t-SNE.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# t-Stochastic Neighbor Embedding (t-SNE)\n",
    "Reference paper: TODO https://jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "t-SNE is a non-linear dimension reduction technique. This is usefull for visualizing high dimensional data.\n",
    "\n",
    "TODO add example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other approches\n",
    "- Chernoff faces\n",
    "- PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets define $p_{j|i}$ as the probability that we pick $x_j$ if we choose the points with probability proportional to a gaussian centered at $x_i$.\n",
    "\n",
    "More formally if we choose a gaussian of variance $\\sigma_i$:\n",
    "$$\\forall i, \\forall j \\neq i, p_{j|i}=\\frac{\\exp\\left(-\\frac{||x_i-x_j||}{2\\sigma_i^2}\\right)}{\\sum_{k\\neq i}\\exp\\left(-\\frac{||x_i-x_k||}{2\\sigma_i^2}\\right)}$$\n",
    "$$\\forall i, p_{i|i}=0$$\n",
    "Note that the denominator is just here for the normalization constraint:\n",
    "$$\\sum_{j}p_{j|i}=1$$\n",
    "\n",
    "Just as we did for the $x_i$, we can define $q_{j|i}$ for the $y_i$.\n",
    "\n",
    "To measure how faithfully $q_{j|i}$ models $p_{j|i}$, we define the Kullback-Leibler divergence:\n",
    "$$C=\\sum_{i,j}p_{j|i}\\log{\\frac{p_{j|i}}{q_{j|i}}}$$\n",
    "By the properties of morphims of the logarithm, this just is the cross entropy up to an additive constant.\n",
    "$$C=-\\sum_{i,j}p_{j|i}\\log{q_{j|i}} + \\text{ cst}$$\n",
    "\n",
    "The gradient is:\n",
    "$$\\frac{\\delta C}{\\delta y_i}=2\\sum_j(p_{j|i}-q_{j|i}+p_{i|j}-q_{i|j})(y_i-y_j)$$\n",
    "\n",
    "Symetric:\n",
    "$$p_{ij}=\\frac{p_{j|i}+p_{i|j}}{2n}$$\n",
    "\n",
    "Gradient for symetric SNE:\n",
    "$$\\frac{\\delta C}{\\delta y_i}=4\\sum_j(p_{ij}-q_{ij})(y_i-y_j)$$\n",
    "\n",
    "To prevent crowding:\n",
    "$$q_{ij}=\\frac{(1+||y_i-y_j||^2)^{-1}}{\\sum_{k\\neq l}(1+||y_k-y_l||^2)^{-1}}$$\n",
    "\n",
    "The gradient now becomes:\n",
    "$$\\frac{\\delta C}{\\delta y_i}=4\\sum_j(p_{ij}-q_{ij})(y_i-y_j)(1+||y_i-y_j||^2)^{-1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm outline\n",
    "\n",
    "### Input\n",
    "\n",
    "- data set $\\mathcal{X}=\\{x_1, \\dots, x_n\\}$\n",
    "- optimization parameters: number of iterations $T$, learning rate $\\eta$, momentum $\\alpha(t)$\n",
    "- cost function parameters: perplexity $Per p$\n",
    "\n",
    "### Output\n",
    "\n",
    "low dimentional representation of the data: $\\mathcal{Y}^{(T)}=\\{y_1, \\dots, y_n\\}$\n",
    "\n",
    "### Initialization\n",
    "\n",
    "- compute $p_{j|i}$ and $p_{ij}$\n",
    "- choose an initial solution $\\mathcal{Y}^{(0)}=\\{y_1, \\dots, y_n\\}$\n",
    "\n",
    "### For $t=1$ to $T$\n",
    "\n",
    "- compute $q_{ij}$\n",
    "- compute the gradient\n",
    "- set $\\mathcal{Y}^{(t)}:=\\mathcal{Y}^{(t-1)}+\\eta\\frac{\\delta C}{\\delta \\mathcal{Y}}+\\alpha(t)\\left(\\mathcal{Y}^{(t-1)}-\\mathcal{Y}^{(t-2)}\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "from math import ceil, sqrt, sin, exp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_search(f, y, a, b, epsilon, max_nb_iter=50):\n",
    "    \"\"\" Find a <= x <= b such that |f(x) - y| <= epsilon. Assumes that f is monotone. \"\"\"\n",
    "    m = (a + b) / 2\n",
    "    fm = f(m)\n",
    "    nb_iter = 0\n",
    "    while abs(fm - y) > epsilon and nb_iter <= max_nb_iter:\n",
    "        if fm > y:\n",
    "            b = m\n",
    "        else:\n",
    "            a = m\n",
    "        m = (a + b) / 2\n",
    "        fm = f(m)\n",
    "        nb_iter += 1\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0000014305114746"
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     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Test.\n",
    "binary_search(lambda x: x ** 2, 9, -1, 10, 10 ** (-5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Toy data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_toy_data(n=50, sigma=0.05, show=False):\n",
    "    # Make sure that n is a square.\n",
    "    sqrt_n = ceil(sqrt(n))\n",
    "    n = sqrt_n ** 2\n",
    "\n",
    "    # Sample the manifold.\n",
    "    xs = np.linspace(-1, 1, sqrt_n)\n",
    "    ys = np.linspace(-1, 1, sqrt_n)\n",
    "    xs, ys = np.meshgrid(xs, ys)\n",
    "    zs = xs + np.sin(4 * (xs ** 2 + ys ** 2))\n",
    "\n",
    "    # Add noise.\n",
    "    zs += sigma * np.random.randn(*zs.shape)\n",
    "    \n",
    "    X = np.array([xs.flatten(), ys.flatten(), zs.flatten()]).T\n",
    "\n",
    "    # Show the generated data.\n",
    "    if show:\n",
    "        fig = plt.figure()\n",
    "        ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "        ax.plot_surface(xs, ys, zs, cmap=cm.coolwarm, linewidth=0, antialiased=False)\n",
    "        plt.show()\n",
    "\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
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       "    // 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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=\"639.4\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "toy_X = gen_toy_data(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the MNIST dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_category_size = 50\n",
    "\n",
    "digits = [3, 4]  # 3 and 4 are cherry picked.\n",
    "# digits = list(range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the MNIST dataset.\n",
    "data = sio.loadmat('mnist_digits.mat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The dataset has 66000 examples of dimension 784.\n",
      "The trimmed down dataset has 100 examples of dimension 784.\n"
     ]
    }
   ],
   "source": [
    "X = data['x']\n",
    "Y = data['y']\n",
    "n, dim = X.shape\n",
    "print(f'The dataset has {n} examples of dimension {dim}.')\n",
    "\n",
    "# Select only the digits in `digits`.\n",
    "categories = [[]] * 10\n",
    "for digit in digits:\n",
    "    category = X[np.argwhere(Y == digit)[:, 0]]\n",
    "    categories[digit] = category[:min(max_category_size, len(category))]\n",
    "\n",
    "X = np.concatenate([categories[digit] for digit in digits], axis=0)\n",
    "Y = np.concatenate([i * np.ones(len(category)) for i, category in enumerate(categories)], axis=0)\n",
    "\n",
    "indices = [[]] * 10\n",
    "for digit in digits:\n",
    "    indices[digit] = np.argwhere(Y == digit)[:, 0]\n",
    "\n",
    "n, dim = X.shape\n",
    "print(f'The trimmed down dataset has {n} examples of dimension {dim}.')\n",
    "\n",
    "# Add noise to the data.\n",
    "sigma = .05\n",
    "noisy_X = X + sigma * np.random.randn(*X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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",
       "    // 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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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       "<img 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\" width=\"639.4\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.reshape(X[0],(28,28)), cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the level of noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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",
       "    // 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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=\"639.4\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.reshape(noisy_X[0],(28,28)), cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pca(X, d=1, plot=False, label=''):\n",
    "    # Assert that the data is centered.\n",
    "    mean = np.mean(X, axis=0)\n",
    "    X_centered = np.array([x - mean for x in X])\n",
    "    \n",
    "    # Compute the eigenvectors and eigenvalues.\n",
    "    eig_val, eig_vect = np.linalg.eig(X_centered.T @ X_centered)\n",
    "    # Remove the imaginary part.\n",
    "    eig_val = np.real(eig_val)\n",
    "    eig_vect = np.real(eig_vect)\n",
    "    \n",
    "    # Sort by eigen value.\n",
    "    sort_idx = np.argsort(eig_val)\n",
    "    sorted_eig_val = eig_val[sort_idx]\n",
    "    sorted_eig_vect = eig_vect[sort_idx]\n",
    "    \n",
    "    # Plot the eigenvalues.\n",
    "    if plot:\n",
    "        plt.plot(np.maximum(sorted_eig_val, 10 ** (-11)), label=label)\n",
    "        plt.yscale('log')\n",
    "\n",
    "    # Compute the projection on the subspace.\n",
    "    sub_space = sorted_eig_vect[-d:]\n",
    "    Z = np.array([np.array([np.dot(v, x) for v in sub_space]) for x in X_centered + mean])\n",
    "    \n",
    "    return Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_2d_pca(X, nb_points=100):\n",
    "    Z = pca(X, d=2)\n",
    "    for digit in digits:\n",
    "        Z_digit = Z[indices[digit]][:nb_points]\n",
    "        plt.scatter(Z_digit[:, 0], Z_digit[:, 1], label=f'{digit}')\n",
    "\n",
    "    plt.title('MNIST PCA 2D')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "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",
