python_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Name: Linear regression | Author: Alf Köhn | Version 01.10.2019 | License: CC BY-SA 4.0\n",
    "***\n",
    "# Linear regression \n",
    "\n",
    "When analyzing a dataset you might be looking for trends or scaling behaviour. Linear regression is often used to find simple relations in your dataset or, in other words, trying to approximate your dataset by a function. This notebook is about how to implement linear regression in Python. As expected, multiple ways exists to realize this: numpy, scipy, stats model and sckit learn. A simple example for the different methods is given and very briefly described."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_dataset( xVals, m_set=.2, b_set=1., noise_level=.2 ):\n",
    "    \"\"\"\n",
    "    function to create a dataset of the form y = (m*x+b) + random_number\n",
    "    \"\"\"\n",
    "    \n",
    "    yVals = m_set*xVals + b_set\n",
    "    \n",
    "    # add noise\n",
    "    for ii in range( len(yVals) ):\n",
    "        yVals[ii] += np.random.rand() * noise_level\n",
    "        \n",
    "    return yVals\n",
    "\n",
    "# create the dataset\n",
    "xVals  = np.linspace( -2, 10, 30 )\n",
    "yVals  = create_dataset( xVals, m_set=.2, b_set=1., noise_level=.4 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure()\n",
    "ax1  = fig1.add_subplot( 1,1,1 )\n",
    "\n",
    "ax1.plot( xVals, yVals, marker='x', linestyle='None')\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. numpy.polyfit()\n",
    "\n",
    "* least squares polynomial fit\n",
    "* fits a polynomial $p(x) = p[0] * x**deg + ... + p[deg]$ of degree deg to points $(x, y)$ \n",
    "* returns a vector of coefficients p that minimises the squared error in the order deg, deg-1, ... 0\n",
    "\n",
    "* input: dataset, polynomial function of degree as specified by the user\n",
    "* output: array of coefficient minimizing the squared error\n",
    "\n",
    "* NOTE: not recommended by official documentations, instead the newer functions should be used https://docs.scipy.org/doc/numpy/reference/routines.polynomials.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.20231498  1.19875724]\n"
     ]
    },
    {
     "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fit a polynomial p(x)=p[0]*x**degree + ... + p[degree]\n",
    "degree = 1\n",
    "coeff  = np.polyfit( xVals, yVals, degree)\n",
    "fit_1  = coeff[0]*xVals + coeff[1]\n",
    "\n",
    "print( coeff )\n",
    "\n",
    "fig2 = plt.figure()\n",
    "ax2  = fig2.add_subplot( 1,1,1 )\n",
    "\n",
    "ax2.plot( xVals, yVals, marker='x', linestyle='None')\n",
    "ax2.plot( xVals, fit_1, marker='None', linestyle='solid' )\n",
    "ax2.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. np.polynomial.polynomial.polyfit\n",
    "* officially recommended instead of np.polyfit\n",
    "* https://docs.scipy.org/doc/numpy/reference/generated/numpy.polynomial.polynomial.polyfit.html#numpy.polynomial.polynomial.polyfit\n",
    "* np.polynomial.polynomial.polyfit returns coefficients in opposite order of that for np.polyfit and np.polyval (or np.poly1d)\n",
    "* np.polynomial.polynomial.polyfit returns coefficients [A, B, C] to A + Bx + Cx^2 + ..., while np.polyfit returns: ... + Ax^2 + Bx + C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy.polynomial.polynomial as poly\n",
    "\n",
    "degree = 1\n",
    "coefs  = poly.polyfit(xVals, yVals, degree)\n",
    "fit_2  = poly.polyval(xVals, coefs)\n",
    "\n",
    "# alternatively, one could also create the polynomial function:\n",
    "#     fit_func = poly.Polynomial(coefs)\n",
    "fig2 = plt.figure()\n",
    "ax2  = fig2.add_subplot( 1,1,1 )\n",
    "\n",
    "ax2.plot( xVals, yVals, marker='x', linestyle='None', label='data')\n",
    "ax2.plot( xVals, fit_2, marker='None', linestyle='solid', label='fit' )\n",
    "ax2.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. scipy.optimize.curve_fit\n",
    "\n",
    "* https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html\n",
    "\n",
    "* like polyfit, but more general: fit a user-defined function to a dataset using non-linear least-square minimization\n",
    "\n",
    "* for linear regression case, $m\\cdot x+b$ is the estimator\n",
    "\n",
    "* output: array of function parameters for which least-square measure and associated covariance matrix is minimized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimized parameters: [ 0.20231498  1.19875724]\n"
     ]
    },
    {
     "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func_fit2(xVals, a, b):\n",
    "    return xVals*a + b\n",
    "\n",
    "popt, pcov = curve_fit(func_fit2, xVals, yVals)\n",
    "print( 'optimized parameters: {0}'.format(popt) )\n",
    "\n",
    "# plot dataset and fit\n",
    "fig4 = plt.figure()\n",
    "ax4  = fig4.add_subplot( 1,1,1 )\n",
    "\n",
    "ax4.plot( xVals, yVals, marker='x', linestyle='None', label='data')\n",
    "ax4.plot( xVals, func_fit2(xVals, *popt), \n",
    "          marker='None', linestyle='solid',\n",
    "          label='fit'\n",
    "        )\n",
    "ax4.legend()\n",
