Example 5.3.1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.1 Gaussian distribution and Hermite Chaos\n",
    "\n",
    "$$ f(k) = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{k^2}{2}}$$\n",
    "\n",
    "$$ \\zeta \\sim N(0,1)$$\n",
    "\n",
    "[Wiki - Hermite Polynomial](https://en.wikipedia.org/wiki/Hermite_polynomials)\n",
    "\n",
    "[Normal distribution in Python](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html)\n",
    "\n",
    "[Hermite Polynomial Python](https://docs.scipy.org/doc/numpy-1.13.0/reference/routines.polynomials.hermite_e.html)\n",
    "\n",
    "\n",
    "Hermite Polynomial: (probabilists' Hermite polynomials)\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "H_0 &= 1\\\\\n",
    "H_1 &= x\\\\\n",
    "H_2 &= x^2 - 1\\\\\n",
    "H_3 &= x^3 - 3x\\\\\n",
    "H_4 &= x^4 - 6x^2 + 3\\\\\n",
    "&\\cdots\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Corresponding Hypergeometric orthogonal polynomial\n",
    "$$ H_n(x) =(2x)^n \\ _2F_0(-\\frac{n}{2},-\\frac{n-1}{2};;-\\frac{1}{x^2})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.polynomial.hermite_e as H \n",
    "from math import factorial\n",
    "from scipy.stats import norm\n",
    "from scipy.integrate import odeint\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`H.hermeval(x, c)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Phi(n):\n",
    "    #define H_n\n",
    "    coeffs = [0]*(n+1)\n",
    "    coeffs[n] = 1\n",
    "    return coeffs\n",
    "\n",
    "def inner2_herm(n):       ###return the denominator when computing $k_i$\n",
    "    return factorial(n)\n",
    "\n",
    "def product3_herm(i,j,l):\n",
    "    #compute \\Phi_i*\\Phi_j*\\Phi_l\n",
    "    return lambda x: H.hermeval(x, H.hermemul(H.hermemul(Phi(i),Phi(j)),Phi(l))) \n",
    "\n",
    "def inner3_herm(P,i,j,l):\n",
    "    #compute <\\Phi_i\\Phi_j\\Phi_l>\n",
    "    \n",
    "    #Set up Gauss-Hermite quadrature, weighting function is exp^{-x^2}\n",
    "    m=(P+1)**2\n",
    "    x, w=H.hermegauss(m)        \n",
    "    inner=sum([product3_herm(i,j,l)(x[idx]) * w[idx] for idx in range(m)])         \n",
    "    \n",
    "    return inner/np.sqrt(2*np.pi)   #because of the weight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Gauss Hermite Quadrature](https://en.wikipedia.org/wiki/Gauss–Hermite_quadrature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_system_herm(y, t, P):   \n",
    "    #P indicates the highest degree\n",
    "    dydt = np.zeros(P+1) \n",
    "    for l in range(len(dydt)):\n",
    "        dydt[l] = -(sum(sum(inner3_herm(P,i,j,l)*ki_herm[i]*y[j] for j in range(P+1)) for i in range(P+1)))/inner2_herm(l)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "P=4\n",
    "ki_herm = [0,1]+[0]*(P-1)\n",
    "sol_herm = odeint(ode_system_herm, [1.0]+[0.0]*P, np.linspace(0,1,101), args=(P,)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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 0x11657c470>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.ylim([-2,2])\n",
    "plt.xlim([0,1])\n",
    "\n",
    "plt.title('Solution of the coefficients in the expansion')\n",
    "for i in range(P+1):\n",
    "    plt.plot(np.linspace(0,1,101),sol_herm[:,i],label='$y_'+str(i)+'$')\n",
    "    \n",
    "plt.axhline(y=1.0, color='r', linestyle='-.',label='Deterministic')\n",
    "plt.legend(fontsize=12)#prop={'size': 8}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error plot\n",
    "$$\n",
    "\\bar{y}_{exact}(t) = \\hat{y_0} e^{\\frac{t^2}{2}}\\ \\ \\ \\ \\ \\ \\ \\ \\bar{y}(t) = y_0\n",
    "$$\n",
    "So \n",
    "$$\n",
    "\\epsilon_{mean}(t) = \\left| \\frac{y_0 - \\hat{y_0} e^{\\frac{t^2}{2}}}{\\hat{y_0}e^{\\frac{t^2}{2}}}\\right|\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_{exact}(t) = \\hat{y_0}^2 (e^{2t^2} - e^{t^2}) \\ \\ \\ \\ \\ \\ \\ \\ \\sigma(t) = y_1^2 +2y_2^2+6y_3^2+24y_4^2\n",
    "$$\n",
    "The coefficients in $\\sigma(t)$ can be obtained by code below.\n",
    "\n",
    "So\n",
    "$$\n",
    "\\epsilon_{variance}(t) = \\left| \\frac{\\sigma(t) - \\sigma_{exact}(t)}{\\sigma_{exact}(t)} \\right|= \\ldots\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`expect(func, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.e**2-np.e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.000000000000001\n",
      "2.000000000000005\n",
      "6.000000000000001\n",
