNode","text":"GenericFactorNode(functionalform, interfaces)\n\nGeneric factor node object that represents a factor node with a given functionalform and interfaces.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.FactorNodeLocalMarginal","page":"Factor nodes","title":"ReactiveMP.FactorNodeLocalMarginal","text":"FactorNodeLocalMarginal\n\nThis object represents local marginals for some specific factor node. The local marginal can be joint in case of structured factorisation. Local to factor node marginal also can be shared with a corresponding marginal of some random variable.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.NodeInterface","page":"Factor nodes","title":"ReactiveMP.NodeInterface","text":"NodeInterface\n\nNodeInterface object represents a single node-variable connection.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.IndexedNodeInterface","page":"Factor nodes","title":"ReactiveMP.IndexedNodeInterface","text":"IndexedNodeInterface\n\nIndexedNodeInterface object represents a repetative node-variable connection. Used in cases when a node may connect to a different number of random variables with the same name, e.g. means and precisions of a Gaussian Mixture node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.messagein","page":"Factor nodes","title":"ReactiveMP.messagein","text":"messagein(interface)\n\nReturns an inbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.messageout","page":"Factor nodes","title":"ReactiveMP.messageout","text":"messageout(interface)\n\nReturns an outbound messages stream from the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.tag","page":"Factor nodes","title":"ReactiveMP.tag","text":"tag(interface)\n\nReturns a tag of the interface in the form of Val{ name(interface) }. The major difference between tag and name is that it is possible to dispath on interface's tag in message computation rule.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.name","page":"Factor nodes","title":"ReactiveMP.name","text":"name(interface)\n\nReturns a name of the interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.interfaces","page":"Factor nodes","title":"ReactiveMP.interfaces","text":"interfaces(fform)\n\nReturns a Val object with a tuple of interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.getvariable","page":"Factor nodes","title":"ReactiveMP.getvariable","text":"getvariable(interface)\n\nReturns a variable connected to the given interface.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.inputinterfaces","page":"Factor nodes","title":"ReactiveMP.inputinterfaces","text":"inputinterfaces(fform)\n\nSimilar to interfaces, but returns a Val object with a tuple of input interface names for a given factor node type. Returns nothing for unknown functional form.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.alias_interface","page":"Factor nodes","title":"ReactiveMP.alias_interface","text":"alias_interface(factor_type, index, name)\n\nConverts the given name to a correct interface name for a given factor node type and index.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_factorisation","page":"Factor nodes","title":"ReactiveMP.collect_factorisation","text":"collect_factorisation(nodetype, factorisation)\n\nThis function converts given factorisation to a correct internal factorisation representation for a given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_pipeline","page":"Factor nodes","title":"ReactiveMP.collect_pipeline","text":"collect_pipeline(nodetype, pipeline)\n\nThis function converts given pipeline to a correct internal pipeline representation for a factor given node.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.collect_meta","page":"Factor nodes","title":"ReactiveMP.collect_meta","text":"collect_meta(nodetype, meta)\n\nThis function converts given meta object to a correct internal meta representation for a given node. Fallbacks to default_meta in case if meta is nothing.\n\nSee also: default_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.default_meta","page":"Factor nodes","title":"ReactiveMP.default_meta","text":"default_meta(nodetype)\n\nReturns default meta object for a given node type.\n\nSee also: collect_meta, FactorNode\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.as_node_symbol","page":"Factor nodes","title":"ReactiveMP.as_node_symbol","text":"as_node_symbol(type)\n\nReturns a symbol associated with a node type.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-custom-node","page":"Factor nodes","title":"Adding a custom node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.jl exports the @node macro that allows for quick definition of a factor node with a fixed number of edges. The example application can be the following:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"struct MyNewCustomNode end\n\n@node MyNewCustomNode Stochastic [ x, y, (z, aliases = [ d ] ) ]\n# ^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^\n# Node's tag/name Node's type A fixed set of edges\n# Another possible The very first edge (in this example `x`) is considered\n# value is to be the output of the node\n# `Deterministic` - Edges can have aliases, e.g. `z` can be both `z` or `d`","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"This expression registers a new node that can be used with the inference engine. Note, however, that the @node macro does not generate any message passing update rules. These must be defined using the @rule macro. ","category":"page"},{"location":"lib/nodes/#lib-node-types","page":"Factor nodes","title":"Node types","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We distinguish different types of factor nodes in order to have better control over Bethe Free Energy computation. Each factor node has either the Deterministic or Stochastic functional form type.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Deterministic\nStochastic\nisdeterministic\nisstochastic\nsdtype","category":"page"},{"location":"lib/nodes/#ReactiveMP.Deterministic","page":"Factor nodes","title":"ReactiveMP.Deterministic","text":"Deterministic\n\nDeterministic object used to parametrize factor node object with determinstic type of relationship between variables.\n\nSee also: Stochastic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.Stochastic","page":"Factor nodes","title":"ReactiveMP.Stochastic","text":"Stochastic\n\nStochastic object used to parametrize factor node object with stochastic type of relationship between variables.\n\nSee also: Deterministic, isdeterministic, isstochastic, sdtype\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.isdeterministic","page":"Factor nodes","title":"ReactiveMP.isdeterministic","text":"isdeterministic(node)\n\nFunction used to check if factor node object is deterministic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isstochastic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.isstochastic","page":"Factor nodes","title":"ReactiveMP.isstochastic","text":"isstochastic(node)\n\nFunction used to check if factor node object is stochastic or not. Returns true or false.\n\nSee also: Deterministic, Stochastic, isdeterministic, sdtype\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.sdtype","page":"Factor nodes","title":"ReactiveMP.sdtype","text":"sdtype(object)\n\nReturns either Deterministic or Stochastic for a given object (if defined).\n\nSee also: Deterministic, Stochastic, isdeterministic, isstochastic\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, BayesBase, Distributions, ExponentialFamily","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"For example the + node has the Deterministic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `+` node deterministic: \", isdeterministic(sdtype(+)))\nprintln(\"Is `+` node stochastic: \", isstochastic(sdtype(+)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"On the other hand, the Bernoulli node has the Stochastic type:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"Is `Bernoulli` node deterministic: \", isdeterministic(sdtype(Bernoulli)))\nprintln(\"Is `Bernoulli` node stochastic: \", isstochastic(sdtype(Bernoulli)))\nnothing #hide","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To get an actual instance of the type object we use sdtype function:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"println(\"sdtype() of `+` node is \", sdtype(+))\nprintln(\"sdtype() of `Bernoulli` node is \", sdtype(Bernoulli))\nnothing #hide","category":"page"},{"location":"lib/nodes/#lib-node-functional-dependencies-pipeline","page":"Factor nodes","title":"Node functional dependencies pipeline","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"The generic implementation of factor nodes in ReactiveMP supports custom functional dependency pipelines. Briefly, the functional dependencies pipeline defines what dependencies are need to compute a single message. As an example, consider the belief-propagation message update equation for a factor node f with three edges: x, y and z:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = int mu(y) mu(z) f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Here we see that in the standard setting for the belief-propagation message out of edge x, we need only messages from the edges y and z. In contrast, consider the variational message update rule equation with mean-field assumption:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"mu(x) = exp int q(y) q(z) log f(x y z) mathrmdy mathrmdz","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"We see that in this setting, we do not need messages mu(y) and mu(z), but only the marginals q(y) and q(z). The purpose of a functional dependencies pipeline is to determine functional dependencies (a set of messages or marginals) that are needed to compute a single message. By default, ReactiveMP.jl uses so-called DefaultFunctionalDependencies that correctly implements belief-propagation and variational message passing schemes (including both mean-field and structured factorisations). The full list of built-in pipelines is presented below:","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.DefaultFunctionalDependencies\nReactiveMP.RequireMessageFunctionalDependencies\nReactiveMP.RequireMarginalFunctionalDependencies\nReactiveMP.RequireEverythingFunctionalDependencies","category":"page"},{"location":"lib/nodes/#ReactiveMP.DefaultFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.DefaultFunctionalDependencies","text":"DefaultFunctionalDependencies\n\nThis functional dependencies translate directly to a regular variational message passing scheme. In order to compute a message out of some interface, this strategy requires messages from interfaces within the same cluster and marginals over other clusters.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMessageFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMessageFunctionalDependencies","text":"RequireMessageFunctionalDependencies(specifications::NamedTuple)\nRequireMessageFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the inbound message on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial messages. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the inbound message. If nothing is passed as a value in the named tuple, the initial message is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMessageFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'inbound' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMarginalFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireMarginalFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireMarginalFunctionalDependencies","text":"RequireMarginalFunctionalDependencies(specifications::NamedTuple)\nRequireMarginalFunctionalDependencies(; specifications...)\n\nThe same as DefaultFunctionalDependencies, but in order to compute a message out of some edge also requires the marginal on the this edge.\n\nThe specification parameter is a named tuple that contains the names of the edges and their initial marginals. When a name is present in the named tuple, that indicates that the computation of the outbound message on the same edge must use the marginal on this edge. If nothing is passed as a value in the named tuple, the initial marginal is not set. Note that the construction allows passing keyword argument to the constructor instead of using NamedTuple directly.