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2.1755667174542923</code></pre><p>Select the last value to get the sample entropy for m = 4.</p><pre><code class="language-julia hljs">Samp[end]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2.1755667174542923</code></pre><p>Calculate the sample entropy for each embedding dimension (m) from 0 to 4 with a time delay (tau) of 2 samples.</p><pre><code class="language-julia hljs">Samp, Phi1, Phi2 = SampEn(X, m = 4, tau = 2)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([2.178923612371957, 2.183323250654987, 2.188041075511569, 2.189184333017654, 2.1440802180581136], [1.414258e6, 159224.0, 17843.0, 1998.0, 234.0], [1.24975e7, 1.413233e6, 159119.0, 17838.0, 1997.0])</code></pre><p>Import a signal of uniformly distributed random numbers in the range [-1, 1] and calculate the sample entropy for an embedding dimension (m) of 5, a time delay of 2, and a threshold radius of 0.075. Return the conditional probability (Vcp) and the number of overlapping matching vector pairs of lengths m+1 (Ka) and m (Kb), respectively.</p><pre><code class="language-julia hljs">Samp, _, _, Vcp_Ka_Kb = SampEn(X, m = 5, tau = 2, r = 0.075, Vcp = true)
Vcp, Ka, Kb = Vcp_Ka_Kb</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Vcp = 0.00018629728228987074
Ka = 92
Kb = 3943</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Examples/">« Notes on Examples</a><a class="docs-footer-nextpage" href="../Example2/">Ex.2: Permutation Entropy »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.5 on <span class="colophon-date" title="Sunday 24 March 2024 21:55">Sunday 24 March 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Kb = 3943</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Examples/">« Notes on Examples</a><a class="docs-footer-nextpage" href="../Example2/">Ex.2: Permutation Entropy »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.5 on <span class="colophon-date" title="Sunday 24 March 2024 22:30">Sunday 24 March 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/Examples/Example10/index.html
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Ex.10: Bidimensional Fuzzy Entropy · EntropyHub.jl</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://mattwillflood.github.io/EntropyHub.jl/Examples\\Example10/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.039/juliamono-regular.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.11/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="EntropyHub.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">EntropyHub.jl</a></span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><input class="collapse-toggle" id="menuitem-2" type="checkbox"/><label class="tocitem" for="menuitem-2"><span class="docs-label">Guide</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../Guide/Base_Entropies/">Base Entropies</a></li><li><a class="tocitem" href="../../Guide/Cross_Entropies/">Cross-Entropies</a></li><li><a class="tocitem" href="../../Guide/Multiscale_Entropies/">Multiscale Entropies</a></li><li><a class="tocitem" href="../../Guide/Multiscale_Cross_Entropies/">Multiscale Cross-Entropies</a></li><li><a class="tocitem" href="../../Guide/Bidimensional_Entropies/">Bidimensional Entropies</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-3" type="checkbox" checked/><label class="tocitem" for="menuitem-3"><span class="docs-label">Examples</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../Examples/">Notes on Examples</a></li><li><a class="tocitem" href="../Example1/">Ex.1: Sample Entropy</a></li><li><a class="tocitem" href="../Example2/">Ex.2: Permutation Entropy</a></li><li><a class="tocitem" href="../Example3/">Ex.3: Phase Entropy</a></li><li><a class="tocitem" href="../Example4/">Ex.4: Cross-Distribution Entropy</a></li><li><a class="tocitem" href="../Example5/">Ex.5: Multiscale Entropy Object</a></li><li><a class="tocitem" href="../Example6/">Ex.6: Multiscale [Increment] Entropy</a></li><li><a class="tocitem" href="../Example7/">Ex.7: Refined Multiscale [Sample] Entropy</a></li><li><a class="tocitem" href="../Example8/">Ex.8: Composite Multiscale Cross-Approximate Entropy</a></li><li><a class="tocitem" href="../Example9/">Ex.9: Hierarchical Multiscale corrected Cross-Conditional Entropy</a></li><li class="is-active"><a class="tocitem" href>Ex.10: Bidimensional Fuzzy Entropy</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Ex.10: Bidimensional Fuzzy Entropy</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Ex.10: Bidimensional Fuzzy Entropy</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/MattWillFlood/EntropyHub.jl/blob/master/docs/src/Examples/Example10.