    "ax4.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. numpy.linalg.lstsq\n",
    "\n",
    "* calculates least-square solution to a linear system of equation by matrix factorization\n",
    "\n",
    "* part of the useful linear algebra module of numpy\n",
    "\n",
    "* solves $Ax = b$ by computing a vector $x$ that minimizes the $L^2$ norm (sometimes called Euclidean 2-norm) $||b - A x||^2$ \n",
    "\n",
    "* lstsq tries to solve $Ax=b$ minimizing $||b - Ax||^2$\n",
    "\n",
    "* equation may be under-, well-, or over- determined (i.e., the number of linearly independent rows of a can be less than, equal to, or greater than its number of linearly independent columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope = 0.20231498150269445, intercept = 1.1987572447804764\n"
     ]
    },
    {
     "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAgAElEQVR4nO3de3zU5Z33//FGwLUKVusZiSe03VK33Vqrt7ulve3WXWH17m7Xaiula3+tcrNbbLsKBUrqCU80SkVbbTUe2mg9QFCIcrCKLR4QDQIhEAQPQRGMkpCEQ8jM+/cHMmRymHySa658r5nv6/l4fP9oSMj01W/j2yTXTEIAAACIlUTUDwAAAAB9iwEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAABAABihgEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAABAABihgEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAABAABihgEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAABAABihgEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAABAABihgEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAABAABihgEIAAAQMwxAAACAmGEAAgAAxAwDEAAAIGYYgAAAADHDAAQAAIgZBiAAAEDMMAAdJJNJ1dbWqr6+Xg0NDVxcXFxcXFx5cNXX16u2tlbJZDLqKREZBqCD2tpaJRIJLi4uLi4urjy8amtro54SkWEAOqivr0/fQLn+t5O6ujqVlZWprq4u8n9TCv2iFa1oRat8uWgVRqu938Cpr6+PekpEhgHooKGhQYlEQg0NDTn/u1taWlReXq6Wlpac/92FhlZ2tLKjlR2t7Ghl57OVz39+5wsGoAMGYBhoZUcrO1rZ0cqOVnYMQL8YgA4YgGGglR2t7GhlRys7WtkxAP1iADpgAIaBVna0sqOVHa3saGXHAPSLAejAcgOlUim1tLRox44dPbq2bdumuXPnatu2bT3+2EK5WlpalEqluv3fgS+odrSyo5UdrexoZccA9IsB6KC7G2jXrl166623tHr16h5fVVVVWrZsmaqqqnr18YVyvfXWW9q1a1fW/x34gmpHKzta2dHKjlZ2DEC/GIAOst1AyWRSa9as0bp161RfX6/t27f36Ltfzc3N2rx5s5qbmyP/TlwU1/bt21VfX69169ZpzZo1WZ+sky+odrSyo5UdrexoZccA9IsB6CDbDbRjxw6tXr1azc3Nvfq7k8mktm7dGutnKZek5uZmrV69Wjt27OjyffiCakcrO1rZ0cqOVnYMQL8YgA4sAzDbcMmGAbiHpSNfUO1oZUcrO1rZ0cqOAegXA9ABA9A/BmBu0cqOVna0sqOVHQPQLwaggzgNwBEjRmj8+PF9/nkZgLlFKzta2dHKjlbZlSxYqxmLaiR1bDVjUY1KFqzNyedhADIAnTAAO/fss88qkUho69atzp+XAZhbtLKjlR2t7GiV3YxFNSqaMFczFtVktGr79lxgADIAnfgcgL+av0Y3zV3R6QDM5b8FWTEACwOt7GhlRys7WnVv79grmV+t8vJylcyvzun4kxiAEgPQic8BeNvCtSqaMFe3Lcwcern+t6DONDU1afTo0frEJz6ho446StOnT88YgA888IC++MUv6qCDDtKRRx6piy++WJs3b5Ykvfnmm0okEhnXmDFjJElPPfWUzj77bA0ePFiHHnqoRo4cqTfeeCPrY2EA5hat7GhlRys7Wtns/WfdiROf9PLPPAYgA9CJ7x8B3zR3RcaN3xfjT5LGjh2roUOHatGiRVqxYoVGjRqlgw8+OD0A77nnHlVUVGj9+vV68cUXddZZZ+lf/uVfJEmtra16/PHHlUgktHbtWm3atEn19fWSpMcee0yPP/641q1bp8rKSv3rv/6rPve5z2X9MTcDMLdoZUcrO1rZ0cru5EnzVDRhrk6eNC/nfzcDkAHopC9+B3DvdwKHTarok/HX2NioAQMG6JFHHkm/7cMPP9Tf/M3fdPkj4FdeeUWJREKNjY2S7D8C/uCDD5RIJLRy5cou34cBmFu0sqOVHa3saGXDdwD9YwA66KtDIHvH37BJFa4PuVvLly9XIpHQ22+/nfH2z3/+8+kBuGzZMo0aNUrHHXecDjroIB144IFKJBKqqqqS1PUArKmp0UUXXaQTTjhBBx98sD7xiU8okUho3ryu/+2OAZhbtLKjlR2t7GjVPX4HsG8wAB0U4ncAuxuATU1NOuyww/Sd73xHzz//vKqrqzV//nwlEglVVlZK6noAnnrqqfrGN76hRYsWafXq1Vq1apUSiYRmz57d5eNhAOYWrexoZUcrO1pl1/4U8NzHyzgF7AkD0EEh/g5gY2Oj+vfvn/Ej4I8++kgHHnigxo8fr2XLlimRSOidd95J//mDDz6YMQCXLFmiRCKhurq69PvU1dUpkUjo+eefT7/tL3/5CwOwj9HKjlZ2tLKjVXbp5wFMpbR7aalarj5Su9fv+ecGzwOYWwxAB4V6Cvjyyy9XUVGRnnnmGa1cuVLnn3++DjroII0fP15btmzRgAEDdOWVV2r9+vWaM2eOTjnllIwBuHHjRu2333667777tGXLFjU2NiqZTOqwww7TJZdconXr1umZZ57Rl770JQZgH6OVHa3saGVHK4PtH0l/Gi0VD5KKByn52A9z/ikYgAxAJ4X6PICNjY265JJLdOCBB+rII4/UzTffnPE0MGVlZTr++OM1cOBAnXXWWXriiScyBqAkXXPNNTrqqKO03377pZ8GZuHChfrMZz6jgQMH6rTTTtNzzz3HAOxjtLKjlR2t7GjVjQ3PS7/6jFQ8SKmrD1XVb3+glp29++doNgxABqCTOL0SSFQYgLlFKzta2dHKLh9atX05tva8fQOitUVaWCwVD97znb8ZX9Dut17itYA9YgA6YAD6xwDMLVrZ0cqOVnb50KqrXzXy9itIdW9Id41I/8hX5eOknY1eWzEAGYBOGID+MQBzi1Z2tLKjlV2+tGo/9ryMv1RKevUB6bqj9wy/G4ZKVeXpP2YA+sUAdMAA9I8BmFu0sqOVHa3s8qnV3tHn5WnImj/MOOih0pFSfW3GuzAA/WIAOmAA+scAzC1a2dHKjlZ2+dbKywsRtDnooasPlf5SIiVbO7wbA9AvBqADBqB/DMDcopUdrexoZZdPrXL+HcDduzoc9NDGV7t8dwagXwxABwxA/xiAuUUrO1rZ0couX1q5/A5gp6eIuzjokQ0D0C8GoAMGoH8MwNyilR2t7Ghllw+tXE8BZ7xfu4MeW6cerbkP/8b0OBiAfjEAHTAA/WMA5hat7GhlRyu7fGiVi+cBnLGoRqdNeFg1t38z/V2/JVPO1D3z/mJ+HAxAvxiADhiA/jEAc4tWdrSyo5VdbFpteF7brh8mFQ9Sy9RP6oZJP9KvF1b36K9gAPrFAHRQqAMwlUrphz/8oT75yU8qkUho8ODB6ZeB62sMwNyilR2t7GhlV/Ct2h302DD1FI2a+OtenSJmAPrFAHRQqAOwoqJC/fv315IlS7Rp0yZt3rxZ27ZtS/95UVGRbr311j55LAzA3KKVHa3saGVX0K0+WJdx0GPlb76nz0x4rNeniBmAfjEAHRTqALz99ts1dOjQLv+cAZi/aGVHKzta2RVkq1RKevV+6bqj0q/oMffh3zi/kggD0C8GoINCHIBjxoxRIpFIX0VFRRoxYkT6R8AjRozI+PNEwu8txADMLVrZ0cqOVnYF16r5Q+nhSzJe0eOeeX/JyWsJMwD9YgA66PEATKWkXU2mK7ljm7ZueVfJHdvMH9PllUqZ/zvV19frmmuu0ZAhQ7Rp0yZt2bIlYwB++OGHGjJkiK655hpt2rRJmzZtcu6YDQMwt2hlRys7WtkVVKsuXtEjF6eIJQagbwxABz0egLua9v1bUl9eu5p69N/r1ltvVVFRUfo/tx2AEj8Czme0sqOVHa3sCqJV+1f0+PXfS+++lvNPwwD0iwHogAHoHwMwt2hlRys7Wtnlfat2Bz005796/M8YKwagXwxAB4X4I2CJAVjIaGVHKzta2eVtq04Oeqiq3OunZAD6xQB0UIiHQKTuB+CwYcM0ffr0PnksDMDcopUdrexoZZeXrTo56KH6jd4/LQPQLwagg7gOwH/6p3/S+eefr40bN+qDDz7w+lgYgLlFKzta2dHKLu9abVgsTf90m4Met0rJ1j751AxAvxiADuI6AF988UWddtppGjhwIE8Dk2doZUcrO1rZ5U2r3bukBVO9H/TIhgHoFwPQQaEOwJAwAHOLVna0sqOVXV60+mCd9Nuv9MlBj2wYgH4xAB0wAP1jAOYWrexoZUcru6BbpVLSsvvaHfSYE9nDYQD6VRAD8M4779TnPvc5HXzwwTr44IN15plnqqIi+wtPP/LIIzr11FM1cOBADR8+XPPmzevx52UA+scAzC1a2dHKjlZ2wbZqf9DjvlF9ctAjGwagXwUxAJ944gnNmzdPNTU1Wrt2rSZNmqT+/ftr1apVnb7/kiVL1K9fP918881avXq1pkyZov79+2vlypU9+rwMQP8YgLlFKzta2dHKLshW659rc9DjMOmvt0kB/LOHAehXQQzAznzyk5/U73//+07/7MILL9TIkSMz3vblL39Zl112WY8+BwPQPwZgbtHKjlZ2tLILqtXuXdKCX0R60CMbBqBfBTcAW1tb9dBDD2nAgAGqqqrq9H2OO+64Dk9kPHXqVJ122mk9+lwMQP8YgLlFKzta2dHKLphWH9S0O+jx35Ec9MiGAehXwQzAFStW6BOf+IT69eunwYMHZ/2dvv79+6usrCzjbXfccYeOOOKIrJ9j586damhoSF+1tbVKJBKqq6tTS0tLxtXY2Kiqqio1NTUpmUz2+GptbdXWrVvV2traq48vlKupqUlVVVVqbGzs0Hjv1dzcrPLycjU3N3f5Ply0ohWtQrgib7Vrl3a//HulPj7okbqxSLtXzI68S1+3qqurYwBG/QByZdeuXVq3bp2WLVumiRMn6lOf+lSX3wHs7QAsLi5WIpHocJWVlam8vDzjmjNnjpYuXap33nlHW7du5erl9c4772jp0qWaM2dOh8ZcXFxcXPZr3mMP6t2Sr6W/67flljP19CP3Rv64orjKysoYgFE/AF/OOecc/ehHP+r0z3r7I+CefAewpaVFtbW1qqqq0pYtW9TU1KTm5mbz1dTUpM2bN/f44wrlampq0pYtW1RVVaXa2tqw/406jy5a0YpW8Wy1u2aRUtNP3fNdv6sPU+viX6ll187Ie0TViu8AFvAA/NrXvqYxY8Z0+mcXXnihRo0alfG2s846K6eHQCQplUrpvffe0+rVq3t8VVVVadmyZaqqqurVxxfK9d577ymVSmX936GlJZDfqckDtLKjlR2t7Pq8VacHPSr75nM78tmK3wEskAE4ceJELV68WG+++aZWrFihiRMnar/99tOCBQskSaNHj9bEiRPT779kyRLtv//+mj59uqqrq1VcXJzzp4Fpq7W1VTt27OjRtW3bNs2dO1fbtm3r8ccWytXaanu9Sf7hY0crO1rZ0cquT1t9UCP99h/3HfR44sfBHfTIhgHoV0EMwEsvvVRFRUUaMGCADj/8cJ1zzjnp8SfteS3b9t8NfOSRR3TKKadowIAB+uxnP5vzJ4J2xRdUO1rZ0cqOVna0suuTVqmUtKx03yt63FgkrX7C3+fzhAHoV0EMwKgwAMNAKzta2dHKjlZ23ls1fyg99J02r+jxr1LDe34+l2cMQL8YgA4YgGGglR2t7GhlRys7r63WPyt9fNBjzyt6zAjiFT16iwHoFwPQAQMwDLSyo5UdrexoZeel1e5d0vwpbQ56fDFvDnpkwwD0iwHogAEYBlrZ0cqOVna0sst5qy1r8/qgRzYMQL8YgA4YgGGglR2t7GhlRyu7nLVKpaRX7pWuPTKvD3pkwwD0iwHogAEYBlrZ0cqOVna0sstJqwI66JENA9AvBqADBmAYaGVHKzta2dHKzrnV+mcL6qBHNgxAvxiADhiAYaCVHa3saGVHK7tetyrQgx7ZMAD9YgA6YACGgVZ2tLKjlR2tOleyYK1mLKrJeNveViXzq1WyYK3tL9qyVvrNP7Q56DG+YA56ZMMA9IsB6IABGAZa2dHKjlZ2tOrcjEU1KpowN2MEtrS0aOzMOR3e3qlOD3o86fdBB4QB6BcD0AEDMAy0sqOVHa3saNW19iOwZH61iibMVcn86uwfGJODHtkwAP1iADpgAIaBVna0sqOVHa2y2zsCh02qUNGEuRo7c072Vm/8OTYHPbJhAPrFAHTAAAwDrexoZUcrO1p1b+/4O3nSvK5b7d4pzZ+877t+MTjokQ0D0C8GoAMGYBhoZUcrO1rZ0So703cA2x30eP3O7+uO+Su6/Pu6O0DS2QGUnnx8CBiAfjEAHTAAw0ArO1rZ0cqOVl3r9ncAUynplXvaHPQ4Xlr9ZKcHSDr7+6yft6cfHwIGoF8MQAcMwDDQyo5WdrSyo1XnujsFfNdTS6Wyi/f9yPf+8zMOerT/+J6ON9ePjxoD0C8GoAMGYBhoZUcrO1rZ0apz2Z4H8LE/3a/G607cd9Bjya87PejR/sfHPR1vrh8fJQagXwxABwzAMNDKjlZ2tLKjlV3L9katu+Pb+77rd/vp0nvLs37M3vE2bFJFrz6n68dHhQHoFwPQAQMwDLSyo5UdrexoZbRlrVJ3nr1v/D15hbSrOeuH8B1ABqAvDEAHDMAw0MqOVna0sqNVN9od9Nh5zTHavbK82w/jdwAZgD4xAB0wAMNAKzta2dHKjlZZNNVlHPRI3ne+nnr0vm5bcQqYAegbA9ABAzAMtLKjlR2t7GjVhTeekW45Zc/4u+ZT0pLb1bJrp6mV6/P48TyA2TEAGYBOGIBhoJUdrexoZUerdnbvlJ6e1O6gx+uSaNUTDEC/GIAOGIBhoJUdrexoZUerNraskX7T9qDHTzIOetDKjgHoFwPQAQMwDLSyo5UdrexopT0HPZb+PvMVParndXg3WtkxAP1iADpgAIaBVna0sqOVXexbtTvoofsvkLZt6vRdY9+qBxiAfjEAHTAAw0ArO1rZ0cou1q3eeEa6ZVjGQY/OXtFjr1i36iEGoF8MQAcMwDDQyo5WdrSyi2WrDgc9vpQ+6JFNLFv1EgPQLwagAwZgGGhlRys7WtnFrlU3Bz2yiV0rBwxAvxiADhiAYaCVHa3saGUXm1btD3rcdEKnBz2yiU2rHGAA+sUAdMAADAOt7GhlRyu7WLRqqpPKLjId9MgmFq1yhAHoFwPQAQMwDLSyo5UdrewKvlX7gx4vzMx60CObgm+VQwxAvxiADhiAYaCVHa3saGVXsK16edAjm4Jt5QED0C8GoAMGYBhoZUcrO1rZFWQrh4Me2RRkK08YgH4xAB0wAMNAKzta2dHKrqBapVLS0t9J1x7R64Me2RRUK88YgH4xAB0wAMNAKzta2dHKrmBaNX2QedDjgf/bq4Me2RRMqz7AAPSLAeiAARgGWtnRyo5WdgXRat2inB30yKYgWvURBqBfDEAHDMAw0MqOVna0ssvrVrt3Sk/9PKcHPbLJ61Z9jAHoFwPQAQMwDLSyo5UdrezyttXmaunONgc95v40Jwc9ssnbVhFgAPrFAHTAAAwDrexoZUcru7xr1dlBjzUVffKp865VhBiAfjEAHTAAw0ArO1rZ0cour1o1fSD98dteD3pkk1etIsYA9IsB6IABGAZa2dHKjlZ2edOqw0GPO7wc9Mgmb1oFgAHoFwPQAQMwDLSyo5UdreyCb9X+oMfMM6RNKyJ5KMG3CggD0C8GoAMGYBhoZUcrO1rZBd2q/UGPHL2iR28F3SowDEC/GIAOGIBhoJUdrexoZRdkq1RKevnuSA56ZBNkq0AxAP1iADpgAIaBVna0sqOVXXCtIj7okU1wrQLGAPSLAeiAARgGWtnRyo5WdkG1CuCgRzZBtQocA9AvBqADBmAYaGVHKzta2QXRavdO6amJQRz0yCaIVnmCAegXA9ABAzAMtLKjlR2t7CJv1dkrerRsj+axdCPyVnmEAegXA9ABAzAMtLKjlR2t7Hy2KlmwVjMW1XT6ZzMWrtWi+69rd9Djqb753ItqVLJgbY//Tu4rOwagXwxABwzAMNDKjlZ2tLLrrpXLkJqxqEZFE+Z2+Pi7K17WgilfbXPQ45vStvd7/1+iB5+7q7dbcF/ZMQD9YgA6YACGgVZ2tLKjlV13rVyHVPv3m/3oA9o8dWifHPRo/7ldxp/EfdUTDEC/GIAOGIBhoJUdrexoZWdp5TqkZiyq0bAJs3XvlG/3+UGPvY912KQKp/EncV/1BAPQLwagAwZgGGhlRys7WtlZWzkNqc3VWj31c20OevzMdNAjV7/Ht/cxD5vk9mTS3Fd2DEC/GIAOGIBhoJUdrexoZdeTVj0eUh+/osfuqw+Xigfpw6nH6j9/fk2PvnPo+nt8fAcwGgxAvxiADhiAYaCVHa3saGXn7TuA7V7R463bzpW2vd+rHx/39sfP/A5gdBiAfhXEAJw2bZpOP/10HXTQQTr88MN1wQUXaM2aNVk/prS0VIlEIuMaOHBgjz4vAzAMtLKjlR2t7Lz8DuC6hdLNJ0vFg7Rz6qFafP8vMw569HYE9uS7eJwCjhYD0K+CGIDnnnuuSktLtWrVKi1fvlznnXeehg4dqqampi4/prS0VIMGDdKmTZvS1/vv9+wpBBiAYaCVHa3saGWX01PALTsyXtGj7sa/0x/mzOvy7+3Jc/H19MfPPA9gtBiAfhXEAGxvy5YtSiQSWrx4cZfvU1paqsGDBzt9HgZgGGhlRys7Wtnl7HkAN1dLd/7vfQc95v1Pzl7RI5e/x+eC+8qOAehXQQ7AdevWKZFIaOXKlV2+T2lpqfr166ehQ4dqyJAhOv/887Vq1aoefR4GYBhoZUcrO1rZObf6+KDHvlf0OFFa+3TOHl+uf4/PBfeVHQPQr4IbgMlkUiNHjtTZZ5+d9f1eeOEF3X///aqsrNRzzz2nUaNGadCgQaqtre3yY3bu3KmGhob0VVtbq0Qiobq6OrW0tOT0am5uVnl5uZqbm3P+dxfaRSta0crvNf3p1SqZX93pn5XMr9ZN81b1vtXWd5V88Fvp7/ol7/+mWj6qzdljL5lfraIJczs8/q7e7vvivgqjVV1dHQMw6geQa5dffrmKioqyDrnOtLS06KSTTtKUKVO6fJ/i4uIOB0cSiYTKyspUXl7OxcXFVZDX2JlzVDRhrsbOnGN6u/Va8sA12nHtcVLxILX+8lCtuHusymfPyuljv+z2J7p8fGNnztFltz8ReV+uvr/KysoYgFE/gFwaN26chgwZog0bNvTq47/1rW/poosu6vLP+Q5gmBetaEUr/1f775i1/c89brV9m1rnXZn+rl9q5hlqqa2M/L9jX1zcV2G04juABTIAU6mUxo0bp2OOOUY1Nb37nY7W1ladeuqp+slPfmL+GH4HMAy0sqOVHa066uogRY9abV7t7aBHPuC+svPZit8BLJABOHbsWA0ePFjPPfdcxtO6bN++74vK6NGjNXHixPR/vvrqqzV//nytX79er776qi666CIdcMABqqqqMn9eBmAYaGVHKztada6zp1IxtfJ80CNfcF/ZMQD9KogB2Nnv5SUSCZWWlqbfZ8SIERozZkz6P19xxRUaOnSoBgwYoCOPPFLnnXeeXnvttR59XgZgGGhlRys7WnXU6+8ANm6R/njhvu/6Pfhv0raePe9qoeC+smMA+lUQAzAqDMAw0MqOVna0ypTtqVSytqrZ94oeuuZw6cXf7PluYExxX9kxAP1iADpgAIaBVna0sqPVPt29kkfJ/OqOrVp2SBUT9n3Xb+aXpfd79lyrhYj7yo4B6BcD0AEDMAy0sqOVHa326e6VPKY/vTqz1ftV0h1nxfagRzbcV3YMQL8YgA4YgGGglR2t7AqplY/XtG0r3WrXLumlu/Yd9Lj5JGntfKe/u9AU0n3lGwPQLwagAwZgGGhlRyu7QmrV3Y9wXV8SraWlRRWPPqDkg//e5qDHv0uNm53+3kJUSPeVbwxAvxiADhiAYaCVHa3sCq2Vz9fD3V39VPoVPTjokV2h3Vc+MQD9YgA6YACGgVZ2tLIrxFZdPY1Lr7XskCquynhFDw56ZFeI95UvDEC/GIAOGIBhoJUdrewKtVVnT+TcK+0Oeqyf+e9qaY7vP0ytCvW+8oEB6BcD0AEDMAy0sqOVXSG2ysl3AFOpPQc9rjk8fdBj9+p5BdfKl0K8r3xhAPrFAHTAAAwDrexoZVdorXLyO4CNW6Q//EeHgx6F1sonWtkxAP1iADpgAIaBVna0siukVjk5BVyzYM/Tuuw96PHSb9MHPQqplW+0smMA+sUAdMAADAOt7GhlV0itnJ4HsN1BD91xZoeDHoXUyjda2TEA/WIAOmAAhoFWdrSyo5U6eUWPKzt9RQ9a2dHKjgHoFwPQAQMwDLSyo5VdrFt1ctAj2yt6xLpVD9HKjgHoFwPQAQMwDLSyo5VdbFs1bpH+8K193/X7w7e6fUWP2LbqBVrZMQD9YgA6YACGgVZ2tLKLZassBz2yiWWrXqKVHQPQLwagAwZgGGhlRyu7XLdyOojhW6cHParsH859ZUYrOwagXwxABwzAMNDKjlZ2uW6Vk6di8eH9qj2Db+/4q7hqzyDsAe4rO1rZMQD9YgA6YACGgVZ2tLLz0SonT8acK6nUnh/xtj3oUbOgV38V95UdrewYgH4xAB0wAMNAKzta2flqlZOXY3PVuLmTgx5bev3XcV/Z0cqOAegXA9ABAzAMtLKjlZ3PVnvH37BJFTn/u7vV4aDHXaaDHtlwX9nRyo4B6BcD0AEDMAy0sqOVXcF9B7Blx54nck4f9DirRwc9sv7V3FdmtLJjAPrFAHTAAAwDrexoZVdQvwOYg4Me2dpm+jIAACAASURBVHBf2dHKjgHoFwPQAQMwDLSyo5VdQZwC7nDQ4+ReH/TIhvvKjlZ2DEC/GIAOGIBhoJUdrezy/nkAGzdLD/57zg56ZMN9ZUcrOwagXwxABwzAMNDKjlZ2ed1q7fx9Bz2uPUJ6+W7ngx7Z5HWrPkYrOwagXwxABwzAMNDKjlZ2edmqZXvHgx6bV/v/tPnYKiK0smMA+sUAdMAADAOt7Ghll3et3l/V7qDHhJwe9Mgm71pFiFZ2DEC/GIAOGIBhoJUdrexCa9Xl7xCmUnru/mu0+5efanPQY2GfPrbQWoWMVnYMQL8YgA4YgGGglR2t7EJr1elp4cbNevO2f25z0OM/vB30yCa0ViGjlR0D0C8GoAMGYBhoZUcruxBbZYzAtU+r+boiqXiQdl99uPeDHtmE2CpUtLJjAPrFAHTAAAwDrexoZRdqq5nzV6h08r7X8f3gpr/vk4Me2YTaKkS0smMA+sUAdMAADAOt7GhlF2Sr91dJM7+cHn+lU77dZwc9sgmyVaBoZccA9IsB6IABGAZa2dHKLqhWqZT04p3pV/TYMvU4XTp5Wt++lnAWQbUKHK3sGIB+MQAdMADDQCs7WtkF06pxs/Tgv6W/67doygjdXfGSpD58LeFuBNMqD9DKjgHoFwPQAQMwDLSyo5VdEK3WPi3ddGL6oMeUST/WjIWZLxkXwggMolWeoJUdA9AvBqADBmAYaGVHK7tIW7Vsl+b+bN/Tu9z5v3V/eUXfvpZwD3Bf2dHKjgHoFwPQAQMwDLSyo5VdZK02rcw46KGnJgZx0CMb7is7WtkxAP1iADpgAIaBVna0suvzVu0OekTxih69xX1lRys7BqBfDEAHDMAw0MqOVnZ92mrb+xkHPfTHC6WmD/x/3hzhvrKjlR0D0C8GoAMGYBhoZUcruz5r1eagh649ItJX9Ogt7is7WtkxAP1iADpgAIaBVna0svPeqpODHlG/okdvcV/Z0cqOAegXA9ABAzAMtLKjlZ3XVh0Oevw8+IMe2XBf2dHKjgHoFwPQAQMwDLSyo5Wdl1bJZMeDHuvy46BHNtxXdrSyYwD6xQB0wAAMA63saGWX81bb3pce+GbmQY/GLbn5uyPGfWVHKzsGoF8MQAcMwDDQyo5WdjltteapvD/okQ33lR2t7BiAfjEAHTAAw0ArO1rZ5aRVAR30yIb7yo5WdgxAvxiADhiAYaCVHa3snFttWinNPCPzoMfunbl9kIHgvrKjlR0D0C8GoAMGYBhoZUcru163SialF+6QrvnUnuF3y7CCOOiRDfeVHa3sGIB+MQAdMADDQCs7Wtn1qtW2Te0Oenw7r17Ro7e4r+xoZccA9IsB6IABGAZa2dHKrset1jwl3XTCvoMeS39XUAc9suG+sqOVHQPQLwagAwZgGGhlRys7c6tdzdLcn7Y56HG2tLm6bx5kILiv7GhlxwD0iwHogAEYBlrZ0cqus1YlC9ZqxqKafe+0aYV0+5fS42/ZXZcX7EGPbLiv7GhlxwD0iwHogAEYBlrZ0cqus1YzFtWoaMJczVi4RnphZvqgR9N1J+iSn0/LHIcxwn1lRys7BqBfDEAHDMAw0MqOVnZdtfpdxQtaPOXs9Hf91s8YpS9MKIvt+JO4r3qCVnYMQL8YgA4YgGGglR2t7DpttaYifdBjx9TDNHXKFSqa8GSsx5/EfdUTtLJjAPrFAHTAAAwDrexoZZfRalez9ORPMg56/POk36lowlwNm1QR9UONHPeVHa3sGIB+FcQAnDZtmk4//XQddNBBOvzww3XBBRdozZo13X7cI488olNPPVUDBw7U8OHDNW/evB59XgZgGGhlRyu7dKva1zIOeujpSZq5YFV6/BVNmMt3ALmvzGhlxwD0qyAG4LnnnqvS0lKtWrVKy5cv13nnnaehQ4eqqampy49ZsmSJ+vXrp5tvvlmrV6/WlClT1L9/f61cudL8eRmAYaCVHa3sWnbt1Iq7L1cq4xU9Fu07CPLx6Gv/n+OI+8qOVnYMQL8KYgC2t2XLFiUSCS1evLjL97nwwgs1cuTIjLd9+ctf1mWXXWb+PAzAMNDKjlZG2zYpef8F+77rV3aR1FTX5diL+wjkvrKjlR0D0K+CHIDr1q1TIpHI+t284447TrfeemvG26ZOnarTTjuty4/ZuXOnGhoa0ldtba0SiYTq6urU0tKS06u5uVnl5eVqbm7O+d9daBetaJXLa/eqJ5T6+KDH7l9+Srv+eqdadu1SS0uLpj+9WiXzqzv9uJL51Zr+9OrIH38UF/cVrfKtVV1dHQMw6geQa8lkUiNHjtTZZ5+d9f369++vsrKyjLfdcccdOuKII7r8mOLiYiUSiQ5XWVmZysvLubi48vh6ctaftOH2/5v+rl/9jcO16OE7In9cXFxcub/KysoYgFE/gFy7/PLLVVRUpNra2qzv15sByHcAw7xoRSvnq/Y1pW4/PT3+WismqrnhI1oZL+4rWuVbK74DWGADcNy4cRoyZIg2bNjQ7fv25kfA7fE7gGGglV3cW3V4KbdkMuMVPRqvO1F64xlJtOoJWtnRys5nK34HsEAGYCqV0rhx43TMMceopsb2S9gXXnihRo0alfG2s846i0MgeYhWdnFvlXFYY9sm6YF9P/JdMOVruuuppen3jXurnqCVHa3sGIB+FcQAHDt2rAYPHqznnntOmzZtSl/bt29Pv8/o0aM1ceLE9H9esmSJ9t9/f02fPl3V1dUqLi7maWDyFK3saLVnBP7g51dr+7XHScWD1HL14Zo06QrNWLg24/1oZUcrO1rZMQD9KogB2NnBjEQiodLS0vT7jBgxQmPGjMn4uEceeUSnnHKKBgwYoM9+9rM8EXSeopVd7FvtapaevCL9Xb+qqafp/0y8q9Onb4l9qx6glR2t7BiAfhXEAIwKAzAMtLKLdav3Xs94RY/fT7lYwybM7vKl3GLdqodoZUcrOwagXwxABwzAMNDKLpatkklpye3pgx665RTNevSBbl/KLZateolWdrSyYwD6xQB0wAAMA63sYteq4T0p4xU9LtZdTy01vZRb7Fo5oJUdrewYgH4xAB0wAMNAK7tcterwdCptzFhUo5IFazv9sz5VPU+68fg9w+/aI6VX7tGMhWvNL+XGfWVHKzta2TEA/WIAOmAAhoFWdrlqFfRr4rY76KHfnC1tWSOpZ8OV+8qOVna0smMA+sUAdMAADAOt7HLZqv3YC2L8vbdcavOKHpo/Wdq9s1d/FfeVHa3saGXHAPSLAeiAARgGWtnlutXe0ZftMEWfSCalJb+Wrj4sfdBDb/zZ6a/kvrKjlR2t7BiAfjEAHTAAw0ArOx+t9o6/rp5OxbuG96T7z8846KGmOue/lvvKjlZ2tLJjAPrFAHTAAAwDrewK7juA1XPbHfS4V0qlcvJXc1/Z0cqOVnYMQL8YgA4YgGGglV3B/A7grmbpifFtDnr8g7QltyePua/saGVHKzsGoF8MQAcMwDDQyq4gTgG/t1z69RdzctAjG+4rO1rZ0cqOAegXA9ABAzAMtLLL6+cBTCalv87Yd9Bj+qnOBz2y4b6yo5UdrewYgH4xAB0wAMNAK7u8bdX+oMdD35GaP/T6KfO2VQRoZUcrOwagXwxABwzAMNDKLi9brX7S20GPbPKyVURoZUcrOwagXwxABwzAMNDKLq9a7WqSnvix14Me2eRVq4jRyo5WdgxAvxiADhiAYaCVXd606nDQY4qXgx7Z5E2rANDKjlZ2DEC/GIAOGIBhoJVd8K06O+ix/tlIHkrwrQJCKzta2TEA/WIAOmAAhoFWdiG06vIEccN7evvWr/fpQY9sQmiVL2hlRys7BqBfDEAHDMAw0MouhFadPlfg6ie1/drjpOJBarn68D476JFNCK3yBa3saGXHAPSLAeiAARgGWtmF0mrvCLxj/usZBz0233JGnx70yCaUVvmAVna0smMA+sUAdMAADAOt7EJqVVb+hN74xanp8bfsd+Ok3buiflhpIbUKHa3saGXHAPSLAeiAARgGWtkF0ardQY9NU4v0vck3Rfd4uhBEqzxBKzta2TEA/WIAOmAAhoFWdpG3anhXuu9f09/1e2rKOfrSpD/5f/3gXoi8VR6hlR2t7BiAfjEAHTAAw0Aru0hbrX5SurHo44MeR2jCpJ9qxsI9v+/X6cGQiHFf2dHKjlZ2DEC/GIAOGIBhoJVdJK3avaLH5lvO0Ncm3t1h7IU2Armv7GhlRys7BqBfDEAHDMAw0Mquz1u9W9nmFT0GSwt+odueXtXlyJuxqEYlCzgFnG9oZUcrOwagXwxABwzAMNDKrs9aJZPSX29r94oez+Xkr+7yiaSV2wHJfWVHKzta2TEA/WIAOmAAhoFWdn3Sqt1Bj1y/okdXPyrO9Y+Qua/saGVHKzsGoF8MQAcMwDDQys57qzYHPXTdUdKy+7y8okf7sefj9we5r+xoZUcrOwagXwxABwzAMNDKzlurdgc99NuvSB/4Pcyxd/QNm1Th5fAI95UdrexoZccA9IsB6IABGAZa2Xlp1clBj756RY+942/YpIqc/93cV3a0sqOVHQPQLwagAwZgGGhll9NWHQ56fDpnBz0s+A5gOGhlRys7BqBfDEAHDMAw0MouZ63aH/R4+Ls5PejRHX4HMCy0sqOVHQPQLwagAwZgGGhll5NWq5/IPOjx6v1eDnp0hVPA4aGVHa3sGIB+MQAdMADDQCs7p1a7mqQ5/93uoMe63D/IbvA8gOGhlR2t7BiAfjEAHTAAw0Aru163evc16dd/3+agx9Q+O+gRFe4rO1rZ0cqOAegXA9ABAzAMtLLrcatkUvrLrZkHPTYs9vsgA8F9ZUcrO1rZMQD9YgA6YACGgVZ2PWrV8K5036g2Bz0u6dODHlHjvrKjlR2t7BiAfjEAHTAAw0ArO3OriA96hID7yo5WdrSyYwD6xQB0wAAMA63sum21q0ma81+RH/QIAfeVHa3saGXHAPSLAeiAARgGWtllbdX+oMfC4oI/6JEN95UdrexoZccA9IsB6IABGAZa2XXaKsYHPbLhvrKjlR2t7BiAfjEAHTAAw0Aruw6t6jfG+qBHNtxXdrSyo5UdA9AvBqADBmAYaGWX0apqjnTD0Fgf9MiG+8qOVna0smMA+sUAdMAADAOt7FpaWvTk439Scvb/46BHN7iv7GhlRys7BqBfDEAHDMAw0Mpu91svq3HaKRz0MOC+sqOVHa3sGIB+MQAdMADDQCuDZFL6S4lSVx8qFQ9SavqpHPToBveVHa3saGXHAPSLAeiAARgGWnWjfqNUOjL9I993bz1HLQ2bo35UweO+sqOVHa3sGIB+MQAdMADDQKssqsrbHPQ4WruXlqp89mxaGXBf2dHKjlZ2DEC/GIAOGIBhoFUndjZK5eP2HfS4a4RU9wateoBWdrSyo5UdA9AvBqADBmAYaNXOxlelGV/o9KAHrexoZUcrO1rZMQD9YgA6YACGgVYfS7ZKfymRPj7osecVPZ7PeBda2dHKjlZ2tLJjAPrFAHTAAAwDrdThoIf+NLrTV/SglR2t7GhlRys7BqBfDEAHDMAwxL5Vu4MeevWBLl/RI/ateoBWdrSyo5UdA9AvBqADBmAYYtuqi4Me2cS2VS/Qyo5WdrSyYwD6xQB0wAAMQyxbZTnokU0sW/USrexoZUcrOwagXwUzABcvXqxRo0bp6KOPViKR0OzZs7O+/7PPPqtEItHh2rRpk/lzMgDDEKtWyVbp+V/tO+jxq890OOiRTaxaOaKVHa3saGXHAPSrYAZgRUWFJk+erFmzZvVoAK5du1abNm1KX8lk0vw5GYBhiE0r40GPbGLTKgdoZUcrO1rZMQD9KpgB2FZPBuDWrVt7/XkYgGGIRav2Bz1ee7DLgx7ZxKJVjtDKjlZ2tLJjAPoV+wFYVFSko446Sl//+tf117/+tUefhwEYhoJutbNRKv9/bQ56fLXbgx7ZFHSrHKOVHa3saGXHAPQrtgNwzZo1+u1vf6tly5ZpyZIl+s///E/tv//+evXVV7v8mJ07d6qhoSF91dbWKpFIqK6uTi0tLTm9mpubVV5erubm5pz/3YV2FWqr3W+9pNRtfycVD1KqeLBa509Vyw63/46F2srHRSta0apwW9XV1TEAo34APlgGYGe+8pWv6JJLLunyz4uLizs9OFJWVqby8nIurh5dl93+hMbOnNPxz2bPUvnNP1Br8Sel4kHaft3x+suDN0b+eLm4uLgK5SorK2MARv0AfOjtAPyf//kfnXnmmV3+Od8BDPPK11Yl86tVNGGuSuZX73t73Zt651dfTf/IN/nwaLU0bIl9qyguWtGKVoXbiu8AMgAzfP3rX9c3v/lN8/vzO4BhyOdWMxbVqGjCXM1YVCOtmq0d1w6Rigdp19VH9vqgRzb53Kqv0cqOVna0svPZit8BLKAB2NjYqMrKSlVWViqRSKikpESVlZV6++23JUkTJ07U6NGj0+9/6623qry8XOvWrdPKlSs1fvx4/a//9b+0aNEi8+dkAIYh31vdOX+5Hp58fvq7fptuOdPpoEc2+d6qL9HKjlZ2tLJjAPpVMAOwqyd2HjNmjCRpzJgxGjFiRPr9b7rpJp100kk64IADdOihh+qrX/2q/vznP/foczIAwxBVq5IFa/d8564TMxbVqGTB2u7/ko3LpBmf3/Pj3qmDdeeU70mt/v577G01/enV7o+9wPH/QTta2dHKjgHoV8EMwCgwAMMQVauMH98a3p4h2So9Pz39ih4bp56g70ye3v3HOdrbau/vH/bqsccE/x+0o5UdrewYgH4xAB0wAMMQZav2g8k0oOprpXvPS//I98kp39Bvn1pm/3gHbVv16rHHCP8ftKOVHa3sGIB+MQAdMADDEHWrvcNp2KSK7gfUqlnSDcelD3r8bNKVmrEw88etPodY+1Y9euwxE/V9lU9oZUcrOwagXwxABwzAMITQau+AGjapovN32Nkozc58RY975izq89/D66xVt489pkK4r/IFrexoZccA9IsB6IABGIaoW3X7XbTafQc9VDxYWnSN14Me2fAdQLuo76t8Qis7WtkxAP1iADpgAIYh2N8BTLZKi29JH/TQr/5WerNnrzeda/wOoB3/H7SjlR2t7BiAfjEAHTAAwxDiKeAzJ9yv2pJ9r+ihR8ZI2z/q08fXGU4B2/H/QTta2dHKjgHoFwPQAQMwDME9D+CqWdpx7bF7ht91R0uv/SHnr+jRWzwPoB3/H7SjlR2t7BiAfjEAHTAAwxBMq53bMg963P01b6/o0VvBtMoDtLKjlR2t7BiAfjEAHTAAwxBEq9pl0m1/12cHPXr7KiRBtMoTtLKjlR2t7BiAfjEAHTAAwxBpq4gOevT2VUi4r+xoZUcrO1rZMQD9YgA6YACGIbJW9bXSvf8S2UGP3pzi5b6yo5UdrexoZccA9IsB6IABGAaXVr39UapWPp5+RQ9df4xU+cdIDnr09Hn8uK/saGVHKzta2TEA/WIAOmAAhsGlVY9/lLpzmzR7bFAHPXrySh7cV3a0sqOVHa3sGIB+MQAdMADD4NrK/KPUPj7oYcF3AP2hlR2t7GhlxwD0iwHogAEYhly0yjqkkq3S4pulX35yz/gr+Wzkr+gh8TuAvtHKjlZ2tLJjAPrFAHTAAAxDrlp1+qPUre+0O+jxfWn7VsdH7I5TwP7Ryo5WdrSyYwD6xQB0wAAMg7fvAAZy0KMzPA+gf7Syo5UdrewYgH4xAB0wAMOQ698BvPPpSj06ZVSbgx7/R/pwfS4fcmS4r+xoZUcrO1rZMQD9YgA6YACGIaengGtfSR/0aJ06WC///ieRH/TIJe4rO1rZ0cqOVnYMQL8YgA4YgGHIyfMAtj/o8au/1aOP/6nr5wHMU9xXdrSyo5UdrewYgH4xAB0wAMPg3GrrO9I9/xzcQQ8fuK/saGVHKzta2TEA/WIAOmAAhsGp1crHpWltD3qUBXPQwwfuKzta2dHKjlZ2DEC/GIAOGIBh6FWrndukWZcX5EGPbLiv7GhlRys7WtkxAP1iADpgAIahx61qX5FuO23P8PvlIdIz1xbUQY9suK/saGVHKzta2TEA/WIAOmAAhsHcKtkqPdfuFT3eWtI3DzIQ3Fd2tLKjlR2t7BiAfjEAHTAAw2BqtfXtzIMej/5nwR70yIb7yo5WdrSyo5UdA9AvBqADBmAYum214tFYHfTIhvvKjlZ2tLKjlR0D0C8GoAMGYBi6bLVzmzTrstgd9MiG+8qOVna0sqOVHQPQLwagAwZgGDpt9c7Sdgc9rovNQY9suK/saGVHKzta2TEA/WIAOmAAhiGjVbJVeu6mWB/0yIb7yo5WdrSyo5UdA9AvBqADBmAY0q0+WC/dc27sD3pkw31lRys7WtnRyo4B6BcD0AEDcI/06+l2YsaiGu+vp9vS0qJXSicqNW3Ixwc9jpWWPxTbgx7Z5NN9FTVa2dHKjlZ2DEC/GIAOGIB7zFhUo6IJczuMwK7enlM7GpR87If7vuv3u3OkDzf4+3x5Lp/uq6jRyo5WdrSyYwD6xQB0wADcp/3Y65Px1+agR6p4sFoXXs1Bj27k230VJVrZ0cqOVnYMQL8YgA4YgJn2jr5hkyr8jr92Bz1Sv/pbPf+Hm/KqVVTy8b6KCq3saGVHKzsGoF8MQAeFNABz9Xt8e8ffsEkVuXx4+3z0VruDHpeqZdsHfEE14h8+drSyo5UdrewYgH4xAB0U0gDMxe/xef8O4IpHpYyDHg9LqRRfUHuAVna0sqOVHa3sGIB+MQAdFNIAlNx+j8/r7wDuaJAe/1GXBz34gmpHKzta2dHKjlZ2DEC/GIAOCm0ASr37Lp7XU8DvvCzd+rl9r+jx5+ul1t0Z78IXVDta2dHKjlZ2tLJjAPrFAHRQiANQ6vnv8Xl5HsDW3dKzN7Z5RY/h0tsvdvq5S+ZXd9qqL56DMN/wDx87WtnRyo5WdgxAvxiADgpxAPbZSd5sPnpL+v039v3I97EfSDvqO33XvY937Mw5Ga365Glo8hD/8LGjlR2t7GhlxwD0iwHooNAGYCTP5ddeZwc9ulEyv1pFE+aqZH61JMZfNvzDx45WdrSyo5UdA9AvBqCDQhqAkb6ah/TxQY+2r+jxdemjN00f2tLSorEz50T/ncs8wD987GhlRys7WtkxAP1iADoopAEY5ev5PvTYo6q/4TNtDnpMSx/0sHzuva1OnjTP73MQFgD+4WNHKzta2dHKjgHoFwPQQSENwEh8fNAjWbznoEf9tE9nHPSwfveR7wDaxeK+yhFa2dHKjlZ2DEC/GIAOGIAO2h30qJ75bQ2f8Eivfv+Q3wG0K/j7KodoZUcrO1rZMQD9YgA6YAD20uuPZB70eP1Pktyeg5BTwDYFfV/lGK3saGVHKzsGoF8MQAcMwB4yHPTozXMQ8jyAdgV5X3lCKzta2dHKjgHoFwPQAQOwB9q/osezN3R4RY/ePgdhwbXyiFZ2tLKjlR2t7BiAfjEAHTAADdq/osetw6W3X+rwbi7PQVgwrfoArexoZUcrO1rZMQD9YgA6YAB2o8Mrevx/nb6ih+tzEBZEqz5CKzta2dHKjlZ2DEC/GIAOGIBZdHHQozOuz0GY9636EK3saGVHKzta2TEA/WIAOmAAdqL9QY/f/5P5FT16K29bRYBWdrSyo5UdrewYgH4xAB0wANt5+6VuD3r4kJetIkIrO1rZ0cqOVnYMQL8YgA4YgB9r3b1n7HVz0MOXvGoVMVrZ0cqOVna0smMA+lUwA3Dx4sUaNWqUjj76aCUSCc2ePbvbj3n22Wf1hS98QQMGDNBJJ52k0tLSHn1OBqA+PujxT90e9PApb1oFgFZ2tLKjlR2t7BiAfhXMAKyoqNDkyZM1a9Ys0wDcsGGDDjzwQP30pz/V6tWrdfvtt6tfv356+umnzZ8z9gPw9T/tO+gxbUjWgx4+5UWrQNDKjlZ2tLKjlR0D0K+CGYBtWQbgVVddpc9+9rMZb/v2t7+tc8891/x5YjsAd9Tv+U5fHx70yCboVoGhlR2t7GhlRys7BqBfsR2A//iP/6jx48dnvO3ee+/VoEGDzJ8nlgPw7Zf2/I5fHx/0yCbYVgGilR2t7GhlRys7BqBfsR2Aw4YN07Rp0zLeNm/ePCUSCW3fvr3Tj9m5c6caGhrSV21trRKJhOrq6tTS0pLTq7m5WeXl5Wpubs75392ra+d2tS66VqlfHiIVD1Lq1s9p94a/Rv+4QmwV8EUrWtGKVvly+WxVV1fHAIz6AfjgawAWFxcrkUh0uMrKylReXl6w14I//U51N38x/SPfd277Z819/KHIHxcXFxcXF1dvrrKyMgZg1A/AB18/Ao7jdwB3v/ZHpaYdu+e7ftOO1e7XyiL/t8JQW+XDRSta0YpW+XLxHUC/YjsAr7rqKg0fPjzjbRdffDGHQPbqcNDjG3ue8iVAkbfKI7Syo5UdrexoZeezFb8DWEADsLGxUZWVlaqsrFQikVBJSYkqKyv19ttvS5ImTpyo0aNHp99/79PAXHnllaqurtYdd9zB08DslXHQ45PSszdGftAjG76g2tHKjlZ2tLKjlR0D0K+CGYDPPvtsp7+fN2bMGEnSmDFjNGLEiA4f8/nPf14DBgzQiSeeyBNBp1/R45CPX9Hjc9I7L/fd5+8lvqDa0cqOVna0sqOVHQPQr4IZgFEoqAH40ZuZr+jx+A+lHfnxfwy+oNrRyo5WdrSyo5UdA9AvBqCDghmA7V/RY8Wj/j9nDvEF1Y5WdrSyo5UdrewYgH4xAB3k/QDcUS899oO8OOiRDV9Q7WhlRys7WtnRyo4B6BcD0EFeD8C3X8w86PHcTUEf9MiGL6h2tLKjlR2t7GhlxwD0iwHoIC8HYOtu6c/T8u6gRzZ8QbWjlR2t7GhlRys7BqBfDEAHeTcAP3pT+t3X2xz0+FHeHPTIhi+odrSyo5UdrexoZccA9IsB6CCvBuDyYpB68wAADMBJREFUh6Xrj83bgx7Z8AXVjlZ2tLKjlR2t7BiAfjEAHeTFAGx/0OOec/PyoEc2fEG1o5UdrexoZUcrOwagXwxAB8EPwLdflEoK46BHNnxBtaOVHa3saGVHKzsGoF8MQAfBDsDW3dKfry+ogx7Z8AXVjlZ2tLKjlR2t7BiAfjEAHQQ5AD/cUJAHPbLhC6odrexoZUcrO1rZMQD9YgA6CGoAplLS8ocK9qBHNnxBtaOVHa3saGVHKzsGoF8MQAfBDMAd9dKjl2Ye9Nj6ds4fU6j4gmpHKzta2dHKjlZ2DEC/GIAOghiAb70Qi4Me2fAF1Y5WdrSyo5UdrewYgH4xAB1EOgBbd0vPXNfuoMfSnD+OfMAXVDta2dHKjlZ2tLJjAPrFAHQQ2QD8cIP0u3P2/ch31mUFf9AjG76g2tHKjlZ2tLKjlR0D0C8GoIM+H4AdDnocF5uDHtnwBdWOVna0sqOVHa3sGIB+MQAd9OkA3L411gc9suELqh2t7GhlRys7WtkxAP1iADroswHY4aDHzVKyNeefM1/xBdWOVna0sqOVHa3sGIB+MQAd+B6Ac2Y/rtaFV+876HHbabE96JENX1DtaGVHKzta2dHKjgHoFwPQgdcBuLlGH970BQ56GPAF1Y5WdrSyo5UdrewYgH4xAB14u4GWP6zU9cdIxYOUitErevQWX1DtaGVHKzta2dHKjgHoFwPQgbcb6M/XS8WDVHfz6Wr5YL3pQ0oWrNWMRTWd/tmMRTUqWbA2l48wKHxBtaOVHa3saGVHKzsGoF8MQAfebqDW3dq99F6Vz55lvvFnLKpR0YS5HUZgV28vJHxBtaOVHa3saGVHKzsGoF8MQAdBvBRcG+3HXhzGn8QX1J6glR2t7GhlRys7BqBfDEAHoQ1Aad/oGzapIhbjT+ILak/Qyo5WdrSyo5UdA9AvBqCDEAegpPT4GzapIuePK0R8QbWjlR2t7GhlRys7BqBfDEAHub6B2h7kaH/jWw9y8B1AZEMrO1rZ0cqOVnYMQL8YgA5yfQO1/Z29tje+9Xf5+B1AvqB2h1Z2tLKjlR2t7BiAfjEAHfi4gfaOtpL51SovL1fJ/Opejb/u3l5I+IJqRys7WtnRyo5WdgxAvxiADnzdQHtH24kTnzSPN54HkC+oFrSyo5UdrexoZccA9IsB6MDnDXTypHkqmjBXJ0+al/O/u9DwBdWOVna0sqOVHa3sGIB+MQAdhPQdwDjjC6odrexoZUcrO1rZMQD9YgA6COl3AOOML6h2tLKjlR2t7GhlxwD0iwHoILRTwHHFF1Q7WtnRyo5WdrSyYwD6xQB0EOLzAMYRX1DtaGVHKzta2dHKjgHoFwPQQaivBBI3tLKjlR2t7GhlRys7BqBfDEAHDMAw0MqOVna0sqOVHa3sGIB+MQAdMADDQCs7WtnRyo5WdrSyYwD6xQB0wAAMA63saGVHKzta2dHKjgHoFwPQAQMwDLSyo5UdrexoZUcrOwagXwxABwzAMNDKjlZ2tLKjlR2t7BiAfjEAHTAAw0ArO1rZ0cqOVna0smMA+sUAdMAADAOt7GhlRys7WtnRyo4B6BcD0AEDMAy0sqOVHa3saGVHKzsGoF8MQAcMwDDQyo5WdrSyo5UdrewYgH4xAB0wAMNAKzta2dHKjlZ2tLJjAPrFAHRQX1+vRCKh2tpaNTQ05PSqq6tTWVmZ6urqcv53F9pFK1rRilb5ctEqjFa1tbVKJBKqr6+PekpEhgHoYO8NxMXFxcXFxZV/V21tbdRTIjIMQAfJZFK1tbWqr6/39m8nPr67WGgXrWhFK1rly0WrMFrV19ertrZWyWQy6ikRGQZgoBoa+P0EK1rZ0cqOVna0sqOVHa38YgAGihvfjlZ2tLKjlR2t7GhlRyu/GICB4sa3o5UdrexoZUcrO1rZ0covBmCgdu7cqeLiYu3cuTPqhxI8WtnRyo5WdrSyo5UdrfxiAAIAAMQMAxAAACBmGIAAAAAxwwAEAACIGQYgAABAzDAAA/fmm2/q0ksv1fHHH68DDjhAJ554oqZOnapdu3ZF/dCCMHPmTBUVFWngwIE644wz9PLLL0f9kIIzbdo0nX766TrooIN0+OGH64ILLtCaNWuiflh54YYbblAikdD48eOjfijB2rhxo7773e/q0EMP1QEHHKDhw4frlVdeifphBae1tVVTpkzJ+Fp+zTXXKJVKRf3QIrd48WKNGjVKRx99tBKJhGbPnp3x56lUSr/4xS901FFH6YADDtA555yjmpqaiB5t4WAABu6pp57S97//fc2fP1/r16/XnDlzdMQRR+hnP/tZ1A8tcg8//LAGDBige++9V1VVVfrhD3+oQw45RJs3b476oQXl3HPPVWlpqVatWqXly5frvPPO09ChQ9XU1BT1Qwva0qVLdfzxx+u0005jAHbho48+UlFRkb7//e/r5Zdf1oYNGzR//ny98cYbUT+04Fx//fU67LDDNHfuXL355pt69NFHddBBB2nGjBlRP7TIVVRUaPLkyZo1a1anA/DGG2/U4MGDVV5ertdff13nn3++TjjhBO3YsSOiR1wYGIB56Oabb9YJJ5wQ9cOI3BlnnKFx48al/3MymdQxxxyjG264IcJHFb4tW7YokUho8eLFUT+UYDU2NmrYsGFauHChRowYwQDswoQJE/QP//APUT+MvDBy5EhdeumlGW/7t3/7N333u9+N6BGFqf0ATKVSOuqoo3TLLbek31ZfX6+BAwfqoYceiuIhFgwGYB6aPHmyvvjFL0b9MCK1a9cu9evXr8O/KX7ve9/T+eefH9Gjyg/r1q1TIpHQypUro34owfre976nK664QpIYgFl85jOf0RVXXKFvfetbOvzww/X5z39ed999d9QPK0jXX3+9ioqKtHbtWknS8uXLdcQRR+gPf/hDxI8sLO0H4Pr165VIJFRZWZnxfl/5ylf04x//uK8fXkFhAOaZdevWadCgQbH/Ivvuu+8qkUjohRdeyHj7lVdeqTPOOCOiRxW+ZDKpkSNH6uyzz476oQTroYce0vDhw9M/XmIAdm3gwIEaOHCgfv7zn+u1117TXXfdpQMOOED33Xdf1A8tOMlkUhMmTNB+++2n/fffX/vtt5+mTZsW9cMKTvsBuGTJEiUSCb333nsZ7/cf//EfuvDCC/v64RUUBmBEJkyYoEQikfWqrq7O+JiNGzfqpJNO0g9+8IOIHnU4GIC9c/nll6uoqEi1tbVRP5QgvfPOOzriiCP0+uuvp9/GAOxa//79ddZZZ2W87b//+7915plnRvSIwvXQQw9pyJAheuihh7RixQo98MADOvTQQxnL7TAA+w4DMCJbtmxRdXV11qvtSd93331Xw4YN0+jRo5VMJiN85GHgR8A9N27cOA0ZMkQbNmyI+qEEa/bs2UokEurXr1/6SiQS2m+//dSvXz+1trZG/RCDMnTo0A7/QnrnnXfqmGOOiegRhWvIkCGaOXNmxtuuvfZanXrqqRE9ojDxI+C+wwDMAxs3btSwYcN00UUX8Q+gNs444wz913/9V/o/J5NJHXvssRwCaSeVSmncuHE65phjeOqEbmzbtk0rV67MuE4//XRdcskl/M5kJy6++OIOh0CuuOKKDt8VhHTooYfqzjvvzHjbtGnTNGzYsIgeUZi6OgQyffr09NsaGho4BJIDDMDAbdy4USeffLLOOeccbdy4UZs2bUpfcffwww9r4MCBuu+++7R69Wr96Ec/0iGHHKL3338/6ocWlLFjx2rw4MF67rnnMu6f7du3R/3Q8gI/Au7a0qVLtf/+++v666/XunXr9Mc//lEHHnggBxs6MWbMGB177LHpp4GZNWuWPvWpT+mqq66K+qFFrrGxUZWVlaqsrFQikVBJSYkqKyv19ttvS9rzNDCHHHKI5syZoxUrVuiCCy7gaWBygAEYuNLS0i5/RxDS7bffrqFDh2rAgAE644wz9NJLL0X9kILT1f1TWloa9UPLCwzA7J588kkNHz5cAwcO1Kc//enYH1DryrZt2zR+/HgNHTo0/UTQkydP5kn9JT377LOdfo0aM2aMpH1PBH3kkUdq4MCBOuecc9KnqdF7rAgAAICYYQACAADEDAMQAAAgZhiAAAAAMcMABAAAiBkGIAAAQMwwAAEAAGKGAQgAABAzDEAAAICYYQACAADEDAMQAAAgZhiAAAAAMcMABAAAiBkGIAAAQMwwAAEAAGKGAQgAABAzDEAAAICYYQACAADEDAMQAAAgZhiAAAAAMcMABAAAiBkGIAAAQMwwAAEAAGKGAQgAABAzDEAAAICYYQACAADEDAMQAAAgZhiAAAAAMcMABAAAiBkGIAAAQMwwAAEAAGKGAQgAABAz/z/2DG2Kv9mSNwAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# first guess from looking at dataset: \n",
    "# gradient of roughly 1, intercept (cut the y-axis) at +1\n",
    "\n",
    "# equation for linear function y=mx+b can rewritten as y=Ap,\n",
    "# where A = [[x 1]] and p = [[m], [b]]\n",
    "# now use lstsq to solve for p\n",
    "\n",
    "# add column of 1 to allow for matrix multiplication (as just explained)\n",
    "A = np.vstack( [xVals, np.ones(len(xVals))] ).T\n",
    "\n",
    "# perform the fit\n",
    "fit3_m, fit3_b = np.linalg.lstsq(A, yVals)[0]\n",
    "print('slope = {0}, intercept = {1}'.format(fit3_m, fit3_b) )\n",
    "\n",
    "# plot the data along with the fitted line\n",
    "fig5 = plt.figure()\n",
    "ax5  = fig5.add_subplot( 1,1,1 )\n",
    "\n",
    "ax5.plot( xVals, yVals, marker='x', linestyle='None', label='data' )\n",
    "ax5.plot( xVals, fit3_m*xVals+fit3_b, \n",
    "          marker='None', linestyle='solid',\n",
    "          label='fit'\n",
    "        )\n",
    "ax5.legend()\n",
    "ax5.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. scipy.stats.linregress\n",
    "\n",
    "* https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html\n",
    "\n",
    "* calculate a linear least-squares regression for two sets of measurements\n",
    "\n",
    "* specialized linear regression function from the `stats` module of `Scipy`\n",
    "\n",
    "* somewhat restricted in its flexibility (optimized to calculate a linear least-squares regression for two sets of measurements only) \n",
    "\n",
    "* cannot fit a generalized linear model or multi-variate regression\n",
    "\n",
    "* one of the fastest methods when it comes to simple linear regression\n",
    "\n",
    "* return fitted coefficients, intercept term, and also basic statistics such as $R^2$ coefficient and standard error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope: 0.20231498150269456  |  intercept: 1.1987572447804768\n",
      "R-squared: 0.977431091905829\n"
     ]
    },
    {
     "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff03530d400>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "# perform the linear regression:\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(xVals, yVals)\n",
    "print(\"slope: {0}  |  intercept: {1}\".format(slope, intercept) )\n",
    "\n",
    "# get coefficient of determination (R-squared)\n",
    "print(\"R-squared: {0}\".format(r_value**2) )\n",
    "\n",
    "# plot the data along with the fitted line:\n",
    "fig6 = plt.figure()\n",
    "ax6  = fig6.add_subplot( 1,1,1 )\n",
    "\n",
    "ax6.plot( xVals, yVals, marker='x', linestyle='None', label='data')\n",
    "ax6.plot( xVals, intercept + slope*xVals, \n",
    "          marker='None', linestyle='solid',\n",
    "          label='fit'\n",
    "        )\n",
    "ax6.grid()\n",
    "ax6.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Statsmodels.OLS\n",
    "\n",
    "* http://www.statsmodels.org/dev/index.html\n",
    "\n",
    "* `StatsModels` is built on top of `NumPy` and `SciPy`\n",
    "* it is designed for a statistically-oriented approach to data analysis, with emphasis on econometric analyses\n",
    "* has built-in support for many statistical tests to check quality of fit and dedicated set of plotting functions (for visualizing and diagnosing the fit)\n",
    "* for linear regression the Ordinary Least-Squares (OLS) function provides extensive set of statistical information on estimation process\n",
    "* note: constant needs to be added manually to x-data for calculating the intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.977\n",
      "Model:                            OLS   Adj. R-squared:                  0.977\n",
      "Method:                 Least Squares   F-statistic:                     1213.\n",
      "Date:                Tue, 01 Oct 2019   Prob (F-statistic):           1.34e-24\n",
      "Time:                        22:26:47   Log-Likelihood:                 23.621\n",