\n\nRequireMarginalFunctionalDependencies(μ = vague(NormalMeanPrecision), τ = nothing)\n # ^^^ ^^^\n # request 'marginal' for 'x' we may do the same for 'τ',\n # and initialise with `vague(...)` but here we skip initialisation\n\nSee also: ReactiveMP.DefaultFunctionalDependencies, ReactiveMP.RequireMessageFunctionalDependencies, ReactiveMP.RequireEverythingFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.RequireEverythingFunctionalDependencies","page":"Factor nodes","title":"ReactiveMP.RequireEverythingFunctionalDependencies","text":"RequireEverythingFunctionalDependencies\n\nThis pipeline specifies that in order to compute a message of some edge update rules request everything that is available locally. This includes all inbound messages (including on the same edge) and marginals over all local edge-clusters (this may or may not include marginals on single edges, depends on the local factorisation constraint).\n\nSee also: DefaultFunctionalDependencies, RequireMessageFunctionalDependencies, RequireMarginalFunctionalDependencies\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#lib-node-traits","page":"Factor nodes","title":"Node traits","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"Each factor node has to define the ReactiveMP.is_predefined_node trait function and to specify a ReactiveMP.PredefinedNodeFunctionalForm singleton as a return object. By default ReactiveMP.is_predefined_node returns ReactiveMP.UndefinedNodeFunctionalForm. Objects that do not specify this property correctly cannot be used in model specification.","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"note: Note\n@node macro does that automatically","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.PredefinedNodeFunctionalForm\nReactiveMP.UndefinedNodeFunctionalForm\nReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/#ReactiveMP.PredefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.PredefinedNodeFunctionalForm","text":"PredefinedNodeFunctionalForm\n\nTrait specification for an object that has been marked as a valid factor node with the @node macro.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.UndefinedNodeFunctionalForm","page":"Factor nodes","title":"ReactiveMP.UndefinedNodeFunctionalForm","text":"UndefinedNodeFunctionalForm\n\nTrait specification for an object that has not been marked as a factor node with the @node macro. Note that it does not necessarily mean that the object is not a valid factor node, but rather that it has not been marked as such. The ReactiveMP inference engine support arbitrary deterministic function as factor nodes, but they require manual specification of the approximation method.\n\nSee also: ReactiveMP.is_predefined_node, ReactiveMP.PredefinedNodeFunctionalForm\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.is_predefined_node","page":"Factor nodes","title":"ReactiveMP.is_predefined_node","text":"is_predefined_node(object)\n\nDetermines if the object has been marked as a factor node with the @node macro. Returns either PredefinedNodeFunctionalForm() or UndefinedNodeFunctionalForm().\n\nSee also: ReactiveMP.PredefinedNodeFunctionalForm, ReactiveMP.UndefinedNodeFunctionalForm\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-node-pipelines","page":"Factor nodes","title":"Node pipelines","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"ReactiveMP.AbstractPipelineStage\nReactiveMP.apply_pipeline_stage\nReactiveMP.EmptyPipelineStage\nReactiveMP.CompositePipelineStage\nReactiveMP.LoggerPipelineStage\nReactiveMP.DiscontinuePipelineStage\nReactiveMP.AsyncPipelineStage\nReactiveMP.ScheduleOnPipelineStage\nReactiveMP.schedule_updates","category":"page"},{"location":"lib/nodes/#ReactiveMP.AbstractPipelineStage","page":"Factor nodes","title":"ReactiveMP.AbstractPipelineStage","text":"AbstractPipelineStage\n\nAn abstract type for all custom pipelines stages\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.apply_pipeline_stage","page":"Factor nodes","title":"ReactiveMP.apply_pipeline_stage","text":"apply_pipeline_stage(stage, factornode, tag, stream)\n\nApplies a given pipeline stage to the stream argument given factornode and tag of an edge.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#ReactiveMP.EmptyPipelineStage","page":"Factor nodes","title":"ReactiveMP.EmptyPipelineStage","text":"EmptyPipelineStage <: AbstractPipelineStage\n\nDummy empty pipeline stage that does not modify the original pipeline.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.CompositePipelineStage","page":"Factor nodes","title":"ReactiveMP.CompositePipelineStage","text":"CompositePipelineStage{T} <: AbstractPipelineStage\n\nComposite pipeline stage that consists of multiple inner pipeline stages \n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.LoggerPipelineStage","page":"Factor nodes","title":"ReactiveMP.LoggerPipelineStage","text":"LoggerPipelineStage <: AbstractPipelineStage\n\nLogs all updates from stream into output\n\nArguments\n\noutput: (optional), an output stream used to print log statements\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.DiscontinuePipelineStage","page":"Factor nodes","title":"ReactiveMP.DiscontinuePipelineStage","text":"DiscontinuePipelineStage <: AbstractPipelineStage\n\nApplies the discontinue() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.AsyncPipelineStage","page":"Factor nodes","title":"ReactiveMP.AsyncPipelineStage","text":"AsyncPipelineStage <: AbstractPipelineStage\n\nApplies the async() operator from Rocket.jl library to the given pipeline\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.ScheduleOnPipelineStage","page":"Factor nodes","title":"ReactiveMP.ScheduleOnPipelineStage","text":"ScheduleOnPipelineStage{S} <: AbstractPipelineStage\n\nApplies the schedule_on() operator from Rocket.jl library to the given pipeline with a provided scheduler\n\nArguments\n\nscheduler: scheduler to schedule updates on. Must be compatible with Rocket.jl library and schedule_on() operator.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/#ReactiveMP.schedule_updates","page":"Factor nodes","title":"ReactiveMP.schedule_updates","text":"schedule_updates(variables...; pipeline_stage = ScheduleOnPipelineStage(PendingScheduler()))\n\nSchedules posterior marginal updates for given variables using stage. By default creates ScheduleOnPipelineStage with PendingScheduler() from Rocket.jl library. Returns a scheduler with release! method available to release all scheduled updates.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/#lib-predefined-nodes","page":"Factor nodes","title":"List of predefined factor node","text":"","category":"section"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"To quickly check the list of all predefined factor nodes, call ?ReactiveMP.is_predefined_node or Base.doc(ReactiveMP.is_predefined_node).","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"?ReactiveMP.is_predefined_node","category":"page"},{"location":"lib/nodes/","page":"Factor nodes","title":"Factor nodes","text":"using ReactiveMP, Markdown\nMarkdown.parse(string(Base.doc(Base.Docs.Binding(ReactiveMP, :is_predefined_node))))","category":"page"},{"location":"lib/nodes/logical/#lib-nodes-logical","page":"Logical","title":"Logical operations","text":"","category":"section"},{"location":"lib/nodes/logical/","page":"Logical","title":"Logical","text":"ReactiveMP.AND\nReactiveMP.OR\nReactiveMP.IMPLY\nReactiveMP.NOT","category":"page"},{"location":"lib/nodes/logical/#ReactiveMP.AND","page":"Logical","title":"ReactiveMP.AND","text":"AND node implements logic AND function (conjuction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.OR","page":"Logical","title":"ReactiveMP.OR","text":"OR node implements logic OR function (disjunction) that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.IMPLY","page":"Logical","title":"ReactiveMP.IMPLY","text":"IMPY node implements implication function that can be desribed by the followsing table: | in1 in2 | out | | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/logical/#ReactiveMP.NOT","page":"Logical","title":"ReactiveMP.NOT","text":"NOT node implements negation function that can be desribed by the followsing table: | in | out | | 0 | 1 | | 1 | 0 |\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#lib-nodes-ctransition","page":"Continuous transition","title":"Continous transition node","text":"","category":"section"},{"location":"lib/nodes/ctransition/","page":"Continuous transition","title":"Continuous transition","text":"ReactiveMP.ContinuousTransition\nReactiveMP.ContinuousTransitionMeta\nReactiveMP.ctcompanion_matrix","category":"page"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransition","page":"Continuous transition","title":"ReactiveMP.ContinuousTransition","text":"The functional form of the ContinuousTransition node is given by: y ~ Normal(K(a) * x, W⁻¹)\n\nThis node transforms an m-dimensional vector x into an n-dimensional vector y via a linear (or nonlinear) transformation with a n×m-dimensional matrix A that is constructed from a vector a via a transformation K(a). ContinuousTransition node is primarily used in two regimes:\n\nWhen no structure on A is specified:\n\ntransformation = a -> reshape(a, 2, 2)\n...\na ~ MvNormalMeanCovariance(zeros(2), Diagonal(ones(2)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nWhen some structure if A is known:\n\ntransformation = a -> [cos(a[1]) -sin(a[1]); sin(a[1]) cos(a[1])]\n...\na ~ MvNormalMeanCovariance(zeros(1), Diagonal(ones(1)))\ny ~ ContinuousTransition(x, a, W) where {meta = CTMeta(transformation)}\n...\n\nTo construct the matrix A, the elements of a are reshaped into A according to the transformation function provided in the meta. If you intend to use univariate Gaussian distributions, use it as a vector of length 1, e.g.a ~ MvNormalMeanCovariance([0.0], [1.;])`.\n\nCheck ContinuousTransitionMeta for more details on how to specify the transformation function that must return a matrix.\n\ny ~ ContinuousTransition(x, a, W) where {meta = ContinuousTransitionMeta(transformation)}\n\nInterfaces:\n\ny - n-dimensional output of the ContinuousTransition node.\nx - m-dimensional input of the ContinuousTransition node.\na - any-dimensional vector that casts into the matrix A. \nW - n×n-dimensional precision matrix used to soften the transition and perform variational message passing.\n\nNote that you can set W to a fixed value or put a prior on it to control the amount of jitter.\n\nThe ContinuousTransition node support two factorizations:\n\nMean-field factorization:\n\n@constraints begin\n q(y, x, a, W) = q(y)q(x)q(a)q(W)\nend\n\nStructured factorization:\n\n@constraints begin\n q(y, x, a, W) = q(y, x)q(a)q(W)\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ContinuousTransitionMeta","page":"Continuous transition","title":"ReactiveMP.ContinuousTransitionMeta","text":"ContinuousTransitionMeta is used as a metadata flag in ContinuousTransition to define the transformation function for constructing the matrix A from vector a.\n\nContinuousTransitionMeta requires a transformation function and the length of vector a, which acts as an expansion point for approximating the transformation linearly. If transformation appears to be linear, then no approximation is performed.\n\nConstructors:\n\nContinuousTransitionMeta(transformation::Function, â::Vector{<:Real}): Constructs a ContinuousTransitionMeta struct with the transformation function and allocated basis vectors.\n\nFields:\n\nf: Represents the transformation function that transforms vector a into matrix A\n\nThe ContinuousTransitionMeta struct plays a pivotal role in defining how the vector a is transformed into the matrix A, thus influencing the behavior of the ContinuousTransition node.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/ctransition/#ReactiveMP.ctcompanion_matrix","page":"Continuous transition","title":"ReactiveMP.ctcompanion_matrix","text":"`ctcompanion_matrix` casts a vector `a` into a matrix `A` by means of linearization of the transformation function `f` around the expansion point `a0`.