Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"color: #5e9ca0;\"><span style=\"color: #000000;\">Learning the XOR function and Visualizing the Hidden Layer output.</span></h1>\n",
    "<p><span style=\"color: #000000;\">We would be using a basic feedforward network with one hidden layer to learn the&nbsp; XOR function .</span></p>\n",
    "<p>The XOR truth table is given as follows:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<table style=\"height: 190px; width: 110px;\">\n",
    "<tbody>\n",
    "<tr>\n",
    "<td style=\"width: 29px;\">0</td>\n",
    "<td style=\"width: 29px;\">0</td>\n",
    "<td style=\"width: 36px;\"><span style=\"color: #ffcc00;\"><strong>0</strong></span></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td style=\"width: 29px;\">1</td>\n",
    "<td style=\"width: 29px;\">0</td>\n",
    "<td style=\"width: 36px;\"><span style=\"color: #003366;\"><strong>1</strong></span></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td style=\"width: 29px;\">1</td>\n",
    "<td style=\"width: 29px;\">1&nbsp;</td>\n",
    "<td style=\"width: 36px;\"><span style=\"color: #ffcc00;\"><strong>0</strong></span></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td style=\"width: 29px;\">0</td>\n",
    "<td style=\"width: 29px;\">1</td>\n",
    "<td style=\"width: 36px;\"><span style=\"color: #003366;\"><strong>1</strong></span></td>\n",
    "</tr>\n",
    "</tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Importing Libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0]\n",
      " [1 0 1]\n",
      " [1 1 0]\n",
      " [0 1 1]]\n"
     ]
    }
   ],
   "source": [
    "# Create the training data for XOR.\n",
    "\n",
    "data = np.array([[0,0,0],[1,0,1],[1,1,0],[0,1,1]])\n",
    "print(data)\n",
    "\n",
    "#First two columns are the inputs,3rd Column consists of the labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Create the X_train(Co-oridinates) and Y_train(Labels) Matrices.\n",
    "\n",
    "Y_train = data[:,2].reshape(data.shape[0],1) #SHAPE(4,1)\n",
    "X_train = data[:,:2]   #SHAPE (4,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x94f1668>"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f57390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let us Visualise how the input space looks like:\n",
    "plt.scatter(X_train[:,0],X_train[:,1],c=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In the above plot, we can clearly see that the <strong>yellow</strong> and <strong>purple</strong> points cannot be separated&nbsp;by a straight line. XOR function is not linearly separable.</p>\n",
    "<p>A linear model applied <strong>directly</strong> to the original input <strong>cannot implement the XOR function.</strong></p>\n",
    "<p>We should try&nbsp;to make the input to the linear model such that the <strong>points can be separated&nbsp;by a straight line.</strong>It is for this purpose do we use a <strong>hidden layer which transforms the input</strong> so that it becomes linearly separable.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Creating the neural network\n",
    "#Network Parameters:\n",
    "X = X_train.T\n",
    "y = Y_train.T\n",
    "\n",
    "n_input = 2\n",
    "n_hidden = 2\n",
    "n_output=1\n",
    "iterations =500\n",
    "\n",
    "m = X.shape[1]# m is the number of training samples\n",
    "\n",
    "learning_rate = 1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Defining non-linear function\n",
    "def sigmoid(z):\n",
    "    return 1/(1+np.exp(-z))\n",
    "\n",
    "def sigmoid_prime(z):\n",
    "    return sigmoid(z)*(1-sigmoid(z))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "#Helper Functions for Plotting\n",
    "\n",
    "def plot_hiddenlayer_output(X,W1):\n",
    "    #%matplotlib inline\n",
    "    z1 = np.dot(W1,X)+b1 #Forward Propagation Step\n",
    "    a1 = sigmoid(z1) #Applying Sigmoid Non linearity\n",
    "    plt.scatter(a1[0,:],a1[1,:],c=y,alpha=1)\n",
    "    plt.xlabel(\"X axis\")\n",
    "    plt.ylabel(\"Y axis\")\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In the <em>plot_hiddenlayer_output</em> function, we forward propagate the input.</p>\n",
    "<p><strong>Z = W*X + b&nbsp; &nbsp;&nbsp;</strong>#This is a linear Transform</p>\n",
    "<p><strong>A = sigmoid(Z)&nbsp; </strong>#Adding Non-linearity</p>\n",
    "<p>The sigmoid function is given by:</p>\n",
    "<h1>f(z) =1/(1+e^(-z))</h1>\n",
    "<p><strong>A is the output of the hidden layer.</strong></p>\n",
    "<p>&nbsp;</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_decision_boundry(fig,W2,b2):\n",
    "    cx = W2[0,0]\n",
    "    cy = W2[0,1]\n",
    "    c = -b2\n",
    "    fig.plot(([-1,2]),([(c/cy-cx*-1/cy).reshape(1,),(c/cy-cx*2/cy).reshape(1,)]),c='r',marker='x')\n",
    "    plt.xlabel(\"X axis\")\n",
    "    plt.ylabel(\"Y axis\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#initializing weights and biases\n",
    "np.random.seed(1)\n",
    "#You can change the seed if you want,it might take more(or less) number of iterations to reduce the cost\n",
    "\n",
    "W1 = np.random.normal(0,1/np.sqrt(2),size=[n_hidden,n_input])#Shape 2,2\n",
    "W2 = np.random.normal(0,1/np.sqrt(2),size=[n_output,n_hidden])#Shape1,2\n",
    "b1 = np.zeros((n_hidden,1))#Shape2,1\n",