      "No. Observations:                  30   AIC:                            -43.24\n",
      "Df Residuals:                      28   BIC:                            -40.44\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.1988      0.031     38.430      0.000       1.135       1.263\n",
      "x1             0.2023      0.006     34.823      0.000       0.190       0.214\n",
      "==============================================================================\n",
      "Omnibus:                        1.302   Durbin-Watson:                   1.863\n",
      "Prob(Omnibus):                  0.521   Jarque-Bera (JB):                0.924\n",
      "Skew:                          -0.019   Prob(JB):                        0.630\n",
      "Kurtosis:                       2.141   Cond. No.                         8.21\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "Parameters:  [ 1.19875724  0.20231498]\n",
      "Standard errors:  [ 0.03119359  0.0058098 ]\n",
      "Predicted values:  [ 0.79412728  0.87784383  0.96156037  1.04527691  1.12899346  1.21271\n",
      "  1.29642655  1.38014309  1.46385963  1.54757618  1.63129272  1.71500927\n",
      "  1.79872581  1.88244235  1.9661589   2.04987544  2.13359199  2.21730853\n",
      "  2.30102508  2.38474162  2.46845816  2.55217471  2.63589125  2.7196078\n",
      "  2.80332434  2.88704088  2.97075743  3.05447397  3.13819052  3.22190706]\n"
     ]
    },
    {
     "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff02cc9e0f0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "# model needs an intercept => add a column of 1\n",
    "# here, the statsmodels tool add_constant is used for this\n",
    "\n",
    "model = sm.OLS( yVals, sm.add_constant(xVals) )\n",
    "results = model.fit()\n",
    "print( results.summary() )\n",
    "\n",
    "print('Parameters: ', results.params)\n",
    "print('Standard errors: ', results.bse)\n",
    "print('Predicted values: ', results.predict())\n",
    "\n",
    "# get the confidence interval\n",
    "from statsmodels.sandbox.regression.predstd import wls_prediction_std\n",
    "prstd, iv_l, iv_u = wls_prediction_std(results)\n",
    "\n",
    "# plot the data along with the fitted line:\n",
    "fig7 = plt.figure()\n",
    "ax7  = fig7.add_subplot( 1,1,1 )\n",
    "\n",
    "ax7.plot( xVals, yVals, marker='x', linestyle='None', label='data')\n",
    "ax7.plot( xVals, results.fittedvalues, \n",
    "          marker='None', linestyle='solid',\n",
    "          label='fit'\n",
    "        )\n",
    "ax7.plot( xVals, iv_u, linestyle='dashed', color='red')\n",
    "ax7.plot( xVals, iv_l, linestyle='dashed', color='red')\n",
    "ax7.grid()\n",
    "ax7.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. sklearn.linear_model.LinearRegression()\n",
    "\n",
    "* https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\n",
    "\n",
    "* scikit-learn is a powerful Python module for machine learning\n",
    "* contains functions for regression, classification, clustering, model selection and dimensionality reduction\n",
    "* `sklearn.linear_model` module contains methods intended for regression in which the target value is expected to be a linear combination of the input variables\n",
    "* Ordinary least squares Linear Regression\n",
    "* Note: from implementation point of view, this is plain Ordinary Least Squares (scipy.linalg.lstsq) wrapped as a predictor object\n",
    "\n",
    "  \n",
    "  \n",
    "* `sklearn` has a few maybe more interesting datasets included: example is the https://archive.ics.uci.edu/ml/datasets/Housing Boston Housing dataset which contains information about the housing values in suburbs of Boston\n",
    "* accessed as follows:\n",
    "\n",
    "    `from sklearn.datasets import load_boston`\n",
    "    \n",
    "    `boston = load_boston()`\n",
    "    \n",
    "    `print( boston.keys() )`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimized coefficients: [ 0.20231498  0.        ]\n",
      "optimized intercept: 1.1987572447804768\n",
      "[ 1.80570219]\n"
     ]
    },
    {
     "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",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7ff0297f8b70>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "X = np.vstack( [xVals, np.ones(len(xVals))] ).T\n",
    "\n",
    "# perform the fit\n",
    "reg = LinearRegression().fit( X , yVals)\n",
    "reg.score(X, yVals)\n",
    "\n",
    "print( 'optimized coefficients: {0}'.format(reg.coef_) )\n",
    "print( 'optimized intercept: {0}'.format(reg.intercept_) )\n",
    "\n",
    "# make a prediction using the test data set\n",
    "print( reg.predict(np.array([[3, 5]])) )\n",
    "\n",
    "# plot the data along with the fitted line:\n",
    "fig8 = plt.figure()\n",
    "ax8  = fig8.add_subplot( 1,1,1 )\n",
    "\n",
    "ax8.plot( xVals, yVals, marker='x', linestyle='None', label='data')\n",
    "ax8.plot( xVals, reg.coef_[0]*xVals + reg.intercept_, \n",
    "          marker='None', linestyle='solid',\n",
    "          label='fit'\n",
    "        )\n",
    "ax8.grid()\n",
    "ax8.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}