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#lib-helpers-algebra-common","page":"Algebra utils","title":"Algebra common utilities","text":"","category":"section"},{"location":"lib/algebra/#lib-helpers-algebra-diageye","page":"Algebra utils","title":"diageye","text":"","category":"section"},{"location":"lib/algebra/","page":"Algebra utils","title":"Algebra utils","text":"diageye\nReactiveMP.CompanionMatrix\nReactiveMP.PermutationMatrix\nReactiveMP.StandardBasisVector\nReactiveMP.GammaShapeLikelihood\nReactiveMP.ImportanceSamplingApproximation\nReactiveMP.mul_inplace!\nReactiveMP.negate_inplace!\nReactiveMP.mul_trace\nReactiveMP.rank1update\nReactiveMP.v_a_vT\nReactiveMP.powerset\nReactiveMP.besselmod","category":"page"},{"location":"lib/algebra/#ReactiveMP.diageye","page":"Algebra utils","title":"ReactiveMP.diageye","text":"diageye(::Type{T}, n::Int)\n\nAn alias for the Matrix{T}(I, n, n). Returns a matrix of size n x n with ones (of type T) on the diagonal and zeros everywhere else.\n\n\n\n\n\ndiageye(n::Int)\n\nAn alias for the Matrix{Float64}(I, n, n). Returns a matrix of size n x n with ones (of type Float64) on the diagonal and zeros everywhere else.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.CompanionMatrix","page":"Algebra utils","title":"ReactiveMP.CompanionMatrix","text":"CompanionMatrix\n\nRepresents a matrix of the following structure:\n\nθ1 θ2 θ3 ... θn-1 θn 1 0 0 ... 0 0 0 1 0 ... 0 0 . . . ... . . . . . ... . . 0 0 0 ... 0 0 0 0 0 ... 1 0\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.PermutationMatrix","page":"Algebra utils","title":"ReactiveMP.PermutationMatrix","text":"PermutationMatrix(ind::Array{T}) creates a permutation matrix with ones at coordinates (k, ind[k]) for k = 1:length(ind).\n\nA permutation matrix represents a matrix containing only zeros and ones, which basically permutes the vector or matrix it is multiplied with. These matrices A are constrained by:\n\n A_ij = 0 1\n _i A_ij = 1\n _j A_ij = 1\n\nAn example is the 3-dimensional permutation matrix\n\nA = beginbmatrix 1 0 0 0 0 1 1 0 0 endbmatrix\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.StandardBasisVector","page":"Algebra utils","title":"ReactiveMP.StandardBasisVector","text":"StandardBasisVector{T, len, ind}(scale::T)\n\nStandardBasisVector creates a standard Cartesian basis vector of zeros of length len with a single element scale at index ind.\n\nAn example is the 3-dimensional standard basis vector for the first dimension\n\ne = beginbmatrix 1 0 0 endbmatrix\n\nWhich can be constructed by calling e = StandardBasisVector(3, 1, 1)\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.GammaShapeLikelihood","page":"Algebra utils","title":"ReactiveMP.GammaShapeLikelihood","text":"ν(x) ∝ exp(p*β*x - p*logГ(x)) ≡ exp(γ*x - p*logГ(x))\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.ImportanceSamplingApproximation","page":"Algebra utils","title":"ReactiveMP.ImportanceSamplingApproximation","text":"ImportanceSamplingApproximation\n\nThis structure stores all information needed to perform an importance sampling procedure and provides convenient functions to generate samples and weights to approximate expectations\n\nFields\n\nrng: random number generator objects\nnsamples: number of samples generated by default\n\n\n\n\n\n","category":"type"},{"location":"lib/algebra/#ReactiveMP.mul_inplace!","page":"Algebra utils","title":"ReactiveMP.mul_inplace!","text":"mul_inplace!(alpha, A)\n\nReturns alpha * A, modifying and reusing A storage if possible.\n\nSee also: negate_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.negate_inplace!","page":"Algebra utils","title":"ReactiveMP.negate_inplace!","text":"negate_inplace!(A)\n\nReturns -A, modifying and reusing A storage if possible.\n\nSee also: mul_inplace!\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.mul_trace","page":"Algebra utils","title":"ReactiveMP.mul_trace","text":"mul_trace(A, B)\n\nComputes tr(A * B) without allocating A * B.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.rank1update","page":"Algebra utils","title":"ReactiveMP.rank1update","text":"rank1update(A, x)\nrank1update(A, x, y)\n\nHelper function for A + x * y'. Uses optimised BLAS version for AbstractFloats and fallbacks to a generic implementation in case of differentiation\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.v_a_vT","page":"Algebra utils","title":"ReactiveMP.v_a_vT","text":"v_a_vT(v, a)\n\nComputes vav^T efficiently.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.powerset","page":"Algebra utils","title":"ReactiveMP.powerset","text":"powerset(iterator)\n\nComputes the set of all possible sets of the iterator.\n\n\n\n\n\n","category":"function"},{"location":"lib/algebra/#ReactiveMP.besselmod","page":"Algebra utils","title":"ReactiveMP.besselmod","text":"Modified-bessel function of second kind\n\nmx, vx : mean and variance of the random variable x my, vy : mean and variance of the random variable y rho : correlation coefficient\n\n\n\n\n\n","category":"function"},{"location":"extra/contributing/#Contribution-guidelines","page":"Contributing","title":"Contribution guidelines","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome all possible contributors. This page details the some of the guidelines that should be followed when contributing to this package.","category":"page"},{"location":"extra/contributing/#Reporting-bugs","page":"Contributing","title":"Reporting bugs","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We track bugs using GitHub issues. We encourage you to write complete, specific, reproducible bug reports. Mention the versions of Julia and ReactiveMP for which you observe unexpected behavior. Please provide a concise description of the problem and complement it with code snippets, test cases, screenshots, tracebacks or any other information that you consider relevant. This will help us to replicate the problem and narrow the search space for solutions.","category":"page"},{"location":"extra/contributing/#Suggesting-features","page":"Contributing","title":"Suggesting features","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We welcome new feature proposals. However, before submitting a feature request, consider a few things:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Does the feature require changes in the core ReactiveMP.jl code? If it doesn't (for example, you would like to add a factor node for a particular application), you can add local extensions in your script/notebook or consider making a separate repository for your extensions.\nIf you would like to add an implementation of a feature that changes a lot in the core ReactiveMP.jl code, please open an issue on GitHub and describe your proposal first. This will allow us to discuss your proposal with you before you invest your time in implementing something that may be difficult to merge later on.","category":"page"},{"location":"extra/contributing/#Contributing-code","page":"Contributing","title":"Contributing code","text":"","category":"section"},{"location":"extra/contributing/#Installing-ReactiveMP","page":"Contributing","title":"Installing ReactiveMP","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We suggest that you use the dev command from the new Julia package manager to install ReactiveMP.jl for development purposes. To work on your fork of ReactiveMP.jl, use your fork's URL address in the dev command, for example:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] dev git@github.com:your_username/ReactiveMP.jl.git","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The dev command clones ReactiveMP.jl to ~/.julia/dev/ReactiveMP. All local changes to ReactiveMP code will be reflected in imported code.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nIt is also might be useful to install Revise.jl package as it allows you to modify code and use the changes without restarting Julia.","category":"page"},{"location":"extra/contributing/#Committing-code","page":"Contributing","title":"Committing code","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the standard GitHub Flow workflow where all contributions are added through pull requests. In order to contribute, first fork the repository, then commit your contributions to your fork, and then create a pull request on the master branch of the ReactiveMP.jl repository.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Before opening a pull request, please make sure that all tests pass without failing! All demos (can be found in /demo/ directory) and benchmarks (can be found in /benchmark/ directory) have to run without errors as well.","category":"page"},{"location":"extra/contributing/#Style-conventions","page":"Contributing","title":"Style conventions","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"note: Note\nReactiveMP.jl repository contains scripts to automatically format code according to our guidelines. Use make format command to fix code style. This command overwrites files.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use default Julia style guide. We list here a few important points and our modifications to the Julia style guide:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"Use 4 spaces for indentation\nType names use UpperCamelCase. For example: AbstractFactorNode, RandomVariable, etc..\nFunction names are lowercase with underscores, when necessary. For example: activate!, randomvar, etc..\nVariable names and function arguments use snake_case\nThe name of a method that modifies its argument(s) must end in !","category":"page"},{"location":"extra/contributing/#Unit-tests","page":"Contributing","title":"Unit tests","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"We use the test-driven development (TDD) methodology for ReactiveMP.jl development. The test coverage should be as complete as possible. Please make sure that you write tests for each piece of code that you want to add.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"All unit tests are located in the /test/ directory. The /test/ directory follows the structure of the /src/ directory. Each test file should have following filename format: test_*.jl. Some tests are also present in jldoctest docs annotations directly in the source code. See Julia's documentation about doctests.","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"The tests can be evaluated by running following command in the Julia REPL:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"] test ReactiveMP","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"In addition tests can be evaluated by running following command in the ReactiveMP root directory:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make test","category":"page"},{"location":"extra/contributing/#Fixes-to-external-libraries","page":"Contributing","title":"Fixes to external libraries","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"If a bug has been discovered in an external dependencies of the ReactiveMP.jl it is the best to open an issue directly in the dependency's github repository. You use can use the fixes.jl file for hot-fixes before a new release of the broken dependecy is available.","category":"page"},{"location":"extra/contributing/#Makefile","page":"Contributing","title":"Makefile","text":"","category":"section"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"ReactiveMP.jl uses Makefile for most common operations:","category":"page"},{"location":"extra/contributing/","page":"Contributing","title":"Contributing","text":"make help: Shows help snippet\nmake test: Run tests, supports extra arguments\nmake test test_args=\"distributions:normal_mean_variance\" would run tests only from distributions/test_normal_mean_variance.jl\nmake test test_args=\"distributions:normal_mean_variance models:lgssm\" would run tests both from distributions/test_normal_mean_variance.jl and models/test_lgssm.jl\nmake docs: Compile documentation\nmake benchmark: Run simple benchmark\nmake lint: Check codestyle\nmake format: Check and fix codestyle ","category":"page"},{"location":"lib/nodes/flow/#lib-nodes-flow","page":"Flow","title":"Flow node","text":"","category":"section"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"See also Flow tutorial for a comprehensive guide on using flows in RxInfer.jl.","category":"page"},{"location":"lib/nodes/flow/","page":"Flow","title":"Flow","text":"PlanarFlow\nRadialFlow\nFlowModel\nCompiledFlowModel\ncompile\nAdditiveCouplingLayer\nInputLayer\nPermutationLayer\nFlowMeta","category":"page"},{"location":"lib/nodes/flow/#ReactiveMP.PlanarFlow","page":"Flow","title":"ReactiveMP.PlanarFlow","text":"The PlanarFlow function is defined as\n\nf(bfx) = bfx + bfu tanh(bfw^top bfx + b)\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfuin mathbbR^D, bfwin mathbbR^D and binmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.RadialFlow","page":"Flow","title":"ReactiveMP.RadialFlow","text":"The RadialFlow function is defined as\n\nf(bfx) = bfx + fracbeta(bfz - bfz_0)alpha + bfz - bfz_0\n\nwith input and output dimension D. Here bfxin mathbbR^D represents the input of the function. Furthermore bfz_0in mathbbR^D, alphain mathbbR and betainmathbbR represent the parameters of the function. The function contracts and expands the input space. \n\nThis function has been introduced in:\n\nRezende, Danilo, and Shakir Mohamed. \"Variational inference with normalizing flows.