    "b2 = np.zeros((n_output,1))#shape1,1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8f75668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hiddenlayer_output(X,W1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The plot you see above is the what the <strong>hidden layer outputs right now</strong>.Even after applying the sigmoid transformation, the points <strong>cannot</strong> be separated by drawing a straight line.</p>\n",
    "<p>Now we will train the neural network, which will <strong>change</strong> the Weights and Biases<strong> using gradient descent,in order to reduce the cost function(thus making the points linearly separable)</strong>.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the Weights and Biases are changed, <strong>observe how the output of the hidden layer changes</strong>.The yellow and purple points <strong>can</strong> now be separated&nbsp;by a straight line!</p>\n",
    "\n",
    "<p>Run the below cell to train the Neural Network</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"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\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // 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",
       "\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"718.8889079329414\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"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\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // 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",
       "\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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\" width=\"718.8889079329414\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Array to save cost after each iteration:\n",
    "cost = []\n",
    "\n",
    "#PLOTTING\n",
    "%matplotlib notebook\n",
    "f = plt.figure(figsize= (10,15))\n",
    "\n",
    "pa1 = f.add_subplot(311)\n",
    "plt.ion()\n",
    "\n",
    "\n",
    "for i in range(iterations):\n",
    "    \n",
    "    #FORWARD PROPAGATION\n",
    "    z1 = np.dot(W1,X)+b1  #Shape2,4\n",
    "    a1 = sigmoid(z1)  #Shape2,4\n",
    "    z2 = np.dot(W2,a1)+b2  #Shape1,4\n",
    "    a2 = sigmoid(z2)   #Shape1,4\n",
    "\n",
    "    #PLOTTING\n",
    "        \n",
    "    if (iterations<1001):\n",
    "        pa1.clear()\n",
    "        pa1.scatter(a1[0,:],a1[1,:],c=y,alpha=1)\n",
    "        plot_decision_boundry(pa1,W2,b2)\n",
    "        f.tight_layout()\n",
    "        f.canvas.draw()\n",
    "\n",
    "    \n",
    "    \n",
    "   \n",
    "    \n",
    "    #CALCULATE COST(MAXIMUM LIKELIHOOD COST)\n",
    "    \n",
    "    c = (-np.dot(y,np.log(a2).T)-np.dot(1-y,np.log(1-a2).T))/m\n",
    "    cost.append(c)\n",
    "    \n",
    "    \n",
    "    #BACK PROPAGATION\n",
    "    \n",
    "    dz2 = a2-y  #SHAPE 1,4\n",
    "    dW2 = np.dot(dz2,a1.T)/m #SHAPE 1,2\n",
    "    db2 = np.sum(dz2,axis=1,keepdims=True)/m\n",
    "    \n",
    "    dz1 = np.multiply(np.dot(W2.T,dz2),sigmoid_prime(z1))  #SHAPE 2,4\n",
    "    dW1 = np.dot(dz1,X.T)/m #SHAPE 2,2\n",
    "    db1 = np.sum(dz1,axis=1,keepdims=True)/m\n",
    "    \n",
    "   \n",
    "    \n",
    "        \n",
    "    #GRADIENT DESCENT\n",
    "    W2 = W2 - learning_rate*dW2\n",
    "    W1 = W1 - learning_rate*dW1\n",
    "    b2 = b2 - learning_rate*db2\n",
    "    b1 = b1 -learning_rate*db1\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><strong>After</strong> the input space has been transformed, all the output neuron is doing is <strong>simple logistic regression</strong> (with the outputs of the hidden layer as inputs)</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Outputs of the Neural network are:   [[ 0.02749139  0.92995242  0.15403097  0.93032697]]\n",
      "The expected Outputs are  [[0 1 0 1]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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YtAkefBCuvRaqaCCaiOS2dG6qmgocZmaHmFlV4EJgWFI+qVs3GDv2p+MlS6Bx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e8b978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "z1 = np.dot(W1,X)+b1 #Forward Propagation Step\n",
    "a1 = sigmoid(z1) #Applying Sigmoid Non linearity\n",
    "z2 = np.dot(W2,a1)+b2 #Shape1,4\n",
    "a2 = sigmoid(z2)\n",
    "\n",
    "\n",
    "plt.scatter(a1[0,:],a1[1,:],c=y,alpha=1)\n",
    "plot_decision_boundry(plt,W2,b2)\n",
    "\n",
    "\n",
    "print(\"The Outputs of the Neural network are:  \",a2)\n",
    "print(\"The expected Outputs are \",y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"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\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // 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",
       "\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
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     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x93ec390>"
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     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"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\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // 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",
       "\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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   ],
   "source": [
    "#Now lets see how the cost decreases with each increase in iteration\n",
    "plt.plot(range(iterations),np.array(cost).reshape(iterations,),c='g')\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Cost\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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