rk.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1e234b91",
   "metadata": {},
   "source": [
    "# Absolute stability for time-integration schemes\n",
    "\n",
    "Jupyter notebook to compute the region of absolute stability for various time-integration schemes.\n",
    "\n",
    "Philipp Schlatter, January 2022\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e4446e6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook \n",
    "# possible options: notebook, inline or widget\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.pylab as pylab\n",
    "import matplotlib.animation\n",
    "import math \n",
    "params = {'legend.fontsize': 12,\n",
    "          'legend.loc':'best',\n",
    "          'figure.figsize': (8,5),\n",
    "          'lines.markerfacecolor':'none',\n",
    "          'axes.labelsize': 12,\n",
    "          'axes.titlesize': 12,\n",
    "          'xtick.labelsize':12,\n",
    "          'ytick.labelsize':12,\n",
    "          'grid.alpha':0.6}\n",
    "pylab.rcParams.update(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed3c3844",
   "metadata": {},
   "source": [
    "## Characteristic polynomial\n",
    "\n",
    "Consider the differential equation $y' = \\lambda y$. The amplification factor $G(z)$ is obtained as $G(z) = y^{n+1} / y^{n}$. The neutral curve is defined as the locus with $|G(z)| = 1$, which can be simply achieved by plotting contours of $|G(z)|$ at level 1.\n",
    "\n",
    "### Single-step schemes\n",
    "\n",
    "Runge-Kutta (RK) scheme of order $N$:\n",
    "$$G(z) = \\xi(z) = \\sum_{k=0}^N \\frac{z^k}{k!}$$\n",
    "\n",
    "with $z=\\lambda \\Delta t$. \n",
    "For instance, the RK1 scheme corresponds to the Euler forward scheme, and has the characteristic polynomial $\\xi(z)=1+z$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2583da15",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
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       "        return MozWebSocket;\n",
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       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
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       "\n",
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       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
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       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
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       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
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       "    canvas_div.setAttribute(\n",
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       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
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       "            'position: relative;' +\n",
       "            'resize: both;'\n",
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       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
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       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
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       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
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       "\n",
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       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
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       "\n",
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       "\n",
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       "            event.step = 1;\n",
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       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
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       "    // Disable right mouse context menu.\n",
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       "        event.preventDefault();\n",
       "        return false;\n",
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       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.subplot(111,aspect='equal')\n",
    "\n",
    "X,Y = np.meshgrid(np.arange(-5,2.1,.2),np.arange(-4,4,.2))\n",
    "Z = X +1j*Y;\n",
    " \n",
    "for N in range(1,4+1):\n",
    "    G = np.real(Z*0)\n",
    "    for k in range(0,N+1):\n",
    "        rksum = 1/math.factorial(k)\n",
    "        G = G + rksum*Z**k\n",
    "\n",
    "    plt.contour(X,Y,np.abs(G),colors='r',levels=[1])\n",
    "\n",
    "plt.title('Absolute stability RK schemes')\n",
    "plt.xlabel(r'$Re(z)$')\n",
    "plt.ylabel(r'$Im(z)$')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1caa0ee6",
   "metadata": {},
   "source": [
    "### Multistep schemes\n",
    "\n",
    "The Adams-Bashforth third-order scheme (AB3) is a multi-step scheme, which leads to a characteristic polynomial nonlinear  in $\\xi$:\n",
    "\n",
    "$$\\xi^3 + (-1 - \\frac{23}{12}z)\\xi^2 + (\\frac{16}{12}z)\\xi - \\frac{5}{12} z = 0$$\n",
    "\n",
    "Therefore, we first need to compute the roots of this polynomial, take the maximum, and then plot the contours. Again, the AB1 scheme is equivalent to the Euler forward scheme with $\\xi = 1+z$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "534a0cbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.subplot(111,aspect='equal')\n",
    "\n",
    "X,Y = np.meshgrid(np.arange(-3,1,.02),np.arange(-1.5,1.5,.02))\n",
    "Z = X +1j*Y;\n",
    "\n",
    "Gabs1 = np.real(Z*0)\n",
    "Gabs2 = np.real(Z*0)\n",
    "Gabs3 = np.real(Z*0)\n",