\" International conference on machine learning. PMLR, 2015.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowModel","page":"Flow","title":"ReactiveMP.FlowModel","text":"The FlowModel structure is the most generic type of Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimensionality and a tuple of layers and can be constructed as FlowModel( dim, (layer1, layer2, ...) ).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.CompiledFlowModel","page":"Flow","title":"ReactiveMP.CompiledFlowModel","text":"The CompiledFlowModel structure is the most generic type of compiled Flow model, in which the layers are not constrained to be of a specific type. The FlowModel structure contains the input dimension and a tuple of compiled layers. Do not manually create a CompiledFlowModel! Instead create a FlowModel first and compile it with compile(model::FlowModel). This will make sure that all layers/mappings are configured with the proper dimensionality and with randomly sampled parameters. Alternatively, if you would like to pass your own parameters, call compile(model::FlowModel, params::Vector).\n\nNote: this model can be specialized by constraining the types of layers. This potentially allows for more efficient specialized methods that can deal with specifics of these layers, such as triangular jacobian matrices.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.compile","page":"Flow","title":"ReactiveMP.compile","text":"compile() compiles a model by setting its parameters. It randomly sets parameter values in the layers and flows such that inference in the model can be obtained.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\ncompile(model::FlowModel, params::Vector) lets you initialize a model model with a vector of parameters params.\n\nInput arguments\n\nmodel::FlowModel - a model of which the dimensionality of its layers/flows has been initialized, but its parameters have not been set.\nparams::Vector - a vector of parameters with which the model should be compiled.\n\nReturn arguments\n\n::CompiledFlowModel - a compiled model with set parameters, such that it can be used for processing data.\n\n\n\n\n\n","category":"function"},{"location":"lib/nodes/flow/#ReactiveMP.AdditiveCouplingLayer","page":"Flow","title":"ReactiveMP.AdditiveCouplingLayer","text":"The additive coupling layer specifies an invertible function bfy = g(bfx) following the specific structure (for the mapping g mathbbR^2 rightarrow mathbbR^2):\n\n beginalign\n y_1 = x_1 \n y_2 = x_2 + f(x_1)\n endalign\n\nwhere f(cdot) denotes an arbitrary function with mapping f mathbbR rightarrow mathbbR. This function can be chosen arbitrarily complex. Non-linear functions (neural networks) are often chosen to model complex relationships. From the definition of the model, invertibility can be easily achieved as\n\n beginalign\n x_1 = y_1 \n x_2 = y_2 - f(y_1)\n endalign\n\nThe current implementation only allows for the mapping g mathbbR^2 rightarrow mathbbR^2, although this layer can be generalized for arbitrary input dimensions.\n\nAdditiveCouplingLayer(f <: AbstractCouplingFlow) creates the layer structure with function f.\n\nExample\n\nf = PlanarFlow()\nlayer = AdditiveCouplingLayer(f)\n\nThis layer structure has been introduced in:\n\nDinh, Laurent, David Krueger, and Yoshua Bengio. \"Nice: Non-linear independent components estimation.\" arXiv preprint arXiv:1410.8516 (2014).\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.InputLayer","page":"Flow","title":"ReactiveMP.InputLayer","text":"The input layer specifies the input dimension to a flow model.\n\nlayer = InputLayer(3)\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.PermutationLayer","page":"Flow","title":"ReactiveMP.PermutationLayer","text":"The permutation layer specifies an invertible mapping bfy = g(bfx) = Pbfx where P is a permutation matrix.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/flow/#ReactiveMP.FlowMeta","page":"Flow","title":"ReactiveMP.FlowMeta","text":"The FlowMeta structure contains the meta data of the Flow factor node. More specifically, it contains the model of the Flow factor node. The FlowMeta structure can be constructed as FlowMeta(model). Make sure that the flow model has been compiled.\n\nThe FlowMeta structure is required for the Flow factor node and can be included with the Flow node as: y ~ Flow(x) where { meta = FlowMeta(...) }\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/#lib-marginal","page":"Marginals","title":"Marginal implementation","text":"","category":"section"},{"location":"lib/marginal/#Marginal-type","page":"Marginals","title":"Marginal type","text":"","category":"section"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"All marginals are encoded with the type Marginal. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"Marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.Marginal","page":"Marginals","title":"ReactiveMP.Marginal","text":"Marginal(data, is_clamped, is_initial, addons)\n\nAn implementation of a marginal in variational message passing framework.\n\nArguments\n\ndata::D: marginal always holds some data object associated with it, which is usually a probability distribution\nis_clamped::Bool, specifies if this marginal was the result of constant computations (e.g. clamped constants)\nis_initial::Bool, specifies if this marginal was used for initialization\naddons::A, specifies the addons of the marginal, which may carry extra bits of information, e.g. debug information, memory, etc.\n\nExample\n\njulia> distribution = Gamma(10.0, 2.0)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> message = Marginal(distribution, false, true, nothing)\nMarginal(Distributions.Gamma{Float64}(α=10.0, θ=2.0))\n\njulia> mean(message) \n20.0\n\njulia> getdata(message)\nDistributions.Gamma{Float64}(α=10.0, θ=2.0)\n\njulia> is_clamped(message)\nfalse\n\njulia> is_initial(message)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"From an implementation point a view the Marginal structure does nothing but hold some data object and redirects most of the statistical related functions to that data object. However, this object is used extensively in Julia's multiple dispatch. ","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"ReactiveMP.getdata(marginal::Marginal)\nReactiveMP.is_clamped(marginal::Marginal)\nReactiveMP.is_initial(marginal::Marginal)\nReactiveMP.getaddons(marginal::Marginal)\nReactiveMP.as_marginal\nReactiveMP.to_marginal","category":"page"},{"location":"lib/marginal/#ReactiveMP.getdata-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getdata","text":"getdata(marginal::Marginal)\n\nReturns data associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_clamped-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_clamped","text":"is_clamped(marginal::Marginal)\n\nChecks if marginal is clamped or not.\n\nSee also: is_initial\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.is_initial-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.is_initial","text":"is_initial(marginal::Marginal)\n\nChecks if marginal is initial or not.\n\nSee also: is_clamped\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.getaddons-Tuple{Marginal}","page":"Marginals","title":"ReactiveMP.getaddons","text":"getaddons(marginal::Marginal)\n\nReturns addons associated with the marginal.\n\n\n\n\n\n","category":"method"},{"location":"lib/marginal/#ReactiveMP.as_marginal","page":"Marginals","title":"ReactiveMP.as_marginal","text":"as_marginal(any)\n\nA function that converts any to an instance of Marginal.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/#ReactiveMP.to_marginal","page":"Marginals","title":"ReactiveMP.to_marginal","text":"to_marginal(any)\n\nTransforms an input to a proper marginal distribution. Called inside as_marginal. Some nodes do not use Distributions.jl, but instead implement their own equivalents for messages for better efficiency. Effectively to_marginal is needed to convert internal effective implementation to a user-friendly equivalent (e.g. from Distributions.jl). By default does nothing and returns its input, but some nodes may override this behaviour (see for example Wishart and InverseWishart).\n\nNote: This function is a part of the private API and is not intended to be used outside of the ReactiveMP package.\n\n\n\n\n\n","category":"function"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"using ReactiveMP, BayesBase, ExponentialFamily\n\ndistribution = ExponentialFamily.NormalMeanPrecision(0.0, 1.0)\nmarginal = Marginal(distribution, false, true, nothing)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"mean(marginal), precision(marginal)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"logpdf(marginal, 1.0)","category":"page"},{"location":"lib/marginal/","page":"Marginals","title":"Marginals","text":"is_clamped(marginal), is_initial(marginal)","category":"page"},{"location":"extra/extensions/#Extensions-and-interaction-with-the-Julia-ecosystem","page":"Extensions","title":"Extensions and interaction with the Julia ecosystem","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"ReactiveMP.jl exports extra functionality if other Julia packages are loaded in the same environment.","category":"page"},{"location":"extra/extensions/#Optimisers.jl","page":"Extensions","title":"Optimisers.jl","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The Optimizers.jl package defines many standard gradient-based optimisation rules, and tools for applying them to deeply nested models. The optimizers defined in the Optimziers.jl are compatible with the CVI approximation method.","category":"page"},{"location":"extra/extensions/#DiffResults.jl-(loaded-automatically-with-the-ForwardDiff.jl)","page":"Extensions","title":"DiffResults.jl (loaded automatically with the ForwardDiff.jl)","text":"","category":"section"},{"location":"extra/extensions/","page":"Extensions","title":"Extensions","text":"The DiffResults.jl provides the DiffResult type, which can be passed to in-place differentiation methods instead of an output buffer. If loaded in the current Julia session enables faster derivatives with the ForwardDiffGrad option in the CVI approximation method (in the Gaussian case).","category":"page"},{"location":"custom/custom-functional-form/#custom-functional-form","page":"Custom functional form","title":"Custom Functional Form Specification","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In a nutshell, functional form constraints defines a function that approximates the product of colliding messages and computes posterior marginal that can be used later on during the inference procedure. An important part of the functional forms constraint implementation is the prod function in the BayesBase package. For example, if we refer to our CustomFunctionalForm as to f we can see the whole functional form constraints pipeline as:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"q(x) = fleft(fracoverrightarrowmu(x)overleftarrowmu(x)int overrightarrowmu(x)overleftarrowmu(x) mathrmdxright)","category":"page"},{"location":"custom/custom-functional-form/#Interface","page":"Custom functional form","title":"Interface","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.jl, however, uses some extra utility functions to define functional form constraint behaviour. Here we briefly describe all utility function. If you are only interested in the concrete example, you may directly head to the Custom Functional Form example at the end of this section.","category":"page"},{"location":"custom/custom-functional-form/#Abstract-super-type","page":"Custom functional form","title":"Abstract super type","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"AbstractFormConstraint\nUnspecifiedFormConstraint\nCompositeFormConstraint\nReactiveMP.preprocess_form_constraints","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.AbstractFormConstraint","page":"Custom functional form","title":"ReactiveMP.AbstractFormConstraint","text":"AbstractFormConstraint\n\nEvery functional form constraint is a subtype of AbstractFormConstraint abstract type.