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Example-10:-Bidimensional-Fuzzy-Entropy"><a class="docs-heading-anchor" href="#Example-10:-Bidimensional-Fuzzy-Entropy">Example 10: Bidimensional Fuzzy Entropy</a><a id="Example-10:-Bidimensional-Fuzzy-Entropy-1"></a><a class="docs-heading-anchor-permalink" href="#Example-10:-Bidimensional-Fuzzy-Entropy" title="Permalink"></a></h1><p>Import an image of a Mandelbrot fractal as a matrix.</p><pre><code class="nohighlight hljs">X = ExampleData(&quot;mandelbrot_Mat&quot;);

using Plots
heatmap(X, background_color=&quot;black&quot;)</code></pre><p><img src="../../assets/mandelbrotjl.png" alt="AlmondBread"/></p><p>Calculate the bidimensional fuzzy entropy in trits (logarithm base 3) with a template matrix of size [8 x 5], and a time delay (<code>tau</code>) of 2 using a <code>&#39;constgaussian&#39;</code> fuzzy membership function (r=24).</p><pre><code class="language-julia hljs">FE2D = FuzzEn2D(X, m = (8, 5), tau = 2, Fx = &quot;constgaussian&quot;, r = 24, Logx = 3)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">1.4885540777860427</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Example9/">« Ex.9: Hierarchical Multiscale corrected Cross-Conditional Entropy</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.5 on <span class="colophon-date" title="Sunday 24 March 2024 21:55">Sunday 24 March 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
heatmap(X, background_color=&quot;black&quot;)</code></pre><p><img src="../../assets/mandelbrotjl.png" alt="AlmondBread"/></p><p>Calculate the bidimensional fuzzy entropy in trits (logarithm base 3) with a template matrix of size [8 x 5], and a time delay (<code>tau</code>) of 2 using a <code>&#39;constgaussian&#39;</code> fuzzy membership function (r=24).</p><pre><code class="language-julia hljs">FE2D = FuzzEn2D(X, m = (8, 5), tau = 2, Fx = &quot;constgaussian&quot;, r = 24, Logx = 3)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">1.4885540777860427</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Example9/">« Ex.9: Hierarchical Multiscale corrected Cross-Conditional Entropy</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.5 on <span class="colophon-date" title="Sunday 24 March 2024 22:30">Sunday 24 March 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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markercolor = &quot;green&quot;, markerstrokecolor = &quot;black&quot;,
markersize = 3, background_color = &quot;black&quot;, grid = false)</code></pre><p><img src="../../assets/lorenzjl.png" alt="Lorenz"/></p><p>Calculate fine-grained permutation entropy of the z component in dits (logarithm base 10) with an embedding dimension of 3, time delay of 2, an alpha parameter of 1.234. Return Pnorm normalised w.r.t the number of all possible permutations (m!) and the condition permutation entropy (cPE) estimate.</p><pre><code class="language-julia hljs">Z = Data[:,3];
Perm, Pnorm, cPE = PermEn(Z, m = 3, tau = 2, Typex = &quot;finegrain&quot;,
tpx = 1.234, Logx = 10, Norm = false)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([-0.0, 0.8686539340402203, 0.946782979031713], [NaN, 0.8686539340402203, 0.4733914895158565], [0.8686539340402203, 0.07812904499149276])</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Example1/">« Ex.1: Sample Entropy</a><a class="docs-footer-nextpage" href="../Example3/">Ex.3: Phase Entropy »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.5 on <span class="colophon-date" title="Sunday 24 March 2024 21:55">Sunday 24 March 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
tpx = 1.234, Logx = 10, Norm = false)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([-0.0, 0.8686539340402203, 0.946782979031713], [NaN, 0.8686539340402203, 0.4733914895158565], [0.8686539340402203, 0.07812904499149276])</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Example1/">« Ex.1: Sample Entropy</a><a class="docs-footer-nextpage" href="../Example3/">Ex.3: Phase Entropy »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.5 on <span class="colophon-date" title="Sunday 24 March 2024 22:30">Sunday 24 March 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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