    "for ii in range(Z.shape[0]):\n",
    "    for jj in range(Z.shape[1]):\n",
    "        a = np.roots([1,-1-Z[ii,jj]])\n",
    "        Gabs1[ii,jj] = np.max(np.abs(a))\n",
    "        a = np.roots([1,-1-3/2*Z[ii,jj],1/2*Z[ii,jj]])\n",
    "        Gabs2[ii,jj] = np.max(np.abs(a))\n",
    "        a = np.roots([1,-1-23/12*Z[ii,jj],16/12*Z[ii,jj],-5/12*Z[ii,jj]])\n",
    "        Gabs3[ii,jj] = np.max(np.abs(a))\n",
    "        \n",
    "plt.contour(X,Y,Gabs1,colors='k',levels=[1])\n",
    "plt.contour(X,Y,Gabs2,colors='g',levels=[1])\n",
    "plt.contour(X,Y,Gabs3,colors='r',levels=[1])\n",
    "\n",
    "plt.title('Absolute stability AB schemes')\n",
    "plt.xlabel(r'$Re(z)$')\n",
    "plt.ylabel(r'$Im(z)$')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00adea1d",
   "metadata": {},
   "source": [
    "### Computing an explicit curve\n",
    "\n",
    "The proper way of calculating the region of absolute stability is to follow the various curves. This is done by computing all $z$ that map to the unit circle\n",
    "\n",
    "$$\\xi (z) = \\exp(i \\phi)$$\n",
    "\n",
    "and combining them into one closed curve.\n",
    "\n",
    "For the Runge-Kutta schemes, a nonlinear equation has to be solved for each angle:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4f7b6305",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.subplot(111,aspect='equal')\n",
    "\n",
    "# discretised unit circle\n",
    "n=100\n",
    "phi = np.exp(1j*np.linspace(0,2*math.pi,n,endpoint=False))\n",
    "\n",
    "for N in range(1,4+1):\n",
    "    # compute coefficients of the characteristic polynomial\n",
    "    rksum = 1\n",
    "    for k in range(2,N+1):\n",
    "        rksum = np.append(1/math.factorial(k), rksum)\n",
    "    # compute the various positions that map to the unit circle\n",
    "    p0 = []\n",
    "    for i in range(phi.size):\n",
    "        a = np.roots(np.append(rksum, 1-phi[i]))\n",
    "        p0 = np.append(p0, a)\n",
    "    # re-order the curve to get a consecutive line    \n",
    "    for i in range(1,p0.size-1):\n",
    "        ii = np.argsort( np.abs( p0[i:p0.size]-p0[i-1] ) )+i\n",
    "        tmp = p0[i]; p0[i] = p0[ii[0]]; p0[ii[0]] = tmp\n",
    "    # close the curve\n",
    "    p0 = np.append(p0,p0[0])\n",
    "    # plot the region of absolute stability\n",
    "    plt.plot(np.real(p0),np.imag(p0),label=\"RK%s\" % N)\n",
    "\n",
    "plt.xlim([-5, 1])\n",
    "plt.title('Absolute stability RK schemes')\n",
    "plt.xlabel(r'$Re(z)$')\n",
    "plt.ylabel(r'$Im(z)$')\n",
    "plt.grid()\n",
    "plt.legend(loc='lower left')\n",
    "plt.plot(0,np.sqrt(3),'ko')\n",
    "plt.plot(0,np.sqrt(8),'ko')\n",
    "plt.show()\n",
    "#plt.savefig('rk.pdf')  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b767e168",
   "metadata": {},
   "source": [
    "The neutral curve crosses the imaginary axis at $\\pm \\sqrt{3}$ for the RK3 scheme, and at $\\pm \\sqrt{8}$ for the RK4 scheme. The RK1 (explicit Euler) and RK2 schemes do not cross the imaginary axis."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47914428",
   "metadata": {},
   "source": [
    "* RK3 stability criterion:\n",
    "     along imaginary axis: sqrt(3.)=1.73, along real axis: 2.52\n",
    "* RK4 stability criterion:\n",
    "     along imaginary axis: sqrt(8.)=2.828, along real axis: 2.785\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74f8841f",
   "metadata": {},
   "source": [
    "For the AB3 scheme, \n",
    "$$\\xi^3 + (-1 - \\frac{23}{12}z)\\xi^2 + (\\frac{16}{12}z)\\xi - \\frac{5}{12} z = 0 \\, ,$$\n",
    "we obtain the following linear equation for $z$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfb3c043",
   "metadata": {},
   "source": [
    "$$ -(\\xi^3-\\xi^2) =   z (-\\frac{23}{12}\\xi^2  + \\frac{16}{12} \\xi  - \\frac{5}{12} ) \\, .$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bd14a266",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_AB=plt.figure()\n",
    "plt.subplot(111,aspect='equal')\n",
    "\n",
    "# discretised unit circle\n",
    "n=1000\n",
    "phi = np.exp(1j*np.linspace(0,2*math.pi,n,endpoint=False))\n",
    "\n",
    "for N in range(1,3+1):\n",
    "    p0 = []\n",
    "    for i in range(phi.size):\n",
    "        if N==1:\n",
    "            a = -(phi[i]-1)/(-1)\n",
    "        elif N==2:\n",
    "            a = -(phi[i]**2 - phi[i] )/ (-3/2*phi[i]+1/2)\n",
    "        elif N==3:\n",
    "            a =  -(phi[i]**3-phi[i]**2)/(-23/12*phi[i]**2+16/12*phi[i]-5/12)\n",
    "        p0 = np.append(p0, a)\n",
    "\n",
    "    # re-order the curve to get a consecutive line    \n",
    "    for i in range(1,p0.size-1):\n",
    "        ii = np.argsort( np.abs( p0[i:p0.size]-p0[i-1] ) )+i\n",
    "        tmp = p0[i]; p0[i] = p0[ii[0]]; p0[ii[0]] = tmp\n",
    "    # close the curve\n",
    "    p0 = np.append(p0,p0[0])\n",
    "    # plot the region of absolute stability\n",
    "    plt.plot(np.real(p0),np.imag(p0),label=\"AB%s\" % N)\n",
    "\n",
    "plt.xlim([-5, 1])\n",
    "plt.title('Absolute stability AB schemes')\n",
    "plt.xlabel(r'$Re(z)$')\n",
    "plt.ylabel(r'$Im(z)$')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d11146eb",
   "metadata": {},
   "source": [
    "As before, only the AB3 scheme includes parts of the imaginary axis, up to $\\pm 0.724$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "82fa664e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9086733",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}