\n\nNote: this is not strictly necessary, but it makes automatic dispatch easier and compatible with the CompositeFormConstraint.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.UnspecifiedFormConstraint","page":"Custom functional form","title":"ReactiveMP.UnspecifiedFormConstraint","text":"UnspecifiedFormConstraint\n\nOne of the form constraint objects. Does not imply any form constraints and simply returns the same object as receives. However it does not allow DistProduct to be a valid functional form in the inference backend.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.CompositeFormConstraint","page":"Custom functional form","title":"ReactiveMP.CompositeFormConstraint","text":"CompositeFormConstraint\n\nCreates a composite form constraint that applies form constraints in order. The composed form constraints must be compatible and have the exact same form_check_strategy. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.preprocess_form_constraints","page":"Custom functional form","title":"ReactiveMP.preprocess_form_constraints","text":"preprocess_form_constraints(constraints)\n\nThis function preprocesses form constraints and converts the provided objects into a form compatible with ReactiveMP inference backend (if possible). If a tuple of constraints is passed, it creates a CompositeFormConstraint object. Wraps unknown form constraints into a WrappedFormConstraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Form-check-strategy","page":"Custom functional form","title":"Form check strategy","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_form_check_strategy function that returns either FormConstraintCheckEach or FormConstraintCheckLast.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"FormConstraintCheckLast: q(x) = f(μ1(x) * μ2(x) * μ3(x))\nFormConstraintCheckEach: q(x) = f(f(μ1(x) * μ2(x)) * μ3(x))","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_form_check_strategy\nFormConstraintCheckEach\nFormConstraintCheckLast\nFormConstraintCheckPickDefault","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_form_check_strategy","page":"Custom functional form","title":"ReactiveMP.default_form_check_strategy","text":"default_form_check_strategy(form_constraint)\n\nReturns a default check strategy (e.g. FormConstraintCheckEach or FormConstraintCheckEach) for a given form constraint object.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckEach","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckEach","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the messages product after each product in an equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed after each subsequent prod function.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckLast","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckLast","text":"FormConstraintCheckEach\n\nThis form constraint check strategy checks functional form of the last messages product in the equality chain. Usually if a variable has been connected to multiple nodes we want to perform multiple prod to obtain a posterior marginal. With this form check strategy constrain_form function will be executed only once after all subsequenct prod functions have been executed.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.FormConstraintCheckPickDefault","page":"Custom functional form","title":"ReactiveMP.FormConstraintCheckPickDefault","text":"FormConstraintCheckPickDefault\n\nThis form constraint check strategy simply fallbacks to a default check strategy for a given form constraint. \n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#Prod-constraint","page":"Custom functional form","title":"Prod constraint","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Every custom functional form must implement a new method for the default_prod_constraint function that returns a proper prod_constraint object.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"default_prod_constraint","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.default_prod_constraint","page":"Custom functional form","title":"ReactiveMP.default_prod_constraint","text":"default_prod_constraint(form_constraint)\n\nReturns a default prod constraint needed to apply a given form_constraint. For most form constraints this function returns ProdGeneric.\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#Constrain-form,-a.k.a-f","page":"Custom functional form","title":"Constrain form, a.k.a f","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"The main function that a custom functional form must implement, which we referred to as f in the beginning of this section, is the constrain_form function.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"constrain_form","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(constraint, something)\n\nThis function applies a given form constraint to a given object. \n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#custom-functional-form-example","page":"Custom functional form","title":"Custom Functional Form Example","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"In this demo, we show how to build a custom functional form constraint that is compatible with the ReactiveMP.jl inference backend. An important part of the functional form constraint implementation is the prod function in the BayesBase package. We present a relatively simple use case, which may not be very practical but serves as a straightforward step-by-step guide.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Assume that we want a specific posterior marginal of some random variable in our model to have a specific Gaussian parameterization, such as mean-precision. Here, how we can achieve this with our custom MeanPrecisionFormConstraint functional form constraint:","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, ExponentialFamily, Distributions, BayesBase\n\n# First, we define our functional form structure with no fields\nstruct MeanPrecisionFormConstraint <: AbstractFormConstraint end\n\nReactiveMP.default_form_check_strategy(::MeanPrecisionFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MeanPrecisionFormConstraint) = GenericProd()\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution) \n # This assumes that the given `distribution` object has `mean` and `precision` defined.\n # These quantities might be approximated using other methods, such as Laplace approximation.\n m = mean(distribution) # or approximate with some other method\n p = precision(distribution) # or approximate with some other method\n return NormalMeanPrecision(m, p)\nend\n\nfunction ReactiveMP.constrain_form(::MeanPrecisionFormConstraint, distribution::BayesBase.ProductOf)\n # `ProductOf` is a special case. Read more about this type in the corresponding \n # documentation section of the `BayesBase` package.\n # ... \nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MeanPrecisionFormConstraint())\n\nconstrain_form(constraint, NormalMeanVariance(0, 2))","category":"page"},{"location":"custom/custom-functional-form/#Wrapped-Form-Constraints","page":"Custom functional form","title":"Wrapped Form Constraints","text":"","category":"section"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Some constraint objects might not be subtypes of AbstractFormConstraint. This can occur, for instance, if the object is defined in a different package or needs to subtype a different abstract type. In such cases, ReactiveMP expects users to pass a WrappedFormConstraint object, which wraps the original object and makes it compatible with the ReactiveMP inference backend. Note that the ReactiveMP.preprocess_form_constraints function automatically wraps all objects that are not subtypes of AbstractFormConstraint.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"Additionally, objects wrapped by WrappedFormConstraints may implement the ReactiveMP.prepare_context function. This function's output will be stored in the WrappedFormConstraints along with the original object. If prepare_context is implemented, the constrain_form function will take three arguments: the original constraint, the context, and the object that needs to be constrained.","category":"page"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"ReactiveMP.WrappedFormConstraint\nReactiveMP.prepare_context\nReactiveMP.constrain_form(::ReactiveMP.WrappedFormConstraint, something)","category":"page"},{"location":"custom/custom-functional-form/#ReactiveMP.WrappedFormConstraint","page":"Custom functional form","title":"ReactiveMP.WrappedFormConstraint","text":"WrappedFormConstraint(constraint, context)\n\nThis is a wrapper for a form constraint object. It allows to pass additional context to the constrain_form function. By default all objects that are not sub-typed from AbstractFormConstraint are wrapped into this object. Use ReactiveMP.prepare_context to provide an extra context for a given form constraint, that can be reused between multiple constrain_form calls.\n\n\n\n\n\n","category":"type"},{"location":"custom/custom-functional-form/#ReactiveMP.prepare_context","page":"Custom functional form","title":"ReactiveMP.prepare_context","text":"prepare_context(constraint)\n\nThis function prepares a context for a given form constraint. Returns WrappedFormConstraintNoContext if no context is needed (the default behaviour).\n\n\n\n\n\n","category":"function"},{"location":"custom/custom-functional-form/#ReactiveMP.constrain_form-Tuple{ReactiveMP.WrappedFormConstraint, Any}","page":"Custom functional form","title":"ReactiveMP.constrain_form","text":"constrain_form(wrapped::WrappedFormConstraint, something)\n\nThis function unwraps the wrapped object and calls constrain_form function with the provided context. If the context is not provided, simply calls constrain_form with the wrapped constraint. Otherwise passes the context to the constrain_form function as the second argument.\n\n\n\n\n\n","category":"method"},{"location":"custom/custom-functional-form/","page":"Custom functional form","title":"Custom functional form","text":"using ReactiveMP, Distributions, BayesBase, Random\n\n# First, we define our custom form constraint that creates a set of samples\n# Note that this is not a subtype of `AbstractFormConstraint`\nstruct MyCustomSampleListFormConstraint end\n\n# Note that we still need to implement `default_form_check_strategy` and `default_prod_constraint` functions\n# which are necessary for the `ReactiveMP` inference backend\nReactiveMP.default_form_check_strategy(::MyCustomSampleListFormConstraint) = FormConstraintCheckLast()\nReactiveMP.default_prod_constraint(::MyCustomSampleListFormConstraint) = GenericProd()\n\n# We implement the `prepare_context` function, which returns a random number generator\nfunction ReactiveMP.prepare_context(constraint::MyCustomSampleListFormConstraint)\n return Random.default_rng()\nend\n\n# We implement the `constrain_form` function, which returns a set of samples\nfunction ReactiveMP.constrain_form(constraint::MyCustomSampleListFormConstraint, context, distribution)\n return rand(context, distribution, 10)\nend\n\nconstraint = ReactiveMP.preprocess_form_constraints(MyCustomSampleListFormConstraint())\n\nconstrain_form(constraint, Normal(0, 10))","category":"page"},{"location":"custom/custom-addons/#custom-addons","page":"Custom addons","title":"Custom Addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Standard message passing schemes only pass along distributions to other nodes. However, for more advanced usage, there might be a need for passing along additional information in messages and/or marginals. One can for example think of passing along the scaling of the distribution or some information that specifies how the message or marginal was computed, i.e. which messages were used for its computation and which node was preceding it. Another use cases is saving extra debugging information inside messages themselves, e.g. what arguments have been used to compute a message.