       "    // 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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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       "<img 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\" width=\"639.4\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_2d_pca(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "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",
       "    // 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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=\"639.4\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_2d_pca(noisy_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## t-SNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tsne(X, T, eta, alpha, per, toy=False, init_with_pca=True):\n",
    "    \"\"\" 2D t-SNE \"\"\"\n",
    "    n = len(X)\n",
    "    \n",
    "    colors = ['green', 'blue', 'orange', 'purple', 'black', 'yelow', 'grey', 'brown', 'cyan', 'red']\n",
    "    \n",
    "    # Compute sigma for a given perplexity.\n",
    "    # TODO\n",
    "    sigma = np.array([\n",
    "        binary_search(lambda x: 2 ** (-sum()), per, a, b, 1e-5) for i in rang(n)])\n",
    "    sigma = np.ones(n) * 10 ** (-3)  # TODO\n",
    "    \n",
    "    # Compute p_{j|i}.\n",
    "    N = np.array([[np.linalg.norm(X[i] - X[j]) ** 2 for i in range(n)] for j in range(n)])\n",
    "    p = np.exp(- N ** 2 / (2 * sigma ** 2))\n",
    "    # Normalize.\n",
    "    for i in range(n):\n",
    "        p[:, i] /= np.sum(p[:, i])\n",
    "    \n",
    "    # Compute p_{ji}.\n",
    "    P = (p + p.T) / (2 * n)\n",
    "    \n",
    "    # Initial solution.\n",
    "    if init_with_pca:\n",
    "        Y = pca(X, d=2)\n",
    "    else:\n",
    "        Y = np.random.normal(0, 10 ** (-4), size=(n, 2))\n",
    "    Y_old = np.copy(Y)\n",
    "    \n",
    "    # Training loop.\n",
    "    for t in range(T):\n",
    "        if t % (T // 10) == 0:\n",
    "            # Plot the actual result.\n",
    "            if toy:\n",
    "                plt.scatter(Y[:, 0], Y[:, 1], label=f'{t}; iter {t}')\n",
    "            else:\n",
    "                for digit in digits:\n",
    "                    plt.scatter(Y[indices[digit], 0], Y[indices[digit], 1], label=f'{digit}; iter {t}', c=colors[digit])\n",
    "                plt.legend()\n",
    "                plt.show()\n",
    "    \n",
    "        # Compute q_{ij}.\n",
    "        Q = np.zeros((n, n))\n",
    "        for i in range(n):\n",
    "            for j in range(n):\n",
    "                if i != j:\n",
    "                    Q[i][j] = 1 / (1 + np.linalg.norm(Y[i] - Y[j]) ** 2)\n",
    "            # Normalize.\n",
    "            Q[i] /= np.sum(Q[i])\n",
    "\n",
    "        # Compute de gradient.\n",
    "        gradient = np.array(\n",
    "            [4 * sum(\n",
    "                (P[i, j] - Q[i, j]) * (Y[i] - Y[j]) / (1 + np.linalg.norm(Y[i] - Y[j]) ** 2)\n",
    "                     for j in range(n))\n",
    "             for i in range(n)])\n",
    "        \n",
    "        if t % (T // 10) == 0:\n",
    "            # Print the cost and the gradient.\n",
    "            cost = np.sum(P * np.maximum(np.log(np.maximum(P / (np.maximum(Q, 10 ** (-10))), 10 ** (-10))), -10 ** 30))\n",
    "            print(f'Iteration {t}/{T}:\\tcost {cost}\\t\\tgradient {np.linalg.norm(gradient)}')\n",
    "        \n",
    "        # Update Y and Y_old.\n",
    "        Y, Y_old = Y + eta * gradient + alpha[t] * (Y - Y_old), Y\n",
    "    \n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters.\n",
    "T = 100\n",
    "eta = .1\n",
    "alpha = 0 * np.ones(T)\n",
    "per = 1\n",
    "\n",
    "Y = tsne(toy_X, T, eta, alpha, per, toy=True, init_with_pca=False)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Parameters.\n",
    "T = 100\n",
    "eta = .05\n",
    "alpha = 0 * np.ones(T)\n",
    "per = 1\n",
    "\n",
    "Y = tsne(X, T, eta, alpha, per, toy=False)\n",
    "# noisy_Y = tsne(noisy_X, T, eta, alpha, per)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO\n",
    "- perplexity/sigma\n",
    "- at first use PCA to reduce the dimention to 30\n",
    "- remove for loops\n",
    "- plot the cost\n",
    "- normalize\n",
    "- log and exp in base 2\n",
    "- springs\n",
    "- add gaussian noise to the map points in the early stages of optimization\n",
    "- early compression\n",
    "- early exaggeration\n",
    "- random walk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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