Example-2.1-case-3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b16ccb14",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from utils import *\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6a06026c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r = k/h**2 = 1\n",
      "Number of discretization on x: 11\n",
      "Number of discretization on t: 11\n"
     ]
    }
   ],
   "source": [
    "L = 1\n",
    "T = .1\n",
    "\n",
    "h = .1\n",
    "k = 0.01\n",
    "\n",
    "r = k / h**2\n",
    "print('r = k/h**2 = %g' % r)\n",
    "\n",
    "Nx = int(np.ceil(L / h)) + 1\n",
    "Nt = int(np.ceil(T / k)) + 1\n",
    "\n",
    "print('Number of discretization on x:', Nx)\n",
    "print('Number of discretization on t:', Nt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3e255551",
   "metadata": {},
   "outputs": [],
   "source": [
    "@np.vectorize\n",
    "def initial(x):\n",
    "    if 0 <= x <= 1 / 2:\n",
    "        return 2 * x\n",
    "    elif 1 / 2 <= x <= 1:\n",
    "        return 2 * (1 - x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1093e809",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([i * h for i in range(Nx)])\n",
    "t = np.array([i * k for i in range(Nt)])\n",
    "\n",
    "u0 = initial(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2e15648b",
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.zeros((Nt, Nx))\n",
    "u[0, :] = u0\n",
    "\n",
    "# for j in range(Nt - 1):\n",
    "#     for i in range(1, Nx - 1):\n",
    "#         u[j + 1, i] = r * u[j, i - 1] + (1 - 2 * r) * u[j, i] + r * u[j, i + 1]\n",
    "\n",
    "# vectorized form\n",
    "for j in range(Nt - 1):\n",
    "    u[j + 1, 1:-1] = r * u[j, :-2] + (1 - 2 * r) * u[j, 1:-1] + r * u[j, 2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "be837689",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═════════════╤═══════╤═══════╤════════╤════════╤════════╤════════╤════════╤════════╤════════╤═══════╤═══════╕\n",
      "│      x      │  0.0  │  0.1  │  0.2   │  0.3   │  0.4   │  0.5   │  0.6   │  0.7   │  0.8   │  0.9  │  1.0  │\n",
      "╞═════════════╪═══════╪═══════╪════════╪════════╪════════╪════════╪════════╪════════╪════════╪═══════╪═══════╡\n",
      "│  j=0(t=0)   │   0   │  0.2  │  0.4   │  0.6   │  0.8   │   1    │  0.8   │  0.6   │  0.4   │  0.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=1(t=0.01) │   0   │  0.2  │  0.4   │  0.6   │  0.8   │  0.6   │  0.8   │  0.6   │  0.4   │  0.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=2(t=0.02) │   0   │  0.2  │  0.4   │  0.6   │  0.4   │   1    │  0.4   │  0.6   │  0.4   │  0.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=3(t=0.03) │   0   │  0.2  │  0.4   │  0.2   │  1.2   │  -0.2  │  1.2   │  0.2   │  0.4   │  0.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=4(t=0.04) │   0   │  0.2  │   -0   │  1.4   │  -1.2  │  2.6   │  -1.2  │  1.4   │   -0   │  0.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=5(t=0.05) │   0   │ -0.2  │  1.6   │  -2.6  │  5.2   │   -5   │  5.2   │  -2.6  │  1.6   │ -0.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=6(t=0.06) │   0   │  1.8  │  -4.4  │  9.4   │ -12.8  │  15.4  │ -12.8  │  9.4   │  -4.4  │  1.8  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=7(t=0.07) │   0   │ -6.2  │  15.6  │ -26.6  │  37.6  │  -41   │  37.6  │ -26.6  │  15.6  │ -6.2  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=8(t=0.08) │   0   │ 21.8  │ -48.4  │  79.8  │ -105.2 │ 116.2  │ -105.2 │  79.8  │ -48.4  │ 21.8  │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=9(t=0.09) │   0   │ -70.2 │  150   │ -233.4 │ 301.2  │ -326.6 │ 301.2  │ -233.4 │  150   │ -70.2 │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│ j=10(t=0.1) │   0   │ 220.2 │ -453.6 │ 684.6  │ -861.2 │  929   │ -861.2 │ 684.6  │ -453.6 │ 220.2 │   0   │\n",
      "├─────────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┼────────┼───────┼───────┤\n",
      "│      x      │   0   │  0.1  │  0.2   │  0.3   │  0.4   │  0.5   │  0.6   │  0.7   │  0.8   │  0.9  │   1   │\n",
      "╘═════════════╧═══════╧═══════╧════════╧════════╧════════╧════════╧════════╧════════╧════════╧═══════╧═══════╛\n"
     ]
    }
   ],
   "source": [
    "print_table(u, x, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "66ec12c2",
   "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_dpi_ratio', { dpi_ratio: fig.ratio });\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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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 http://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",
       " * http://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, CTRL fixes aspect\", \"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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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>"
      ]
     },
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     "output_type": "display_data"
    },
    {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7f5d8f86cd30>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "animate_line(u, t, sampling=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4eb57be9",
   "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_dpi_ratio', { dpi_ratio: fig.ratio });\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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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 http://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",
       " * http://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, CTRL fixes aspect\", \"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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7f5d8d71bf10>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "animate_heatmap(u, t, sampling=1)"
   ]
  }
 ],
 "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
}