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Addons provide a solution here. Basically, addons are structures that contain extra information that are passed along the graph with messages and marginals in a tuple. These addons can be extracted using the getaddons(message/marginal) function. Its usage and operations can differ significantly for each application, yet below gives a concise overview on how to implement them on your own.","category":"page"},{"location":"custom/custom-addons/#Example","page":"Custom addons","title":"Example","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Suppose that we wish to create an addon that counts the number of computations that preceded some message or marginal. This addon can be created by adding the file src/addons/count.jl and by including it in the ReactiveMP.jl file.","category":"page"},{"location":"custom/custom-addons/#Step-1:-Creating-the-addon-structure","page":"Custom addons","title":"Step 1: Creating the addon structure","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"Let's start by defining our new addon structure. This might seem daunting, but basically only requires us to specify the information that we would like to collect. Just make sure that it is specified as a subtype of AbstractAddon. In our example this becomes:","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"struct AddonCount{T} <: AbstractAddon\n count :: T\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"You can add additional fields or functions for improved handling, such as get_count() or show() functions.","category":"page"},{"location":"custom/custom-addons/#Step-2:-Compute-addon-value-after-computing-a-message","page":"Custom addons","title":"Step 2: Compute addon value after computing a message","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"As a second step we need to specify how the addon behaves when a new message is computed in a factor node. For this purpose we need to implement a specialized version of the message_mapping_addon() function. This function accepts the mapping variables of the factor node and updates the addons by extending the tuple.","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"In our example we could write","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"# This specification assumes that the default value for addon is `AddonCount(nothing)`\nfunction message_mapping_addon(::AddonCount{Nothing}, mapping, messages, marginals, result, addons)\n\n # get number of operations of messages\n message_count = 0\n for message in messages\n message_count += getcount(message)\n end\n\n # get number of operations of marginals\n marginal_count = 0\n for marginal in marginals\n marginal_count += getcount(marginal)\n end\n\n # extend addons with AddonCount() structure\n return AddonCount(message_count + marginal_count + 1)\nend\n","category":"page"},{"location":"custom/custom-addons/#Step-3:-Computing-products","page":"Custom addons","title":"Step 3: Computing products","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"The goal is to update the AddonCount structure when we multiply 2 messages. As a result, we need to write a function that allows us to define this behaviour. This function is called multiply_addons and accepts 5 arguments. In our example this becomes","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"function multiply_addons(left_addon::AddonCount, right_addon::AddonCount, new_dist, left_dist, right_dist)\n return AddonCount(left_addon.count + right_addon.count + 1)\nend","category":"page"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"here we add the number of operations from the addons that are being multiplied and we add one (for the current operation). we are aware that this is likely not valid for iterative message passing schemes, but it still serves as a nice example. the left_addon and right_addon argument specify the addoncount objects that are being multiplied. corresponding to these addons, there are the distributions left_dist and right_dist, which might contain information for computing the product. the new distribution new_dist ∝ left_dist * right_dist is also passed along for potentially reusing the result of earlier computations.","category":"page"},{"location":"custom/custom-addons/#More-information","page":"Custom addons","title":"More information","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"For more advanced information check the implementation of the log-scale or memory addons.","category":"page"},{"location":"custom/custom-addons/#Built-in-addons","page":"Custom addons","title":"Built-in addons","text":"","category":"section"},{"location":"custom/custom-addons/","page":"Custom addons","title":"Custom addons","text":"ReactiveMP.AddonDebug","category":"page"},{"location":"custom/custom-addons/#ReactiveMP.AddonDebug","page":"Custom addons","title":"ReactiveMP.AddonDebug","text":"AddonDebug(f :: Function)\n\nThis addon calls the function f over the output of the message mapping and products. The result is expected to be boolean and when returning true, it will throw an error with the debug information. Common applications of this addon are to check for NaNs and Infs in the messages and marginals. \n\nExample\n\ncheckfornans(x) = isnan(x)\ncheckfornans(x::AbstractArray) = any(checkfornans.(x))\ncheckfornans(x::Tuple) = any(checkfornans.(x))\n\naddons = (AddonDebug(dist -> checkfornans(params(dist))),)\n\n\n\n\n\n","category":"type"},{"location":"extra/methods/#lib-using-methods","page":"Exported methods","title":"Using methods from ReactiveMP","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In the Julia programming language (in contrast to Python for example) the most common way of loading a module is:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"A nice explanation about how modules/packages work in Julia can be found in the official documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"In a nutshell, Julia automatically resolves all name collisions and there is no a lot of benefit of importing specific names, e.g.:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"One of the reasons for that is that Julia uses multiple-dispatch capabilities to merge names automatically and will indicate (with a warning) if something went wrong or names have unresolvable collisions on types. As a small example of this feature consider the following small import example:","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"import ReactiveMP: mean as mean_from_reactivemp\nimport Distributions: mean as mean_from_distributions\nimport BayesBase: mean as mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_distributions","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean_from_reactivemp === mean_from_bayes_base","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Even though we import mean function from different packages they actually refer to the same object. Worth noting that this is not always the case - Julia will print a warning in case it finds unresolvable conflicts and usage of such functions will be disallowed unless user import them specifically. Read more about this in the section of the Julia's documentation.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"# It is easier to let Julia resolve names automatically\n# Julia will not overwrite `mean` that is coming from both packages\nusing ReactiveMP, Distributions, BayesBase, ExponentialFamily","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(Normal(0.0, 1.0)) # `Normal` is an object from `Distributions.jl`","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"mean(NormalMeanVariance(0.0, 1.0)) # `NormalMeanVariance` is an object from `ReactiveMP.jl`","category":"page"},{"location":"extra/methods/#lib-list-methods","page":"Exported methods","title":"List of available methods","text":"","category":"section"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"Below you can find a list of exported methods from ReactiveMP.jl. All methods (even private) can be always accessed with ReactiveMP. prefix, e.g ReactiveMP.mean.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"note: Note\nSome exported names are (for legacy reasons) intended for private usage only. As a result some of these methods do not have a proper associated documentation with them. We constantly improve ReactiveMP.jl library and continue to add better documentation for many exported methods, but a small portion of these methods could be removed from this list in the future.","category":"page"},{"location":"extra/methods/","page":"Exported methods","title":"Exported methods","text":"using ReactiveMP #hide\nforeach(println, names(ReactiveMP))","category":"page"},{"location":"lib/rules/#lib-rules","page":"Message update rules","title":"Rules implementation","text":"","category":"section"},{"location":"lib/rules/#lib-message-rules","page":"Message update rules","title":"Message update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"rule\n@rule\n@call_rule\nReactiveMP.call_rule_make_node\nReactiveMP.call_rule_macro_parse_fn_args\nReactiveMP.call_rule_is_node_required\nReactiveMP.rule_macro_parse_on_tag\nReactiveMP.rule_macro_parse_fn_args\nReactiveMP.rule_macro_check_fn_args","category":"page"},{"location":"lib/rules/#ReactiveMP.rule","page":"Message update rules","title":"ReactiveMP.rule","text":"rule(fform, on, vconstraint, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute an outbound message for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Outbound interface's tag for which a message has to be computed, e.g. ::Val{:out} or ::Val{:μ}\nvconstraint: Variable constraints for an outbound interface, e.g. Marginalisation or MomentMatching\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\naddons: Extra addons information\n__node: Node reference\n\nFor all available rules, see ReactiveMP.print_rules_table().\n\nSee also: @rule, marginalrule, @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@rule","page":"Message update rules","title":"ReactiveMP.@rule","text":"@rule NodeType(:Edge, Constraint) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @rule macro help to define new methods for the rule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nEdge: edge label, usually edge labels are defined with the @node macro\nConstrain: DEPRECATED, please just use the Marginalisation label\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nHere are various examples of the @rule macro usage:\n\nBelief-Propagation (or Sum-Product) message update rule for the NormalMeanVariance node toward the :μ edge with the Marginalisation constraint. Input arguments are m_out and m_v, which are the messages from the corresponding edges out and v and have the type PointMass.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (m_out::PointMass, m_v::PointMass) = NormalMeanVariance(mean(m_out), mean(m_v))\n\nMean-field message update rule for the NormalMeanVariance node towards the :μ edge with the Marginalisation constraint. Input arguments are q_out and q_v, which are the marginals on the corresponding edges out and v of type Any.\n\n@rule NormalMeanVariance(:μ, Marginalisation) (q_out::Any, q_v::Any) = NormalMeanVariance(mean(q_out), mean(q_v))\n\nStructured Variational message update rule for the NormalMeanVariance node towards the :out edge with the Marginalisation constraint. Input arguments are m_μ, which is a message from the μ edge of type UnivariateNormalDistributionsFamily, and q_v, which is a marginal on the v edge of type Any.\n\n@rule NormalMeanVariance(:out, Marginalisation) (m_μ::UnivariateNormalDistributionsFamily, q_v::Any) = begin\n m_μ_mean, m_μ_cov = mean_cov(m_μ)\n return NormalMeanVariance(m_μ_mean, m_μ_cov + mean(q_v))\nend\n\nSee also: rule, marginalrule, [@marginalrule], @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_rule","page":"Message update rules","title":"ReactiveMP.@call_rule","text":"@call_rule NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe @call_rule macro helps to call the rule method with an easier syntax. The structure of the macro is almost the same as in the @rule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nThe @call_rule accepts optional list of options before the functional form specification, for example:\n\n@call_rule [ return_addons = true ] NodeType(:edge, Constraint) (argument1 = value1, argument2 = value2, ..., [ meta = ..., addons = ... ])\n\nThe list of available options is:\n\nreturn_addons - forces the @call_rule to return the tuple of (result, addons)\nfallback - specifies the fallback rule to use in case the rule is not defined for the given NodeType and specified arguments\n\nSee also: @rule, rule, @call_marginalrule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.call_rule_make_node","page":"Message update rules","title":"ReactiveMP.call_rule_make_node","text":"call_rule_create_node(::Type{ NodeType }, fformtype)\n\nCreates a node object that will be used inside @call_rule macro. \n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.call_rule_macro_parse_fn_args","text":"call_rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message and marginal calling rules specification. \n\n@call_rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ = NormalMeanPrecision(...), m_τ = PointMass(...)) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, value) elements, specname, name prefix and proxy type. Returns parsed names without prefix and proxied values\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.call_rule_is_node_required","page":"Message update rules","title":"ReactiveMP.call_rule_is_node_required","text":"call_rule_is_node_required(fformtype)\n\nReturns either CallRuleNodeRequired() or CallRuleNodeNotRequired() depending on if a specific fformtype requires an access to the corresponding node in order to compute a message update rule. Returns CallRuleNodeNotRequired() for all known functional forms by default and CallRuleNodeRequired() for all unknown functional forms.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_on_tag","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_on_tag","text":"rule_macro_parse_on_tag(expression)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an on tag for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (...) = begin \n ^^^^\n `on` tag\n ...\nend\n\nor \n\n@rule NormalMixture((:m, k), Marginalisation) (...) = begin \n ^^^^^^^\n `on` tag\n ...\nend\n\nAccepts either a quoted symbol expressions or a (name, index) tuple expression. Returns name expression, index expression and index initialisation expression.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_parse_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_parse_fn_args","text":"rule_macro_parse_fn_args(inputs; specname, prefix, proxy)\n\nDo not use this function directly. This function is private and does not belong to the public API.\n\nThis function is used to parse an arguments tuple for message rules and marginal rules specification. \n\n@rule MvNormalMeanPrecision(:out, Marginalisation) (m_μ::NormalMeanPrecision, m_τ::PointMass) = begin \n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n `arguments` vector\n ...\nend\n\nAccepts a vector of (name, type) elements, specname, name prefix and proxy type. Returns parsed names without prefix, proxied types and initialisation code block.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.rule_macro_check_fn_args","page":"Message update rules","title":"ReactiveMP.rule_macro_check_fn_args","text":"rule_macro_check_fn_args(inputs; allowed_inputs, allowed_prefixes)\n\nThis function checks if all inputs are either in the allowed_inputs or have prefixes in the allowed_prefixes.\n\nSee also: @rule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-marginal-rules","page":"Message update rules","title":"Marginal update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"marginalrule\n@marginalrule\n@call_marginalrule","category":"page"},{"location":"lib/rules/#ReactiveMP.marginalrule","page":"Message update rules","title":"ReactiveMP.marginalrule","text":"marginalrule(fform, on, mnames, messages, qnames, marginals, meta, __node)\n\nThis function is used to compute a local joint marginal for a given node\n\nArguments\n\nfform: Functional form of the node in form of a type of the node, e.g. ::Type{ <: NormalMeanVariance } or ::typeof(+)\non: Local joint marginal tag , e.g. ::Val{ :mean_precision } or ::Val{ :out_mean_precision }\nmnames: Ordered messages names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmessages: Tuple of message of the same length as mnames used to compute an outbound message\nqnames: Ordered marginal names in form of the Val type, eg. ::Val{ (:mean, :precision) }\nmarginals: Tuple of marginals of the same length as qnames used to compute an outbound message\nmeta: Extra meta information\n__node: Node reference\n\nSee also: rule, @rule @marginalrule\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#ReactiveMP.@marginalrule","page":"Message update rules","title":"ReactiveMP.@marginalrule","text":"@marginalrule NodeType(:Cluster) (Arguments..., [ meta::MetaType ]) = begin\n # rule body\n return ...\nend\n\nThe @marginalrule macro help to define new methods for the marginalrule function. It works particularly well in combination with the @node macro. It has a specific structure, which must specify:\n\nNodeType: must be a valid Julia type. If some attempt to define a rule for a Julia function (for example +), use typeof(+)\nCluster: edge cluster that contains joined edge labels with the _ symbol. Usually edge labels are defined with the @node macro\nArguments: defines a list of the input arguments for the rule\nm_* prefix indicates that the argument is of type Message from the edge *\nq_* prefix indicates that the argument is of type Marginal on the edge *\nMeta::MetaType - optionally, a user can specify a Meta object of type MetaType. This can be useful is some attempts to try different rules with different approximation methods or if the rule itself requires some temporary storage or cache. The default meta is nothing.\n\nThe @marginalrule can return a NamedTuple in the return statement. This would indicate some variables in the joint marginal for the Cluster are independent and the joint itself is factorised. For example if some attempts to compute a marginal for the q(x, y) it is possible to return (x = ..., y = ...) as the result of the computation to indicate that q(x, y) = q(x)q(y).\n\nHere are various examples of the @marginalrule macro usage:\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages \n\nfrom the out and μ edges respectively, and q_τ which is the marginal on the edge τ.\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::UnivariateNormalDistributionsFamily, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n xi_out, W_out = weightedmean_precision(m_out)\n xi_μ, W_μ = weightedmean_precision(m_μ)\n\n W_bar = mean(q_τ)\n\n W = [W_out+W_bar -W_bar; -W_bar W_μ+W_bar]\n xi = [xi_out; xi_μ]\n\n return MvNormalWeightedMeanPrecision(xi, W)\nend\n\nMarginal computation rule around the NormalMeanPrecision node for the q(out, μ). The rule accepts arguments m_out and m_μ, which are the messages from the \n\nout and μ edges respectively, and q_τ which is the marginal on the edge τ. In this example the result of the computation is a NamedTuple\n\n@marginalrule NormalMeanPrecision(:out_μ) (m_out::PointMass, m_μ::UnivariateNormalDistributionsFamily, q_τ::Any) = begin\n return (out = m_out, μ = prod(ClosedProd(), NormalMeanPrecision(mean(m_out), mean(q_τ)), m_μ))\nend\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@call_marginalrule","page":"Message update rules","title":"ReactiveMP.@call_marginalrule","text":"@call_marginalrule NodeType(:edge) (argument1 = value1, argument2 = value2, ..., [ meta = ... ])\n\nThe @call_marginalrule macro helps to call the marginalrule method with an easier syntax. The structure of the macro is almost the same as in the @marginalrule macro, but there is no begin ... end block, but instead each argument must have a specified value with the = operator.\n\nSee also: @marginalrule, marginalrule, @call_rule\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-tests","page":"Message update rules","title":"Testing utilities for the update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.@test_rules\nReactiveMP.@test_marginalrules","category":"page"},{"location":"lib/rules/#ReactiveMP.@test_rules","page":"Message update rules","title":"ReactiveMP.@test_rules","text":"@test_rules [options] rule [ test_entries... ]\n\nThe @test_rules macro generates test cases for message update rules for probabilistic programming models that follow the \"message passing\" paradigm. It takes a rule specification as input and generates a set of tests based on that specification. This macro is provided by ReactiveMP.\n\nNote: The Test module must be imported explicitly. The @test_rules macro tries to use the @test macro, which must be defined globally.\n\nArguments\n\nThe macro takes three arguments:\n\noptions: An optional argument that specifies the options for the test generation process. See below for details.\nrule: A rule specification in the same format as the @rule macro, e.g. Beta(:out, Marginalisation) or NormalMeanVariance(:μ, Marginalisation).\ntest_entries: An array of named tuples (input = ..., output = ...). The input entry has the same format as the input for the @rule macro. The output entry specifies the expected output.\n\nOptions\n\nThe following options are available:\n\ncheck_type_promotion: By default, this option is set to false. If set to true, the macro generates an extensive list of extra tests that aim to check the correct type promotion within the tests. For example, if all inputs are of type Float32, then the expected output should also be of type Float32. See the paramfloattype and convert_paramfloattype functions for details.\natol: Sets the desired accuracy for the tests. The tests use the custom_rule_isapprox function from ReactiveMP to check if outputs are approximately the same. This argument can be either a single number or an array of key => value pairs.\nextra_float_types: A set of extra float types to be used in the check_type_promotion tests. This argument has no effect if check_type_promotion is set to false.\n\nThe default values for the atol option are:\n\nFloat32: 1e-4\nFloat64: 1e-6\nBigFloat: 1e-8\n\nExamples\n\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (m_a = PointMass(1.0), m_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (m_a = PointMass(2.0), m_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (m_a = PointMass(3.0), m_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\n@test_rules [check_type_promotion = true] Beta(:out, Marginalisation) [\n (input = (q_a = PointMass(1.0), q_b = PointMass(2.0)), output = Beta(1.0, 2.0)),\n (input = (q_a = PointMass(2.0), q_b = PointMass(2.0)), output = Beta(2.0, 2.0)),\n (input = (q_a = PointMass(3.0), q_b = PointMass(3.0)), output = Beta(3.0, 3.0))\n]\n\nSee also: ReactiveMP.@test_marginalrules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#ReactiveMP.@test_marginalrules","page":"Message update rules","title":"ReactiveMP.@test_marginalrules","text":"@test_marginalrules [options] rule [ test_entries... ]\n\nEffectively the same as @test_rules, but for marginal computation rules. See the documentation for @test_rules for more info.\n\nSee also: ReactiveMP.@test_rules\n\n\n\n\n\n","category":"macro"},{"location":"lib/rules/#lib-rules-fallbacks","page":"Message update rules","title":"Rule fallbacks","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"ReactiveMP.NodeFunctionRuleFallback\nReactiveMP.nodefunction","category":"page"},{"location":"lib/rules/#ReactiveMP.NodeFunctionRuleFallback","page":"Message update rules","title":"ReactiveMP.NodeFunctionRuleFallback","text":"NodeFunctionRuleFallback(extractfn = mean)\n\nA fallback rule for Stochastic nodes that uses a specified function (default: mean) to transform messages and marginals into a value. It calls the nodefunction method to create the message.\n\nWhen a node is defined with the @node macro:\n\n1.\tThe nodefunction typically calls logpdf associated with the node's distribution. 2.\tThe first edge in the @node specification is used to evaluate logpdf at. 3.\tOther edges are used to instantiate the associated distribution object.\n\njulia> using ReactiveMP, BayesBase, Distributions\n\njulia> struct MyBeta{A, B} <: ContinuousUnivariateDistribution\n a::A\n b::B\n end\n\njulia> BayesBase.logpdf(d::MyBeta, x) = logpdf(Beta(d.a, d.b), x)\n\njulia> BayesBase.insupport(d::MyBeta, x::Real) = true\n\njulia> @node MyBeta Stochastic [out, a, b]\n\njulia> message = @call_rule [fallback = NodeFunctionRuleFallback()] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2));\n\njulia> logpdf(message, 0.5)\n-0.5017644952110732\n\njulia> message = @call_rule [fallback = NodeFunctionRuleFallback(mode)] MyBeta(:out, Marginalisation) (m_a = Beta(2, 3), m_b = Beta(3, 2)); # evaluate at `mode`\n\njulia> logpdf(message, 0.5)\n-0.5954237415153454\n\n\n\n\n\n","category":"type"},{"location":"lib/rules/#ReactiveMP.nodefunction","page":"Message update rules","title":"ReactiveMP.nodefunction","text":"nodefunction(::Type{T}) where {T}\n\nReturns a function that represents a node of type T. The function typically takes arguments that represent the node's input and output variables in the same order as defined in the @node macro.\n\n\n\n\n\n","category":"function"},{"location":"lib/rules/#lib-rules-table","page":"Message update rules","title":"Table of available update rules","text":"","category":"section"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"note: Note\nThe list below has been automatically generated with the ReactiveMP.print_rules_table() function.","category":"page"},{"location":"lib/rules/","page":"Message update rules","title":"Message update rules","text":"using ReactiveMP, Markdown\nMarkdown.parse(ReactiveMP.print_rules_table())","category":"page"},{"location":"lib/nodes/bifm/#lib-nodes-bifm","page":"BIFM","title":"BIFM node","text":"","category":"section"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"See also BIFM tutorial for a comprehensive guide on using BIFM node in RxInfer.jl.","category":"page"},{"location":"lib/nodes/bifm/","page":"BIFM","title":"BIFM","text":"ReactiveMP.BIFM\nReactiveMP.BIFMMeta\nReactiveMP.BIFMHelper","category":"page"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFM","page":"BIFM","title":"ReactiveMP.BIFM","text":"The BIFM node is a node that can be used as a substitution for a state space model. It includes all factor of the time slice to perform efficient inference. This node needs to be used in conjuction with the BIFMHelper node for efficient inference.\n\nout ~ BIFM(in, zprev, znext)\n\nInterfaces:\n\nout - latent output (observation) of the BIFM node\nin - latent input of the BIFM node\nzprev - previous latent state of the BIFM node\nznext - next latent state of the BIFM node\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\nExample\n\n# set priors\nz_prior ~ MvNormalMeanPrecision(zeros(latent_dim), diagm(ones(latent_dim)))\nz_tmp ~ BIFMHelper(z_prior)\n\n# update last/previous hidden state\nz_prev = z_tmp\n\n# loop through observations\nfor i in 1:nr_samples\n\n # specify input as random variable\n u[i] ~ MvNormalMeanPrecision(μu, Wu)\n\n # specify observation\n xt[i] ~ BIFM(u[i], z_prev, z[i]) where { meta = BIFMMeta(A, B, C) }\n x[i] ~ MvNormalMeanPrecision(xt[i], Wx)\n \n # update last/previous hidden state\n z_prev = z[i]\n\nend\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMMeta","page":"BIFM","title":"ReactiveMP.BIFMMeta","text":"The BIFMMeta structure contains all characterizing information of the BIFM node. In addition, it stores intermediate variables for efficient computations.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/bifm/#ReactiveMP.BIFMHelper","page":"BIFM","title":"ReactiveMP.BIFMHelper","text":"The BIFMHelper node is a node required to perform efficient message passing inconjuction with the BIFM node. It is required to switch from the backward pass with messages to the forward pass with marginals.\n\nout ~ BIFMHelper(in)\n\nInterfaces:\n\nout - output of the BIFMHelper node, should be connected to the state space model.\nin - input of the BIFMHelper node, should be connected to the prior for the latent state.\n\nNote: When performing inference, first subscribe to the marginals (in the order: z, out, in) and then to the free energy score function.\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#lib-nodes-equality","page":"Equality node","title":"Equality node","text":"","category":"section"},{"location":"lib/nodes/equality/","page":"Equality node","title":"Equality node","text":"ReactiveMP.EqualityNode\nReactiveMP.EqualityChain","category":"page"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityNode","page":"Equality node","title":"ReactiveMP.EqualityNode","text":"EqualityNode\n\nGeneric idea of an equality node is to keep track of intermediate left and right messages in a convenient manner so they can be reused during prod for random variables with large degree.\n\n<- left –––- right -> ––- | = | ––– –––- | | outbound\n\nAttributes:\n\nleft: An observable that indicates that left message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\nright: An observable that indicates that right message can be computed, always sends missing since we are not interested in actual value. Can be treated as notification.\ncache_left: Keeps cached value for left outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\ncache_right: Keeps cached value for right outbound message, node itself does not track if cache is valid or not. Cache integrity is tracked by EqualityChain.\n\nSee also: EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"lib/nodes/equality/#ReactiveMP.EqualityChain","page":"Equality node","title":"ReactiveMP.EqualityChain","text":"EqualityChain\n\n\n\n\n\n","category":"type"},{"location":"#ReactiveMP.jl","page":"Introduction","title":"ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Julia package for reactive message passing Bayesian inference engine on a factor graph.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"note: Note\nThis package exports only an inference engine, for the full ecosystem with convenient model and constraints specification we refer user to the RxInfer.jl package and its documentation.","category":"page"},{"location":"#Ideas-and-principles-behind-ReactiveMP.jl","page":"Introduction","title":"Ideas and principles behind ReactiveMP.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"ReactiveMP.jl is a particular implementation of message passing on factor graphs, which does not create any specific message passing schedule in advance, but rather reacts on changes in the data source (hence reactive in the name of the package). The detailed explanation of the ideas and principles behind the Reactive Message Passing can be found in PhD disseration of Dmitry Bagaev titled Reactive Probabilistic Programming for Scalable Bayesian Inference (link2, link3).","category":"page"},{"location":"#Examples-and-tutorials","page":"Introduction","title":"Examples and tutorials","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The ReactiveMP.jl package is intended for advanced users with a deep understanding of message passing principles. Accesible tutorials and examples are available in the RxInfer documentation.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Pages = [\n \"lib/nodes.md\",\n \"lib/message.md\",\n \"lib/marginal.md\",\n \"lib/rules.md\",\n \"lib/nodes.md\",\n \"lib/helpers.md\",\n \"lib/algebra.md\",\n \"extra/contributing.md\",\n \"extra/extensions.md\",\n \"extra/methods.md\",\n]\nDepth = 2","category":"page"},{"location":"#Index","page":"Introduction","title":"Index","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"lib/helpers/#lib-helpers","page":"Helper utils","title":"Helper utilities","text":"","category":"section"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP implements various structures/functions/methods as \"helper\" structures that might be useful in various contexts.","category":"page"},{"location":"lib/helpers/","page":"Helper utils","title":"Helper utils","text":"ReactiveMP.SkipIndexIterator\nReactiveMP.skipindex\nReactiveMP.MacroHelpers.proxy_type\nReactiveMP.MacroHelpers.ensure_symbol\nReactiveMP.MacroHelpers.@proxy_methods\nReactiveMP.MacroHelpers.upper_type\nReactiveMP.MacroHelpers.bottom_type","category":"page"},{"location":"lib/helpers/#ReactiveMP.SkipIndexIterator","page":"Helper utils","title":"ReactiveMP.SkipIndexIterator","text":"SkipIndexIterator\n\nA special type of iterator that simply iterates over internal iterator, but skips index skip.\n\nArguments\n\niterator: internal iterator\nskip: index to skip (integer)\n\nSee also: skipindex\n\n\n\n\n\n","category":"type"},{"location":"lib/helpers/#ReactiveMP.skipindex","page":"Helper utils","title":"ReactiveMP.skipindex","text":"skipindex(iterator, skip)\n\nCreation operator for SkipIndexIterator.\n\njulia> s = ReactiveMP.skipindex(1:3, 2)\n2-element ReactiveMP.SkipIndexIterator{Int64, UnitRange{Int64}}:\n 1\n 3\n\njulia> collect(s)\n2-element Vector{Int64}:\n 1\n 3\n\nSee also: SkipIndexIterator\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.proxy_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.proxy_type","text":"proxy_type(proxy, type)\n\nReturns a type wrapped with a proxy type in a form of ProxyType{ <: Type }.\n\nArguments\n\nproxy: Proxy type used to wrap type\ntype: Type to be wrapped\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.ensure_symbol","page":"Helper utils","title":"ReactiveMP.MacroHelpers.ensure_symbol","text":"ensure_symbol(input)\n\nThis function ensures that the given argument has a Symbol type\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.@proxy_methods","page":"Helper utils","title":"ReactiveMP.MacroHelpers.@proxy_methods","text":"@proxy_methods(proxy_type, proxy_getter, proxy_methods)\n\nGenerates proxy methods for a specified proxy_type using proxy_getter. For example:\n\n@proxy_methods Message getdata [ \n Distributions.mean, \n Distributions.var \n]\n\ngenerates:\n\nDistributions.mean(proxy::Message) = Distributions.mean(getdata(proxy))\nDistributions.var(proxy::Message) = Distributions.mean(getdata(proxy))\n\n\n\n\n\n","category":"macro"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.upper_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.upper_type","text":"upper_type(type)\n\nThis function returns Type{ <: T } expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be extended\n\n\n\n\n\n","category":"function"},{"location":"lib/helpers/#ReactiveMP.MacroHelpers.bottom_type","page":"Helper utils","title":"ReactiveMP.MacroHelpers.bottom_type","text":"bottom_type(type)\n\nThis function returns T expression for the following input expressions:\n\ntypeof(T)\nType{ <: T }\nType{ T }\nT\n\nArguments\n\ntype: Type expression to be lowered\n\n\n\n\n\n","category":"function"}]
+}
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index 000000000..3c02c8547
--- /dev/null
+++ b/v4.3.0/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v4.3.0";
diff --git a/versions.js b/versions.js
index 043c9551a..665a3a5d1 100644
--- a/versions.js
+++ b/versions.js
@@ -1,5 +1,10 @@
var DOC_VERSIONS = [
"stable",
+ "v4.3",
+ "v4.2",
+ "v4.1",
+ "v4.0",
+ "v3.14",
"v3.13",
"v3.12",
"v3.11",
@@ -26,5 +31,5 @@ var DOC_VERSIONS = [
"v1.0",
"dev",
];
-var DOCUMENTER_NEWEST = "v3.13.0";
+var DOCUMENTER_NEWEST = "v4.3.0";
var DOCUMENTER_STABLE = "stable";