      "24.000000000000007\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (H.hermeval(u,Phi(n)))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    print(norm.expect(g(i), args=(), loc=0, scale=1, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only look at when $t=1$, show the plot of relative error of mean and variance by using different orders of Hermite Chaos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcoeff_531 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_531[1,:]=np.ones(4)\n",
    "y_531 = np.zeros((5,4))   #row 0 stores y0 for each P from 1-4; row 1 stores y1 for P from 1-4;...\n",
    "\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_herm = allcoeff_531[:,i]\n",
    "    y_mid=odeint(ode_system_herm, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, ))[1,:]\n",
    "    y_531[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.54308068,  1.63819256,  1.64796906,  1.64867952],\n",
       "       [-1.17520125, -1.5805867 , -1.6423493 , -1.64828336],\n",
       "       [ 0.        ,  0.63819256,  0.80057968,  0.82228702],\n",
       "       [ 0.        ,  0.        , -0.22373587, -0.26894552],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.05786917]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_531"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "error_mean_531=np.abs((y_531[0,:]-np.e**(1/2))/(np.e**(1/2)))\n",
    "\n",
    "sigma2_531=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_531[i]=y_531[1,i]**2+2*y_531[2,i]**2+6*y_531[3,i]**2+24*y_531[4,i]**2\n",
    "    \n",
    "sigma2_exact_531 = np.e**2-np.e\n",
    "error_var_531=np.abs((sigma2_531-sigma2_exact_531)/sigma2_exact_531)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAAXNSR0IArs4c6QAAQABJREFUeAHsnQeYFFXWhj8EREHBgILKAkYUI+qiqyLoKiYMmLOYFXNcc1rzmtachTXrmteESjCLghnF3wACCooBBAkC858zNQ017UxPT8eq6vc8z5lKN763pvv0DedKCAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIBAbAn0s5JXZdBe9izK0sIKd6zp66a/mM42nWD6iGlPUyR5BC62Kn1rOsf01wzVu8Ce+bs9z3Ql03RpZTemmnqYAaaI1MsgOA8/1idP2IMZpkvUF8Du32/6h2m7DGEa+2i8RbizsZEID4E4EGgWh0JSxsQSONhq9nkdtRtVx72o3GprBXnBdB3Tu03/Zfqz6QqmO5u+YrqB6YemSDIIeLuebXqJ6fOms0wbkmkWwN/vc9MC7mHXzU3dUEGyJ3CXBd3FdF/Tm+uI1sbu9TX9n+mkOp7nemtHizgl18jEgwAEIACB2gT62aX/4t+w9u2srppYqEXrCdnU7nvvXD7SUBrPWeL+5b1lPZn81e53rOdZXG63jEtBS1RON/78fV02i/wuqAl7hx2/NV3INCyv2cUDpm4gDjBFsusB9P/LCabv1QPsKLvvbdSnnueNvV3fZ0xj0yE8BCAAAQiECPSz82wNQA93o6l/wH9m6sOtft7Z1J+dbnqO6TemPjy3ramLG2H3mf5g6j02HvcU0/AXcme7zpSGPa4l3rPn4W+tdTfzxVr2+CnTX0xnmn5gepBpWHrZhae7j6n3Mn1n6sOEL5t2MU3JdXYy3bR16kbo+LCde8+H9y6lZC87ecvU47jB8aJpN9OwDLALf7a26SDT30w9josb22eZjjX1svuX79amQ2vUDvPFy3SV6Tem3kb+Ze3l9SHPsHg9vT0PMPU2+d30Q9O6vrhXt/sPmnq9vA3doPqPaQvTlLS3k9tMfajO8/X8zzfNZnTD3wV/fz439fT9XfH0O5imZIydeJnDeoFd1ycX2AMP+7ea4zZ2TMlqduLPtjJ15gNMw5Itw2Ms0qumXl5v249NvR7htrfL6nb6xI7+o8QNT2f9tekZpl73hqQY+XibvmDqZZlsequp97I5l16mmeRSe+jh/F1Nl3fsxnembiim5CI7GW7qPfT+/zTCtJ+pv9dh8XfnSdM9TP3/c6bpxaYu/uzO6rPgz6J2uMbU39kppp72m6Zeh7A0swsvq/8PHGT6uanX2dPfzjRdutqNh00nmfq76P9zA0zDbbq8XfsPiwmm/q5/ZXqOabjOdolAAAIQiC6BflY0/3DcyNQ/KMOa/mHm4fxD2D9w9zHdwnRN086mqWeD7Xw3061NO5suY+px/AvySFP/Er7B1MPfbJqSznZSXxqpMOHjmTXhU0Zm+Fld513spn/xfGnqBs/2pg+Yep6nm6akl534vW9M7zP1cHub+pfAF6YpJuvYuYc7zDQsS9iFf2ldHbp5lp3PM/Whsx1M+5r6F5UbHv5lk5IBduJfJp73GaZbmvY2dbnU1PO7zdQZer5epu9Mh5qmpKWdvG/6o+lJpn83Pd70V9NXTJuYpsTT87zeMfUvXP8yHGLqvaormaZkXTtxY9TDeht6ufYz9S/JxU1d2pt+azrG9AhTz9e/EJ3FPaYNiderytTfDa+f5/ODqafZ1tSlm6kbAB7Ow2xs2sG0PrnAHnhYj/+qqZc3JZfbyTemzsPbYYBpShrD0A2Qo0y9PFuYnmjq7O82DctQu3Ajy98hr9tWpjeZevkONG1ICp1PO8twkul4036m3vb3mfo75WXqZZpJVrGH/k5fmxbI32ePf1na/YF2fbCp19s/G841nWHq/xth8fL4O+3/p/1Me5luaOriz7z9U7KUnThnfxedvX8W+P/dXNN9TVPSzE68TN+Yvm26u6nXd5jpLNNOpilZ3078ffja1N/jLU33N33U1N8Ll+VNvSwe5nBTf9fPM/W03ChEIAABCMSCQD8rpX841qVz0mrgYdyQWDLtfme79mf+od3cNCz+ReDPuodv2rkbf/NMV6u539mO9aVRE6TW4Zaa8F1q3a3/4kF75MbIX9KCPGfX003b1NzvZUcvx7M116mDG0h+342OlIywkzdSFzXHo+3o4daqufb83KC6vuY6dVjMTr43fTh1w44DTD2uf1GGxXl72R8K37RzL4uHH2qakjPsxL8AU1+aqftulHtY/+JLiV9PNE0ZcX7fDQOP7+mk5BU7+cV0mdSNOo632j03EjumPTvFrj0fNwzqk9XtgYe5KS2AvzN+/5LQ/Qtq7rUN3avvNBy2nwWaaepGQ1NTNzLON3XxL/wBflIjjWGYiuPHhUzd2DjA1P93wv8nQ+3a65L+f/Cp3XvBtDFSiHwutwz9/8+N+7AMsgsvZ6/wzXrOh9p9N3abh55fZecef9XQvfTTVPkvtAeT0h66YTXbdOW0+37pz+6s437qlrer8x9gOtw0JX7Py+Rt3ip1045uyPn9U0P33Cj8yXTp0L30Uy/DFNMOaQ/+Ydfhz7S0x1xCAAIQiBaBflYc/xD0Ly03GsK6gV2HxcM9Hr5Rc97Zjv7MeynS5R274V9y6ZL6cj+q5kFnO9aXRnpcv26sAehfNM/WkdCeds/z3bbmWa+a6yNrrlMHNzQ93F6pG3Y8tuaeP0uJf/GEv3wOs2uP51z9iyisD9l1+AtwgF172NamYdnOLvz+ruGbNeff2HFo6P7rdv6haTgfP3eD07+crjBNiaf5YOoidPzezp2vS0tTN2a8hy6TjLeHT5um59vV7nk+R5vWJ/7Mw/y1jgCj7N7bofsX2LmHbRu6V9/pBfYgFda/+KeaHme6o6mz6GTqMs10gJ/UyOt2zJZhNwvr9XajwfMK60Z2nZKhduJc08X5f5Z+s47rQufzjuXxcR359LN7Xodepg2Jf2Z42N1qAnrbTzR9teY6fNjKLvyHxBTTMCM/Dxtb4+06/P9jl/PFn6UbgP7/+KbpdNNwur/ZdUq8XP7s3tSN0NEN2Btqrv1/ZK7pTTXX9R28jv456OmGdR279nwON0Ug0CgC/qsIgUC5CPiX0HtpOqKOwtT1JZYKVtcz/3Cv677/GncJf/j7dV1h/X66fFtzY8X0B/VcN7Yc/oUeFh/ecVk0OFT/vd/++v1+1VdBL5cbMffUXPuhXc35u3b0nsCw+pdXuiHzu91zQyUsKUaTwjdrztPveX7+RRTOx89/M21imp5fej0tSHWdUvVc0q69Z8W/fDOJ57ujaXq+n9ZESs83nFaqfnW1vb8nqefhOI09dwPhYdNDTA81fdl0rGldki3Djhb5NdMVTE8w7WHq7X+MqUuKYXAVGImp89TR35/0cKlnqWMx8nGmbsikS1330sOkrv9rJ27QHVxzY3s7Oru7aq5Th7/ZifdyunF1mOkmps7pclOX9PrX9R4EIWv/9R9vD5n6Z8F+pp6Pp/sf0/Q07Va1ke7HsIT5O5OFTBt615e1MH1N09/1D+2eS6Z3PQjBXwikEfBfEggEok7Af+HWJ3U9cwNjuToi+PCLy+TgMP9vXWnMfxg6edHOLzXdxTSbIbTGliOUVb2nPiz6lOmBpueY+hfhTNMHTVOSqt/udqM+gyMV1o911T9lpPmXa7q0txtjQjc9vxmmbujUJany1PWsrns/203/4u5Q18PQPU/3I9OzQ/fCpymDP3wvdZ6qn78n6V++/p40tsypdNOPd9sNN0DcQHaDoT7JlqG/e96zuKtpuG3Xqy/hHO8XIx9n7u9OutR1Lz1M6trfM3/XvcfL287fud9MHzUNyz52Mcu0j+ns0AP/n6hL6vofqCvc/nbz/0w9/XCcFnUFzuKeM5ln2tC77uG8l/J807pkQl03uQeBTAQwADPR4VlcCbxiBT/TdH3TkaFKuNHkH9pDQvcac+ppPW/qvTmPmA42TZcN7cYPpt+aejn8V7sbFGFjxMvhvW5vm+Yi91gk74nw3g//QnrC9FfTlLxoJ3NMVzZ9LHWzkcd3LLx/ge5l+ngo7sZ23sl0TOje/+z8LFP/kvomdD/XU/+SH2a6h6kbd/UZY56vM/jK1A3jxkiq7Zyf95SmxHtz1jC9JHUjz+NbFv9u0zam3k71SbYMq2oS8LZJSRM7cYOokFKMfIZYAU83Xdc01XPlZd7X/zRC7rKwR5meZurtP8DU/5/C4uX/w3Re6GZLO/f2zkc8XTcoU3w8Lf//dkMzF5lmkV439f+zc01/Nq1L/P3YytSNzyl1BeAeBBpLAAOwscQIX0gCa1lidb2D/oX+Yx4ZXWtx3ch61vQ8U+8p2cG0v+ktpl+Y5iqe7gumz5veXXP8xY7Lme5ouo/pBqZuAF5o6l8M/sV3kal/uO9n6mXxL8JcP8gHWdzxpjebeu/JPaZhGWMXXm83YlYy9fJ6GduZdjedbnq+aSbxsl5jeqapx33CtIOpx/vedJ5pSq6zk91MXzW91tR75RYy7Wja2/RqUzcoGyMnW+DXTT2eD9t9aerl38n0SFPv9fE6bm36pun1pqNNFzHtbOqGgRsJzqku8bC3mx5n6nXx9uxs+k/TcaZej0KJ/2BoSLJl+JIlNNv0QdMrTb2+R5suaVpIKUY+XsdDTP3/8hzTSab+/7C6aWPkPQvs79iJpk1M3SBMF8/jeNP7TO80bWvq/3O/m+Yjboj5e3ODqf9P+Dvu76H/wPP/tVzkJIvk/zvDTa8wTb3ru9i58/IyO6+/m/q77nn7+7uo6Yqm/nni4SaaIhCAAAQiTaCfla4qgx4WKr2HuzF0nTrtbCf+7NTUjbSjfzDfbzrZ1L8wPzf1sAuZpqSznWRKIxUu/ehfum44+IexG3F/mE4wfczUDY+wuJH7tOmvprNMPzDtZxqWXnbh5dg9fNPOO5v6/X6m6eLGnT/71jRcp3C4ne1isKmXcabpGNNHTf2LJCUD7GRa6iLt6F+uZ5uOM/Wyf2jqXzZeh8dNw9LKLv5p6pw9rNfXv6TdiHTDLSVe5htTF6HjGDsfELr20zVMHzH1NvQ0x5reY9rCNCVt7eTfpl+bejv/ZOoGwsWmXqZM4tzcKBht6nF/NL3XtINpWC6wCy+359WQXGABsgnrzAeYhiVbhn0skrfBDFM3cN0Q3NbU8+1lmpKhdvJJ6iJ0HGDnY0LX9Z0WIx9v00GmXnZvKzfO3KhPL7vdyihu3HmcTzOE8s8Rb1t/9/1Hpbf1EaYeL9zGzvBJ07rEn3kZU+L/E2eZfmPq6Xr+h5hebDrHNCXN7MTzuS51I3RMT9MfrWn6X9PJpv6ujzG927S5aUqWtRP/oeN5p971d+3c/+/cGEQgAAEIQAACRSOwoqXsX1D+JYhAAAIQgEBMCfivGQQCEIBAXQTWtZv7mHpP51TTLqbei9LadC3TSaYIBCAAAQhAAAIQgECCCKxidXnZ1IdGfZjbh6d8mMoNQQQCEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAgWISwA1MsFPD1QbZncJeYRp2+tkQe+e3vKnvSoBAAAIQgAAEIBAfAotbUb8zdafdFSeVbgC6t/ZRpluYup+zkaYbmf5smo2sYIHcqzsCAQhAAAIQgED8CHSwIk+IX7HzL7EbQJUs3a3yvpVPqvGfs/NtTB80zUaqe/7GjRun1q3dNy4CAQhAAAIQgEDUCUydOlV/+ctfvJgVO4IXdwNwc2u800w3MF3OtK9p+p6O/e2eh/HnbuydaPqaqYsP36aMP7/23jzv1WuUuPGHAdgoZASGAAQgAAEIQKCMBHzeW5zFN0/3DeqPracSe9l934z7EtNupm74PW/a0dSlriHwipwLEODgLwQgAAEIQAAClUAg7j2Absy51icn24O7TFMLO7z3z4d4jzY909R7/8I9fj4X4B3T+qSFPXBNiU8gRSAAAQhAAAIQgECsCMS9BzAT7IXtoQ8ND0oL5Neb1Nwbbkff1N6NQDfmtjd90bQ+caNxSkh9yBiBAAQgAAEIQAACsSIQ9x7ATLDb2sOmppPSAvl1+5p7c+x4iukQUzeGrzT9ybQ+ucweXBN66EYjRmAICKcQgAAEkkqgqqpKc+bM0dy5c5NaxcTUq2nTpmrWrJmaNKlrpldiqplXRZJsAKbApM/p87chfO9pu3bNRmZZIFcEAhCAAAQqiMDs2bP1/fff6/fff6+gWse7qi1bttRyyy2nhRf2AUEknUCSDcDJVln/mZbq7UvVfVk7Se8VTD3L9niMBXRN8hB6tiwIBwEIQCDRBObNm6dvvvlG3qu0/PLLVxsU9CxFt8m9p9YN9h9//LG63VZddVUttBBf1+ktlmQDcLZVdoTp1qZPhCru10+FrnM5vckiubrzP58TiEAAAhCAQEIJuDHhRqD7jfNeJST6BBZddFE1b95cY8eOrTYGF1lkkegXusQljLsBuJjxWiXEbEU7X8/Ud/L41tTn691r+p7pW6ZHmLoLmFtNEQhAAAIQgEDWBOhFyhpVJALSXpmbIe4G4IZWPV/AkZLUAo2BdqOf6cOmS5ueZ7qc6SemvtJ3rCkScwLfmok/2Qf665G2tgyoY8rjYz1huA0BCEAAAhCoRAJxNwCHWqP5oo5McrM9dC2kMAewkDRzSMuNvy5dpJkz64/sPf6jR2ME1k+IJxCAAAQgUKkE4m4AlqvdmANYLvI1+XrPXybjz4P5cw9HL2CZG4vsIQABm5TEkAWvQbQIYABGqz0oDQQgAAEIJI0AQxZJa9FE1GehRNSCSkAAAhCAAASiSqAxQxYFrkOvXr103HHH6cQTT9SSSy6pdu3a6fbbb9f06dN18MEHa/HFF9fKK6+s559fsKvqqFGjtP3222uxxRarDn/AAQfYaMqCCdcvvPCCNttsMy2xxBJaeuml1adPH3311VfzSz5mzJhqB8yPP/64tthii+qV0+uuu67eesvXYiJRIYABGJWWoBxFITB+fFGSJVEIQKDSCZivObOistMZM7Kj5eEaStPzbaQMHDhQbW1V3PDhw6uNwaOPPlp77LGHNtlkE40cOVLbbLON3MhzJ9fu7Lpnz55ab7319N5778mNvUmTJmnPPfecn6sbjyeffLLeffddvfLKK9U+9vr27VvtKmd+IDs5++yzdeqpp+qDDz7Qaqutpn322ad6J5VwGM4hEDcCvghklOnnplVTpkwxv5NIKQmMGOGfgtnp6qtXVZ1ySlXV4MFVVbNnl7KU5AUBCCSBwIwZM6qsV6zKj/Nl2rTsPoCy/aDKNpzn2wgxY67Keuvmx7Ct7KpatWpVZQbf/Htm9LlVWWU9dFXnnntuVe/evec/85Nx48ZVPx89enSt+6mLH374ofr5xx9/XH3LnGZXX995552pIFWffvpp9b3PPvts/r1in9TZbjWZ+ve219nU/flWpNADmFuz+yKQrqbdc4tOrFIRMMf9+tzM9KuvlrbcUvYrWNp9d+mee2w7mHz3gylVJcgHAhCAQB4E1llnnfmxfTcTH7Zde+2159/zYWEXM+Q0YsQIDRkypHr414eAXVdfffXq56lhXj/uu+++WmmlldS6dWutuKK74PV1Lt9WH1N/wvn6lmwungcSDQIsAolGO1CKIhGw0Qn7wJGefVY2xyU4f+wxydVlww2lHXYIdIMNbG8/fhIFYPgLAQhkJuA7gkybljlM6qkNgdqkudRV/cfXX7etDHwvgwySw04kviNGWHwbu/C91LZ2vtuJ64477qgrrrgiHKX6PGXE+XPfFeWOO+6o3hrP46y11lrVO26EI9WXRzgM5+UjgAFYPvbknAcB78lzP3+ZXMH4c/9hatNZbL6L7IPN9gYcERiDbhDa9Jb5euGFssnO0nbbBcZg7942LlCxAwN5NAxRIVApBMyIUqtW2dXWtiXLSjxctmlmlWDjA62//vr2A/kxde7cWc2a/dlE+Omnn2TDuLrtttvUo0eP6gxed8MViR2BP7du7KpAgSuRgPv2cyfPoYVpf8KQvhOI9+799a+BXnCBNHFi0CvoxuCgQcGQ8IABkqt/7vlnW6p30J1O++c9AgEIQCDJBI455pjqnj1fsHHaaadVLx758ssv9dBDD1Xf95XEPoTsK4m9R9CHfc8444wkI0ls3TAAc2tadgLJjVtBY7kRmI+T5/btZW4QArW93uU/Yt0YdHXj0qbBVKstYrO5LguMQe9RZF/xgjYliUEg2QSyHbLwcGWW5ZdfXm+88Yb+8Y9/VK8OnjVrljp16qRtt922erWvDxe7MXj88cdXD/t2sV/H119/vdzdDBIvAvRp5NdePkhoi4mmVE+EzS8pYkeJgLu0ShmDQ4fK5rYsKJ1Pwdlqq8AgNFdZ6tBhwTPOIACB5BGYaXNNbGVr9WKHRXL99cdOICV/MTK129SpU9WmTRsvk/+ZWvLCRSBDDMD8GgEDMD9+sYjt87x9MUnKIPzuu9rFNv+m84eKN9pI8pXHCAQgkBwCmQyJ5NQyeTXJ1G4YgDatKXlNXtIaYQCWFHf5M3PHXx9+uMAYfPvtwHlXqmQ2NcaGSgKD0HyraqmlUk84QgACcSWQyZCIa50qodyZ2g0DEAMw3/8BDMB8CcY8vi9CMUf51b2Dfvz11wUV8kUn5mi/unfQh4rd7RYLSRbw4QwCcSGQyZCISx0qsZyZ2g0DEAMw3/8JDMB8CSYo/pw5sr0uF/QOfvJJ7cqZ2yzbXzMwCP/+d9n+mLWfcwUBCESTQCZDIpolplROIFO7YQBiAOb6XxJeBdyFRSC5Ykx2vLFjpeeeCwzCwYOl8HagLVrINklfMHewxpF+soFQOwjElEAmQyKmVaqIYmdqNwxADMB8/wnoAcyXYIXEd+PP3cqkFpK4cRiWNdZYYAxuuqnMS3/4KecQgEA5CWQyJMpZLvLOTCBTu2EAYgBmfnsafooB2DAjQqQR8IUko0YtMAbN5Zbmzl0QyD0T+E4k7oTadyZZdtkFzziDAARKTyCTIVH60pBjtgQytRsGIAZgtu9RfeEwAOsjw/2sCfzyS7ATifcO+n7F4d1NfNGI716S2pGkWzf2K84aLAEhUCACmQyJAmVBMkUgkKndMAAxAPN95TAA8yVI/FoEvCfw3XcX9A6+/36tx/LdS1ILSbbeWlp88drPuYIABApPIJMhUfjcSLFQBDK1GwagdSYUCjTpQAAC+RNwJ9Ibbyz985/SyJHShAmy/TelXXYJ9oj3/YvvvlvabTfZfpzBjiTXXit98UX+eZMCBCAAgWwIjBkzxlxaNdEHH3yQTXDCRJSADTAheRCgBzAPeERtHAHbklOvvrqgd9D2Z68lq6yyYKh4880lX2mMQAAC+RPI1JOUbepJ2glurg1V/Pjjj2prexc3a9YsWwQlD5ep3egBZAg41xcSNzC5kiNewQj83/8tMAaHDZP++GNB0q1aST5E7HMHfcjY9ndHIACBHAlkMiSySdKNvy5d3C9d/aF9i+HRo6WOHesPE4Uns21j9IUXXjgKRWmwDJnaDQOQIeAGX6B6Atxk97uadq/nObchUHQCq64qnXii9NJL0k8/SY8/Lh16qLTcctL06dKTT0qHHy6tsIK0/vrSuedKvnVdeMVx0QtJBhCAQPXCrkzGnyPy5+EFYIXAdtttt9n//wqaN29ereR22mknHXTQQfrqq6+08847q127dlpsscVswdlf9fLLL9cK27lzZ1188cXq16+f2piLgsPtQyV9CNh7BA+1D58VzaHpoosuasZuF/373/+ulY7H38Xmslx11VX2GbWcTWFZWsccc4z9cF3wy3WWDXOcfvrp+ot5zW9hQxir2ofcXXfdNT+dUeY+YXv7Retl9TIfcMABxsy2Y0JyIsAcwJywEQkC0SLgi0H69pXuvFMaP14aMUK66CJpo42sm98mevhiEvsM19/+puqFJAceKD38cO2t66JVI0oDgWgTcHdO/kMrGw07gc9UKw/XUHqeb7ayxx57VBtIQ9wJaY38Ym4HXnzxRe23336aNm1atUHlRt/79iGxjW1gvuOOO+pb77IMyb/+9S+ttdZa9rkywn5I2i/JNHEDs0OHDnrkkUfMxdUonXfeeTrrrLOqr8NBvRxudPpx4MCBGjBgQLWmwhxoH0wPPfSQrr/+en322We69dZbq409f/7999+rZ8+eWm+99fTee+/ZFpwvaNKkSdpzzz1T0TlCoKQEfA5gle0EUoVAIKoEJk2qqho4sKpqzz2rqtq08a+PBdq0aVXV5ptXVV1+eVXVxx9XVc2bF9VaUC4IlI/AjBkzqsywqfJjSqZNW/B/FP6fKva559sYsd6+qkMOOWR+FOsVrGrfvn3VnDlz5t8Ln3Tt2rXqhhtumH+rU6dOVdZzN//aT7755hs3Q6vMaKx1P3zRv3//qt12223+LetxrPK0wvmagVq11157VYcZPXp0dZovvfTS/DjhEzM8q3r37h2+VTVu3LjqOB63Lqmr3VLh/Hvb62Dq3+MVKfQAVmSzU+lKIuCOpFM9fjZvW0OHSqedZnMYbBKDDwf7wpIzzpDWXls2hCP17x/MLcy216KSWFJXCMSNgPf0PfbYY/LhVZf7779fe++9t5qay4Hp1t3oQ65m9GmJJZao7m37/PPP/9QDuOGGGzZYbe+t83DLLLNMdTp3mPuC9J7ENddcszrfVGI+FPzDDz9UX/qKYi+T9/LVJd776D2HPvyb0tVXX706qPcqIo0nEN3lO42vCzEgAIEGCPgWc/756nrllbK5PAsWkvgokW9Rd8stgfqk9C23XLCyuFOn+hNP0grH+mvJEwgsINCypWwIdcF1pjP3lrLZZplCBM9ef102xJk5nOfbGPEhXR+ifdY8zfscv9dee03XXHNNdRKn2S9BHw72eXmrmBsBn7+3++67yxd6hKWVryrLID70e9JJJ+nqq6+2aSZ/M/+ki8uHjd95551asZr7B1BI3JVMan6i551JPJzX5YorrvhTMDckkcYTwABsPDNiQCAxBGx+t03EDvT336XBgxcYhOPGSc89F6iHsR/v83ck2WQTmfuHAEOSVjgmpmGpSNEJ+NzaBuyi+WVowLapFS7bNOdHauDEDatdd921uufvS/Mdtdpqq2mDDTaojuXGYD9bnNHXJxCb+JxAX+DRWPF0NrEPBRv2nR+1sb1ya9sQhBt5w8ylwVZbbTU/ndTJ+raSzXsyO9uHVpRdz6TKG4cjQ8BxaCXKCIESEPCehT59gt4/7wn86CPpssuCnouF7JPi00+DXkPvPbRRHhtGku69V3J3NOVY4VgCJGQBgUQQ8GFg7wG827zI77///vPr5L1+j5v7AB9+/fDDD7XvvvvO75GbHyiLE0/HF2Z4b+IX5pXeF4q861saNULcsPOVyTZf0TwYPCmbZ2jTVYbOX0jiK4Z//vln7bPPPho+fLi+/vprDRo0qDq8r0JGGk8AA7DxzIgBgcQT8N4NnxPocwPtx705fZUeeEC2cjDYgeTXX4NVxD63sI4f64nnQwUh0BgC5i9ZPqUik/hzD1cM2dLmciy11FLmZ3B0tZGXyuNa20ZoySWXrO698+FVXwXsPW2NlaOOOqq6l9EWdJjngY3MLdVPtXoDs03vFpt/4kPQ3pPo8/vc5YzPU3RZ3pyZvvHGGzZveW51OX1V8gknnFDtmmYh/4WKNJqAfcwjORCwATG5+lvXxVYTqXXril1IlAM+osSZgP/Y9qk91qFQrdZxkJW4a5ocvluySptAECgmgUwOhbPNl3my2ZIqXLhM7YYjaJvGUzjUFZXSTVZbV7f6plRUzalsxROwhXrWYxDoJZdIzz8f7DZS8WAAAIEMBHyHj6jv8pGh+DxKIAH6TRPYqFQJAqUkYA75sxJfvOfzCBEIQAACECg/AQzA8rcBJYBARRAwTxG2m0DggsZ3IUnzNFERDKgkBCAAgagQwACMSktQDggknMAWW9ikWfvEccfTvoLYh8POPlvmLDbhFad6EIAABCJIAAMwgo1CkSAQJwLZrnC0bT+rHU3bNqG2GbxsH0/p0kuD3Udsb3rb21PmgiJONaesEIAABOJLgFXA+bVd9SIQVgHnB5HY8SfQ2BWOf/whPfVU4HPQnU+nZKWVJPMooYMPLp5LjFReHCGQLYHUalL3VdfQjhXZpkm44hOwvYCrHVuvaHtcLpLmh4dVwBIGYH7vIAZgfvyIDQHZ1qOybUTlPYTmUalaWrSQ9tgj2Jd4443tg4pPKt6UMhJw33Pu4HhZ21h76aWXLmNJyLoxBNwfoe817Luf+D7DYcEAxAAMvw+5nGMA5kKNOBCog4D7e33oIenmm6WRIxcEWHfdwBC0TQpsE/gF9zmDQCkJfP/99/rVPKC7EdjSts3xfWyRaBKoqqrS77a3pRt/SyyxhE05+fNewRiAGID5vr0YgPkSJD4E0gjYZ7dtIxUMD7tBmNpmzn2t+84jRx8tde2aFolLCBSZgBsVEydOrDYCi5wVyReIgBt/7du3r9NYxwDEAMz3NcMAzJcg8SGQgYBt/Vk9NGw7RMn2sZ8vvh+xG4K+h/3CC8+/zQkEik7Ah4P/8EmsSKQJNG/e/E/DvuECYwBiAIbfh1zOMQBzoUYcCDSSgK8OfuWVYHj46acXrBZ2J9SHHSYdcQS7LDQSKcEhUNEEMAAxAPP9B8AAzJcg8SHQSALjx0t33CHdfrtsSC6I7P4F+/QJegV79w78DTYyWYJDAAIVRAADEAMw39cdAzBfgsSHQI4EUq5kfNHIkCELEll5ZenII3Els4AIZxCAQDoBDEAMwPR3ItvrYyygqzvS7oIfwGyxEQ4CxSHw2WeBK5mBA2u7ktlzz2AF8UYb2YcdizaLA59UIRBDAhiAGID5vrb0AOZLkPgQKCCB+lzJrLdeMDyMK5kCwiYpCMSYAAYgBmC+ry8GYL4EiQ+BIhBIuZLx4eGHH8aVTBEQkyQEYk0AAxADMN8XGAMwX4LEh0CRCdhmANWuZHy3kXRXMv37S7vsgiuZIjcByUMgcgQwADEA830pMQDzJUh8CJSIAK5kSgSabCAQAwIYgBiA+b6mGID5EiQ+BMpAYNy4wJWMu5NJdyXjvYJbb40rmTI0C1lCoGQEMAAxAPN92TAA8yVIfAiUkYC7knnyyWDbuXRXMkcdFbiSWXrpMhaQrCEAgaIQwADEAMz3xcIAzJcg8SEQEQK4kolIQ1AMCJSAAAYgBmC+rxkGYL4EiQ+BiBFwVzIPPhhsO/f++wsK565kfHjYXcm0arXgPmcQgED8CGAAYgDm+9ZiAOZLkPgQiCgBdyUzfHgwPPzQQ9KsWUFBW9t//YEHBn4Fu3aNaOEpFgQgkJEABiAGYMYXJIuHGIBZQCIIBOJOAFcycW9Byg+B2gQwADEAa78Rjb/CAGw8M2JAILYE3JXMyy8HvYJPPy35tUu7dtLhh0tHHCH95S/BPf5CAALRJYABiAGY79uJAZgvQeJDIKYE6nMls+OOwfAwrmRi2rAUuyIIYABiAOb7omMA5kuQ+BCIOQFcycS8ASl+RRLAAMQAzPfFxwDMlyDxIZAgAilXMgMGSFOnBhVr0ULaa6+gV3CjjexDt0mCKkxVIBBTAhiAGID5vroYgPkSJD4EEkigPlcy3boFhiCuZBLY6FQpVgQwAG23o1i1WHEK+4Ql+4vpf4uTPKlCAAKVRsD9BB52mDRihPT224HbGO8JdL+CvlBk+eWl44+XvMcQgQAEIFAOAhiA0vUG3rx6IRCAAAQKS8CHe33Yd+BAacIE6aqrpJVXDoaHb7hBcj+CW2whPfKINHt2YfMmNQhAAAKZCGAASkMM0G+ZIPEMAhCAQL4EfE/hU06RvvhCevFFaeedbQjGPoGHDg3mCHbqJJ17ruSrixEIQAACxSYQdQNwcwPwjOl3puaXX7uYpkt/u/GN6UxTG3BRD1MEAhCAQCQJuNHXu7f05JPSmDHSOedI7dtLEydKF18sde5sH3T2STdo0AI/g5GsCIWCAARiTSDqBqDvuPmh6bH1ULa1dbrO9BJTm16t10yfN+1omhI3Cj+pQ20WDgIBCECgfATcafQ//yl9+20wDNyrV2D0PfWUtM020mqrBcPGvhMJAgEIQKCQBGyGSmzEewD7mtrv5vnyjp2NND16/h2bV23nHubM0L2GTntZADcyd28goE3jlmtKFreT8VOmTFFr3yAUgQAEIJAngVGjpFtvDeYNpruS6W/jHd2740omT8REh4C5aZqqNm3aOAn/U+O0qbLARL0HMFNrLGwPNzC1gZJa4teb1LpTuAs3KqeEdHzhkiYlCEAAAsHCkOttadp3NvHl9tttaMPGNmbNkv7zH2njje1Dzz717rxTclczCAQgAIFcCcS5B3B5q7Stq9Ompm+GAJxl5weZdgndy3Rq07G1vqkPN/9s6r2M75rWJfQA1kWFexCAQNEIVNnYx/Dh0s03Sw8/HBiDnpl3Xhxkn3RHHSWtsUbt7H1IefLk2vfCV23b2jyZ8ESZ8EPOIVABBOgBjJcj6PQh4JQBuIm9q2+F3tez7fwA09VD94p16uO+NgLMEHCxAJMuBCCwgIDPBbznnmCI+KuvFtz3uYM+POyLR77/3n792s/fmb4srh5ZZBFp9GiMwHrwcLsCCGAAxtsRtP++nWtq6+dqybJ2NanWHS4gAAEIJICAu5I59dTAlcwLL9R2JbPnnoFB54tKMhl/jsGfZ+ohTAAqqgABCDRAIM5zAGdb3XyF79ZpdfTr8JBw2uOCXB5jqYwytYEZBAIQgEBpCbgrGV8lHHYl065d4ErG5wciEIAABBoiEHUDcDGrwHo16nVZseY8NXvlGru2DZd0iKnPgrnW1J/dalpMuckS72ravZiZkDYEIACBhgiEXcn4HEFfJIJAAAIQaIhAs4YClPn5hpb/kFAZ3OBzGWjaz9Q+7mSDIjrPdDnTT0y3Nx1rikAAAhCoGAILm18EHwZeZRWMwIppdCoKgTwIRN0AHGp1a2il8s0WxhWBAAQgAIEsCbhrGQQCEKhcAlEfAo5qyzAHMKotQ7kgAIGsCOy0k+T+BmfMyCo4gSAAgYQRwADMrUGZA5gbN2JBAAIRIeCrgE84QVppJdtP8zoMwYg0C8WAQMkINDS8WrKCxDQj/ACWs+HwdltO+uQdUQL+b9GQH8AWLaTzzw/8CXp4F19FfPrpgWPpli2De/yFQFIJ4Aew4fl1SW37QtULA7BQJBubTjbfcni7bSxVwieEQLa/jWabM60BA6RLL7WVczVL55ZddoEh2Mr3R0IgkEACGIAYgLm+1j4H0NWH0LuwE0iuGPOIN3JkdksdR5iryPV9pz8EAhCoj4Abgr7X8CWXSGPGBKGWWUY67bRghxEMwfrIcT+uBDAA470TSDnfO+YAlpM+eUMAAgUl4C5kDjOPql98Id11VzAv8Mcfg57Azp2lK66Qpk0raJYkBgEIlJmA92AhEIAABCAAATVvbl71D5E+/zzYc3jllYMt4844Q3JD8LLLpN9+AxQEIJAEAhiASWhF6gABCECggATcEOzXLzAEfY6gO5f+6SfprLMCQ9DnDE6dWsAMSQoCECg5AQzAkiMnQwhAAALxINDMtgo46CDps8+COYKrrSb9/LN09tmBIXjxxdKUKfGoC6WEAARqE8AArM0j2ytfADLKdHi2EQhXJgI+loVAAAJ5EXBD8IAD7EPPPvXuuy9wM/PLL9K55waG4EUXYQjmBZjIECgDAQzA3KCzCCQ3bqWP5eNYd9whVVWVPm9yhEDCCDRtKu23n/Tpp9IDD0irry79+mvgU7BTJ+mCC4LrhFWb6kAgkQQwABPZrBVQqbZtJffzl0kWstf7jz+kI44IxrGmT88UmmcQgECWBNwQ3Gcf6ZNPpAcflLp2DXoAL7ww6BF0J9PeQ4hAAALRJdAkukWLRclwBF3OZmrI2+1SS0kPPRRMWJo3T1pzTem//w26LcpZbvKGQMII+L+X/2v5ULD3Drq0tk/H44+XTjpJ8n9FBAJRIoAfQBxB5/s+YgDmS7AU8YcNk/beW5o4UVpssWBI2K8RCECgoATcEHz88cAQ/PjjIOnFF5eOO046+WRp6aULmh2JQSBnAhiAOILO+eUhYowI9Owpvf++1KtX4M3Wx66OPVaaNStGlaCoEIg+AZ91sfvu0gcfSI89Jq2zTuA30N3GuB9BdyMzeXL060EJIVAJBOzfFcmBAKuAc4BW1ijt20svvRR8A3lBbrJ1PD16LNj3qqyFI3MIJIuAG4K77hr87vIewfXWC357uSNpNwTdsbTvNIJAAALlI8AcwPzYMwScH7/yxH7uucCnhTs0W3JJ6d57pR12KE9ZyBUCFUDAF+E//bTki0S8M97F9xfu31869VRp2WWDe/yFQKkIMATMEHCp3jXyiRKB7beXRo6UuncPlir26RP0DM6ZE6VSUhYIJIZAE+tq2HlnacSIwBBcf33JF+X/61/SiitKp50mTZqUmOpSEQjEggBDwLFoJgpZcALutOy114LZ6Z64j01ttZX0/fcFz4oEIQCBgIAbgjvuKL33nvTMM9KGG0q//y5ddVVgCJ5ySrBWC14QgEDxCWAAFp8xOUSVwMILS9dfH7iK8dXBvlq4Wzdp6NColphyQSARBNwQ9I734baX0rPPBp3xM2ZI11wTGILuOobfYoloaioRYQIYgBFuHIpWIgJ77RV0Say1VjAO9fe/Bz2C7tMCgQAEikbADUGfkfH229Lzz0sbbyzNnCldd5200krSCSdI331XtOxJGAIVTQADsKKbn8rPJ9Cli/TOO8GOIW74ub8KH6vyhSIIBCBQVAJuCG67rfTmm9KLL0p/+1tgCHoHvRuC7lB6woSiFoHEIVBxBDAAK67JqXC9BFq2lO65R7rzTqlFC8lXC/ts9XffrTcKDyAAgcIRcEOwd2/pjTekQYOkTTcN3HXecENgCLr7zvHjC5cfKUGgkglgAObW+sdYtFGmNoMFSRQB/wY69NBgTGrllaWxY4NvoRtvlNyXBQIBCBSdgP8bbr11sE7r5ZcDl52zZwfuO/3f0t3HjBtX9GKQAQQSTcD+zZA8CLS2uFNMbN9LP0USRcDaVYccEuxt5RXzuYJ33CH53lYIBCBQMgL+28vXZrkfQV+r5dK8efBb7cwzpY4dg3v8hUC2BPADiB/AbN8VwlUigTZtgh3ufWlis2bSww9Lf/2r9MknlUiDOkOgbAS8R3CLLQIjcMiQYFfHP/6Qbr1VWmUV6cgj2dSnbI1DxrElwBBwbJuOgpeEgH/zuE8K73ZYYQVp9OjAZ8V//lOS7MkEAhCoTaBXL8mNQP+X3HJLyQ3B22+XVl1VOvxw6ZtvaofnCgIQqJsABmDdXLgLgdoENtkk2MPKZ6i7w7KDDpKOOCJYqlg7JFcQgEAJCGy+ufTKK9Krr0ruuck38vH1W6utJh12mPT11yUoBFlAIMYEMABj3HgUvcQEllkmWBnsE5G8Z9DnA7q/iq++KnFByA4CEEgR6NFD8oUir78eLBxxQ/CuuwJD0Kfw8u+ZIsURArUJYADW5sEVBDITaNpUOu+8wFlZ27bSBx8ErmKeeCJzPJ5CAAJFJeAuY9x1jPsS3GYbae7cwKuTu/js10/68suiZk/iEIgdAQzA2DUZBY4EAfdR8f77kg8NT50q7bqr5BuZ+oQkBAIQKBsB75R/4QXprbek7bYLDMGBAyU3BA88UPrii7IVjYwhECkCGICRag4KEysCHToEyxLd8HPx1cK9euGpthoGfyBQXgK+rZz7cvcNfny7Od/g5957pTXWkA44IFjPVd4SkjsEyksAAzA3/jiCzo1b8mK5M7Krrgp8BbovSB9/6tZNeuml5NWVGkEghgS6d5eefda89pvb/j59AkPwvvukrl2l/faTPvsshpWiyBAoAAEMwNwg3mTR7OND9tGCQMAI9O0rjRwZGH+TJweTkHyxiE9EQiAAgbITcBeezzwjvfeetNNOgSH4wAPSmmtK++xjWzv53k4IBCqIAAZgBTU2VS0yAd+jynsA3T2Mb11wwQXBJKQffyxyxiQPAQhkS2CDDaSnngp+r+2yS/Cv+tBD0lprBZv94Oc9W5KEizsBDMC4tyDljxaBRRaRbrtNckfRLVsGQ8E+JOy72yMQgEBkCPi/pS/e97Vc3oHvv9keeURae21pzz2ljz+OTFEpCASKQgADsChYSbTiCfgsc5905EsPJ0wIFof4IhH/lkEgAIHIEFhvvWAK74cfSrvtFhTr0UelddaRdt9d+uijyBSVgkCgoAQwAAuKk8QgECLgk4vefVfae+9gmwJfLezfMFOmhAJxCgEIRIGAG3z//W9g8O2xR+Dr/bHHpHXXDbw8uctPBAJJIoABmKTWpC7RI7D44pLPNL/xRslXDPuYk09C4tskem1FiSBgBHwI2IeCfQh4r70CQ9D/bX3I2IeKfcgYgUASCGAAJqEVqUO0Cfi2ccccE8wD7NQp2JvKnZT5xqUMCUe77ShdxRLwDnxfHOKLQrwT3/+Nn3wy2Phn552lESMqFg0VTwgBDMCENCTViAEB90PhrmJ22EGaNUs6/PBgj6rp02NQeIoIgcok4P4CH3xQ+vRTad99pYXsW/Ppp6UNN5R23DFwK1OZZKh13AlgAMa9BSl/vAgstVTw7XHZZcE3ia8W3mgjtiWIVytS2gok4DuI3H9/4C9w//2Df9///U/y33X+m87XfCEQiBMBDMA4tRZlTQYB70I44wxp8GCpffuga8G7Ex5+OBn1oxYQSDABX9jvW8r5DiK+2N//nX3LOf8d51vO+dZzCATiQMBmNSB5EGhtcaeYqLVvA4ZAoLEEJk4MtiEYOjSIeeyxwdZyLVo0NiXCQwACZSDwf/8nXXKJ5NvLpTb+2WYb6fzzpb/9Tfr2W8k3B6pP2raVOnas7yn3i0Vg6tSpatOmjSfvf6YWK58op4sBmF/rYADmx4/YTmDOnODb4tJLAx4+puSOyHzBCAIBCMSCwJdfSv4v7LM6UobgZpsFQ8OzZ9dfBfcdP3o0RmD9hIrzBAPQeq+LgzbxqR5jNfSdI5n1kfimLkEFmzULuhB8QtGSSwa+A93nhO9gj0AAArEgsMoq0t13S198IR16qOT/1q+/LmUy/rxiM2dm7iGMReUpZCwJYADm1mw3WTRbG6buuUUnFgTqIOAzyd3JmPcA/vKL1KePdNZZQQ9hHcG5BQEIRI/ASisFHp7cEPS9hhEIRJUABmBUW4ZyVSYBH/Z97TXJ5wK6+GrhrbeWfK4gAgEIxIbAiitK554bm+JS0AokgAFYgY1OlSNOwBeA3HBD4IV2scUkXyDiQ8LDhkW84BQPAhCAAATiQgADMC4tRTkrj4DvQ/Xee9JaawU9gFtuKV1+uTRvXuWxoMYQgAAEIFBQAhiABcVJYhAoMAF3OuaOxQ48MDD8zjxT8n2ofv65wBmRHAQgAAEIVBIBDMBKam3qGk8CLVtKAwZId9wh+fCwrxZef/1gtXA8a0SpIQABCECgzAQwAMvcAGQPgawI+E70hx0mvfWWtPLK0tixkjsZu/lmqaoqqyQIBAEIlJaAO3l2P3+ZxJ97OAQCpSZg3ypIHgRwBJ0HPKLmSMB2ntHBB0tPPBEksPfe0u23S4svnmOCRIMABIpFgJ1AikU2v3RxBC1hAOb3DmEA5seP2LkS8F6/a6+V/vGPwE+gzxV87DFpzTVzTZF4EIAABCqGAAYgO4FUzMtORRNGwIeETz45cA2zwgrBXlLdzS+571KPQAACEIAABBogwBzABgDxGAKRJrDJJsHuIb17S7//HqwWPuKIYH+pSBecwkEAAhCAQDkJYACWkz55Q6AQBJZZRnruOemCC2xSh/UM+mphNwy/+qoQqZMGBCAAAQgkkAAGYAIblSpVIIGmTaXzz5defDFYUuh7Cm+wgfTkkxUIgypDAAIQgEBDBDAAGyLEcwjEiYDvG+zGn/cA+mrhvn2lU0+V/vgjTrWgrBCAAAQgUGQCGIBFBkzyECg5gQ4dgv2DTzklyPrqq6UttpAmTCh5UcgQAhCAAASiSQADMJrtQqkgkB+B5s2lq66SHn9cam3eit54Q+rWTXr55fzSJTYEIAABCCSCQKUbgH+xVhxqOsr0I9M9TBEIJIeADwGPHCmtt57044+Srxa+8EJp7tzk1JGaQAACEIBAowlUugE4x4idaNrVdCtT86yrVqYIBJJDwLeOe/NN6fDDg23jfLXw9tsHBmFyaklNIAABCECgEQQq3QD83lh9UMPrBzv+bLpUzTUHCCSHwKKLBtvFDRwo+fmgQcGQsBuGCAQgAAEIVByBqBuAm1uLPGP6nanveL+Labr0txvfmM40HWHawzQX2dAiOY9xuUQmDgRiQeDAA6XhwyXfOs4XhfTsGWwp51vLIRCAAAQgUDEEom4A+nDsh6bH1tMie9n960wvMbUZ7nrN9HnTjqYpcaPwkzp0+VQAOy5t+h/TI0L3OIVAMgmstZb07rvSXvbvM8dmQfiWcrvvHriNSWaNqRUEIAABCKQRsG0DYiPeRWEz2vVkqMTv2LnNcNfRoXuf2bmHOTN0L9NpC3v4kqltn6B7MwW0Zx7WNSWL28n4KeZvrbWvtEQgECcC3ut3883SSScFfgJXWUV69NFgwUic6kFZIQABCDSSwNSpU9WmTRuP5X+mNjJ6IoJHvQcwE+SF7aFtdSCbzFRL/HqTWnfqv3ADeIDpYNOGjD8LUm1UTrFjSsf7TQQCsSTg28Ydc4z0+utSp07Sl19KG28s3XVXsFgklpWi0BCAAAQgkA2BOBuAba2CTU0npVXUr9un3avvclN74MPIPrfwgxpd2471yWX2wH8tpLRDfQG5D4HYEOjePXAVs8MO0qxZ0mGHSQcfLP3+e2yqQEEhAAEIQKBxBOJsAKZqmj573Xv10u+lwqYfreujeuHHenZM6cfpgULX9u1Y3VXs3cWuv4WecQqB+BJYainp6aely+w3zkL2seCrhb03cPTo+NaJkkMAAhCAQL0E4mwATrZauTfb9N6+Ze1eeq9gvQB4AAEI1BBww++MM6RXXpHatZM+tt9CG9ri+EceAREEIAABCCSMQJwNwNnWFr7Cd+u0NvHrYjs3s4lT1buHmD8NBAIJI9Crl/T++4GLmGnTgtXCxx8vzfZ/OQQCEIAABJJAIOoG4GIGOTU067xXrLlOuXm5xq5twpIOMV3D9FpTf3araTHlJku8q6lNnkIgkEACyy0X7Bt85plB5W64wTxsmovNsbVz1v4AACiTSURBVGMTWFmqBAEIQKDyCPh8uShLLyvckDoKaBOU1K/mfn87nm5q31jV/v7Mp4VeNS2FuO8X8wKDG5hSwCaPMhF49lnpgAOkX36xfXJsruB990nbbVemwpAtBCAAgfwJ4AZGiroBmH8rFycFHwJ29R7ULhiAxYFMqhEiMGaMtOeegQNpL9ZZZ0kXXig1axahQlIUCEAAAtkRwAAMDJjsaBEqTIAh4DANzpNPoHNn22fnNduTp2ZTnksvlXr3liZOTH7dqSEEIACBBBKI+hzABCKnShCIKYEWtgmOzwV86CFpMZueO8RmZ3TrJg0bFtMKUWwIQAAClUuAIeD82p45gPnxI3ZcCXz+ebB/8KefBn4DT7dpuLvtFpzXVae25re9Y2rtVl0BuAcBCECgdAQYAmYOYL5vGwZgvgSJH18C06fbLtxH2yaKWeyiuMgigVNpjMD4tjclh0CCCGAAMgcw19cZP4C5kiNecgi0ahXsGHL22Q3XaeZMabL7bkcgAAEIQCAKBJgDmFsrsAgkN27EShqBJjaLZNddk1Yr6gMBCEAg8QQwABPfxFQQAhCAAAQgAAEI1CaAAVibB1cQgAAEIAABCEAg8QQwABPfxFQQAhCAAAQgAAEI1CaAAVibR7ZXLALJlhThIJAi8NVXqTOOEIAABCBQZgIYgLk1AItAcuNGrEomcMgh0uDBlUyAukMAAhCIDAEMwMg0BQWBQEwJuJNn9/OXSXy18LRp0rbbZuc3MFNaPIMABCAAgbwJsJN73ghJAAIVTsCdO48endnPn28dd/75wTZyBx4ojRkjnXOOuaJnM6IKf3uoPgQgUCYCfPrmB56dQPLjR+xKIjBvnnTWWdIVVwS19iHhW2+VmjevJArUFQIQiAABdgJhJ5AIvIYUAQIVQmAhm3Fy+eXSLbcEewbffbfUp480dWqFAKCaEIAABKJDgDmAubUFq4Bz40YsCEhHHSU99ZTUsqU0aJDUo4c0YQJkIAABCECghAQwAHODzSrg3LgRCwIBAe/5GzZMatdO+ugjaeONpY8/hg4EIAABCJSIAAZgiUCTDQQgkEZgww2lt9+W1lhDGj9e2mwz6eWX0wJxCQEIQAACxSCAAVgMqqQJAQhkR6BzZ+mNN6SePYO5gNttJw0YkF1cQkEAAhCAQM4EMABzRkdECECgIASWXFJ68UVp332lOXOkgw+WLrhAqqoqSPIkAgEIQAACfyaAAfhnJtyBAARKTaBFi8BBtLuJcbnwwsAQnD07uOYvBCAAAQgUlAAGYEFxkhgEIJAzAXcTc8kl0u23S02bSgMHSttvL02ZknOSRIQABCAAgboJYADWzaWhu7iBaYgQzyGQK4HDD5eeeUby3UNeeSVYHDJuXK6pEQ8CEIAABOoggAFYB5QsbuEGJgtIBIFAzgR8Mcirr0rLLSd98kngJuaDD3JOjogQgAAEIFCbAAZgbR5cQQACUSHQrVvgJmbNNaXvvgscRvtiEQQCEIAABPImgAGYN0ISgAAEikagY0fp9delLbaQpk2TdthBuuuuomVHwhCAAAQqhQAGYKW0NPWEQFwJLLGE9MIL0gEHSHPnSocdJp17Lm5i4tqelBsCEIgEAQzASDQDhYAABDISWHjhYFWwG34uF18sHXSQhJuYgAd/IQABCDSSAAZgI4ERHAIQKBOBJk2kiy4KhoDdTcy990rbbiv9+muZCkS2EIAABOJLAAMwvm1HySFQmQQOOUR69tnATcyQIdKmm0pjx1YmC2oNAQhAIEcCGIA5giMaBCBQRgLbbBMsDllhBWnUqMBNzMiRZSwQWUMAAhCIFwEMwHi1F6WFAARSBNZdN3ATs/ba0sSJ0uabS889l3rKEQIQgAAEMhDAAMwAJ8MjdgLJAIdHECgZgQ4dpNdek7baSpo+Xdppp2AruZIVgIwgAAEIxJMABmBu7cZOILlxIxYECk+gTZug569fv8BNzJFHSmedJc2bV/i8SBECEIBAQghgACakIakGBCqaQPPm0t13SxdeGGC47DJp//2lWbMqGguVhwAEIFAfAQzA+shwHwIQiBcBdxNz3nnSgAFSs2bSgw9Kvljkl1/iVQ9KCwEIQKAEBDAASwCZLCAAgRIScAfRzz8vtW4tDRsWuIkZM6aEBSArCEAAAtEngAEY/TaihBCAQGMJ+KIQ30PYF4l89lngJua99xqbCuEhAAEIJJYABmBim5aKQaDCCbh7mLffltxdzKRJUs+e0jPPVDgUqg8BCEAgIIAByJsAAQgkl4A7in711WAu4O+/S7vsIt18c3LrS80gAAEIZEkAAzBLUASDAARiSsDnAnrP36GHBq5hjjE3nqefjpuYmDYnxYYABApDAAOwMBxJBQIQiDIBdxNzxx3SxRcHpfzXv6R99pFmzoxyqSkbBCAAgaIRwAAsGloShgAEIkXA3cScfbZ0772SG4SPPCJtvbX000+RKiaFgQAEIFAKAhiApaBMHhCAQHQIuIPoF1+UfAcRXym8ySbS119Hp3yUBAIQgEAJCGAAlgAyWUAAAhEjsMUW0htvSB07Sl98EbiJGT48YoWkOBCAAASKRwADMDe2Notco0z5xsiNH7EgUH4Ca64ZuInp1k368UepVy/pqafKXy5KAAEIQKAEBDAAc4N8k0Xrato9t+jEggAEIkFgueUCNzHbbSfNmCH17SvdcEMkikYhIAABCBSTAAZgMemSNgQgEH0Ciy0mPf20dMQRUlWVdPzx0imn4CYm+i1HCSEAgTwIYADmAY+oEIBAQgg0aybdeqt02WVBha65Rtpzz6BXMCFVpBoQgAAEwgQwAMM0OIcABCqXgLuJOeMM6f77pYUXlh57TPr736XJkyuXCTWHAAQSSwADMLFNS8UgAIGcCOy7rzRokLTEEtJbb0l/+5v05Zc5JUUkCEAAAlElgAEY1ZahXBCAQPkI9Owpvfmm1LlzYPy5EejGIAIBCEAgIQQwABPSkFQDAhAoMIE11giMvg02CIaBt9xSevzxAmdCchCAAATKQwADsDzcyRUCEIgDgfbtpWHDpD59gn2Dd99duu66OJScMkIAAhDISAADMCMeHkIAAhVPoFUr6YknpKOPDtzEnHSSdOKJ0ty5FY8GABCAQHwJYADGt+0oOQQgUCoC7ibmJvP/fuWVQY7//re0xx7S77+XqgTkAwEIQKCgBDAAC4qTxCAAgcQScDcxp50mPfRQ4CbGewV9XuAPPyS2ylQMAhBILgEMwOS2LTWDAASKQWCvvaSXX5aWXFJ6553ATcwXXxQjJ9KEAAQgUDQCGIBFQ0vCEIBAYgn06BGsEF5xRenrrwMj8I03EltdKgYBCCSPAAZg8tqUGkEAAqUg0KVLYAT+9a/Szz8Hu4Y8+mgpciYPCEAAAnkTwADMGyEJQAACFUugXTtpyBBp552lWbOC/YOvvjpYLVyxUKg4BCAQBwKVbgAubo30rukHph+bHm6KQAACEMiegLuJ8X2DjzsuiHPqqdLxx+MmJnuChIQABMpAoNINQPfhYHs+aT3TjUzPNF3aFIEABCCQPYGmTSV3DXPNNZKvFr7xRmnXXaXp07NPg5AQgAAESkig0g1A9+SacuS1iJ3bp7js0xuBAAQg0EgCbvi5k+hHHpFatJCeflraYgtp0qRGJkRwCEAAAsUnEHUDcHND8Izpd6ZVpruYpkt/u/GN6UzTEaa2PK9RsoSF/tB0vKl7eZ1sikAAAhDIjYBvFzd4sI0l2GDCuzbDZOONpc8/zy0tYkEAAhAoEoGoG4A2uabaODu2nvqbQy5dZ3qJaTfT10yfN+1omhI3Cj+pQ5evCfCrHdc1XdF0X1Ob1Y1AAAIQyIPAJpsEK4RXXlkaM0by61dfzSNBokIAAhAoLIE4DXd6D2Bf0ydDCMwLq0aa2iad8+UzO/MwPp+vsXKLRbCf7no0y4itLdwUE7Vu7acIBCAAgRCBH3+UdtpJevvtYPeQgQOlvfcOBeAUAhAoB4GpU6eqTZs2nrX/mVqOMpQ7z6j3AGbis7A93MB0UFogv7af21mJ9/alLDc/+pDz6AwxbWJPdXgP67p4hrA8ggAEKp3AMssEw8F97bfr7NnSPvtIV1yBm5hKfy+oPwQiQCDOBmBb4+eLNtJnWPt1+yzZdrBwPi7jcwBfN7Wle/rItD7xXsUpIfV5gwgEIACB+gksuqiNKdigwoknBmHOOEPqb1OX58ypPw5PIAABCBSZQJwNwBQaHxoOiw9rp98LPw+f+/zA9Ux9DuA6pj4EnEkus4feXZxSNyARCEAAApkJuJuYa6+1GcvXBW5ibr3VlrTtIk2bljkeTyEAAQgUiUCcDUBfretuXNJ7+5a1e+m9goXCN8sS8rkCKf2tUAmTDgQgUAEETjghcBq9iHmdevZZ80LaU5o4sQIqThUhAIGoEYizAWgTaqrdvmydBtWv30y7V+jLYyzBUabDC50w6UEAAgkn4PMBffu4tjaLZeTIwE3MKP84QSAAAQiUjkDUDcDFDIUP0bq6uKsWP0+5ebnGzg8zPcR0DVMbY6l+ZuMrRZWbLPWupt2LmguJQwACySTgvgF9ZfCqq0pjx0qbbioNHZrMulIrCEAgkgSibgBuaNTer1EH6AafX1/kFyYPm55oep7pB6a+ind7U/tERSAAAQhEmID7CHzTBivcR+Cvv0q9e0v33x/hAlM0CEAgSQR8wQSSO4HWFhU/gLnzIyYEIDBjhnTggdJ//xuwuOQS82JqDgd8azkEAhAoCgH8AEpR7wEsSsMXIFHmABYAIklAAAJGwN3EPGyDGaeeGuA4+2zpyCNxE8PLAQEIFJUAPzHzw0sPYH78iA0BCIQJ3Hij5CuF582Ttt1WeuQRczePv/kwIs4hUAgC9ADSA1iI94g0IAABCBSGwLG27fkTTwS9gi+8YLOabVrzd98VJm1SgQAEIBAiwBBwCAanEIAABMpOwPcO9hXBy5pL0w9sbZuvGP7kk7IXiwJAAALJIoABmFt7MgcwN27EggAEsiHQ3TxMvfWW1KWLNG5c4CZm8OBsYhIGAhCAQFYEMACzwvSnQPgB/BMSbkAAAgUlsNJKgZuYHj1s7yHbfMjnBN57b0GzIDEIQKByCWAAVm7bU3MIQCDqBJZaSho0SNp7b+mPPwJ3Mf/8p+12nu1251GvIOWDAATKRQADsFzkyRcCEIBANgR832B3EP2PfwShzztPOvTQwCDMJj5hIAABCNRBAAOwDijcggAEIBApAgvZR/Xll0u33GK+G+z8nnukHXYIhoYjVVAKAwEIxIUABmBuLcUikNy4EQsCEMiHwFFHSU89JbVsKb30kuTzA8ePzydF4kIAAhVKAAMwt4ZnEUhu3IgFAQjkS6BPH2nYMKldO+mjjwI3MX5EIAABCDSCAAZgI2ARFAIQgEAkCGy4ofT229Iaa0gTJkibbRb0CEaicBQCAhCIAwEMwDi0EmWEAAQgkE6gc2fpjTeknj2l336Ttt8+mBuYHo5rCEAAAnUQaFbHPW5BAAIQgEAcCCy5pPTii9Ihh0gPPBAcx46VDj5Y+umn+mvQtq3UsWP9z3kCAQgknkCTxNewuBVsbclPMVHr1n6KQAACECgDgXnzpHPPlS69NMi8aVNp7tz6C+KuZUaPxgisnxBPEk5gqjlXb9OmjdfS/5in9coThoBza3NWAefGjVgQgEAxCLhrmEsukW67LXATk8n48/xnzpQmTy5GSUgTAhCICQEMwNwailXAuXEjFgQgUEwCRxwhXXddMXMgbQhAICEEMAAT0pBUAwIQgEA1gU03BQQEIACBBglgADaIiAAQgAAEIAABCEAgWQQwAJPVntQGAhCAAAQgAAEINEgAA7BBRASAAAQgAAEIQAACySKAAZis9qQ2EIAABCAAAQhAoEECGIANIiIABCAAgRgRcCfP7uevIXnzzYZC8BwCEEgwAXYCya1x3Q+gKwZ0bvyIBQEIFIuA7/DhTp7r8vM3Z4504YXSc89Jxx8vtWwZ7B5SrLKQLgQgEFkC7ASSX9OwE0h+/IgNAQiUmoDvGtK/f+A02vO+4Qbp2GNLXQryg0BZCbATCD1YZX0ByRwCEIBAyQn4riG33CKddFKQ9XHHSVdeWfJikCEEIFBeAgxhlpc/uUMAAhAoPYEmNvhz9dXSOecEef/jH9L550tVVaUvCzlCAAJlIYABWBbsZAoBCECgzATcCPznP6XLLgsKctFF0mmnYQSWuVnIHgKlIoABWCrS5AMBCEAgigTOOEP697+DknmvoM8P9HmCCAQgkGgCGICJbl4qBwEIQCALAr4i+M47Je8VvPVW6eCDJV8xjEAAAoklgAGY2KalYhCAAAQaQeDQQ6X77pOaNpX+8x9p332l2bMbkQBBIQCBOBHAAIxTa1FWCEAAAsUk4Ebfo49KzZsHx912k2bOLGaOpA0BCJSJAAZgbuDdCfQo0+G5RScWBCAAgYgS6NtXevrpYDeR//1P2nFHafr0iBaWYkEAArkSwADMjdxNFq2raffcohMLAhCAQIQJbLut9PzzUqtW0ssvS9tsI02ZEuECUzQIQKCxBDAAG0uM8BCAAAQqgUCvXoHx16aN9MYb0lZbST//XAk1p44QqAgCGIAV0cxUEgIQgEAOBDbeWBoyRGrbVnrvPcmNwkmTckiIKBCAQNQIYABGrUUoDwQgAIEoEejWTRo2TFpuOenjj6XNN5fGj49SCSkLBCCQAwEMwBygEQUCEIBARRHoalOeX31V6thR+uILqUcP6euvKwoBlYVA0ghgACatRakPBCAAgWIQWGWVwAj045gxQU/g558XIyfShAAESkAAA7AEkMkCAhCAQCIIdOoUGIHeIzhhgtSzp/TRR4moGpWAQKURwACstBanvhCAAATyIeBzAYcOlXxu4A8/BAtD3n03nxSJCwEIlIEABmAZoJMlBCAAgVgTWGYZafBgyVcJ//KL9Pe/S6+/HusqUXgIVBoBDMBKa3HqCwEIQKAQBJZYQho0KOgB/O03qXfvwG9gIdImDQhAoOgEMACLjpgMIAABCCSUwOKLS889J/nOITNmSH36SM88k9DKUi0IJIsABmCy2pPaQAACECgtgUUXlZ58UvI9hGfNknbdVXrkkdKWgdwgAIFGE8AAbDQyIkAAAhCAQC0CLVoERt+++0pz5kj77CMNHFgrCBcQgEC0CGAA5tYex1i0UabDc4tOLAhAAAIJI9CsmfSf/0iHHSbNmyf16yfdckvCKkl1IJAcAhiAubXlTRbNHGGpe27RiQUBCEAggQSaNpVuv106/vigcv37S1dfncCKUiUIxJ8ABmD825AaQAACEIgOgSZNpOuuk848MyjTqadKF10kVVVFp4yUBAIQEAYgLwEEIAABCBSWgBuBl14qXXxxkO7550tnnIERWFjKpAaBvAhgAOaFj8gQgAAEIFAvgbPPlq69Nnh85ZXScccF8wPrjcADCECgVAQwAEtFmnwgAAEIVCKBE0+UbrtN8l7Bm2z6tC8SmTu3EklQZwhEigAGYKSag8JAAAIQSCCBI44IVggvZF8599wj7bef9McfCawoVYJAfAhgAManrSgpBCAAgfgS2H//wFdg8+bSww9Lu+8uzZwZ3/pQcgjEnAAGYMwbkOJDAAIQiA2B3XYLdg1xx9FPPy3ttJP0+++xKT4FhUCSCGAAJqk1qQsEIACBqBPYfvtg/+BWraSXXgr2EZ46NeqlpnwQSBwBDMDENSkVggAEIBBxAltuKQ0aJLVuLb32mrT11tLPP0e80BQPAskigAGYrPakNhCAAATiQWCTTaTBg6WllrJNNYdLbhT+8EM8yk4pIZAAAhiACWhEqgABCEAglgQ22EAaNkxq10768EOpZ09pwoRYVoVCQyBuBDAA49ZilBcCEIBAkgistZb06qtShw7S559Lm28ujRmTpBpSFwhEkgAGYCSbhUJBAAIQqCACq60WzAVcaSXp66+lHj2kL76oIABUFQKlJ4ABWHrm5AgBCEAAAukEOncOegJXX10aPz7oCfzkk/RQXEMAAgUigAEYgGxph7GmVxWIK8lAAAIQgEBjCaywQjAncN11pUmTgjmBI0Y0NhXCQwACWRDAAAwgnW2Hd7LgRRAIQAACECgmgWWXlYYMkbp3D1zD+OrgN94oZo6kDYGKJIABKK1qLW9jDnquIt8AKg0BCEAgagSWXDJwEu0LQtxJdO/egcuYqJWT8kAgxgSibgDaf7+eMf3OtMp0F9N06W83vjH1TSV9rMBmDzdKfNj3zEbFIDAEIAABCBSXgDuJfv75wPjz7eJ8B5Fnny1unqQOgQoiEHUD0PYKkjmH0rH1tMledv8600tMu5maS3nZJ4Y6mqbEjUKfSZyuy9u9nU19qRnLzQwCAgEIQCBSBFra9GzfM3hn+6ieNUvq21d67LFIFZHCQCCuBJrEqODeA2j//XoyVGaftzfS9OjQvc/s3MNk06t3mYXb33Su6WKmzU2vNr3ItC6xHczlmpLF7WT8lClTbEcj+7WKQAACEIBA4Qn88Yd04IHSQw9JC1m/xYAB0gEHFD4fUqwYAlNtakGbNm28vv6nIjejjnoPYKaXcWF7aG7kNSgtkF9vknavvks3Ev9i2tn0VNM7TOsz/uxRtVE5xY4pNV8FCAQgAAEIFJVAc/ttft990sEHS/PmSQcdJN1+e1GzJHEIJJ1AnA3AttY4TU3NV0At8ev2te4U7sJ7DP3XQkrNdT0CAQhAAAJFJ9DUPu7vvNMmBNmMoCobEDrySOnaa4ueLRlAIKkEmiWgYj40HBYf1k6/F35e3/mA+h6E7tskFLkiEIAABCBQagI+/Hv99ZLPDbzySunkkyVfIHK2e/JCIACBxhCIcw/gZKuoz91L7+1b1u6l9wo2hglhIQABCEAgqgSa2G/8yy+3yTo1s3XOOUc666ygVzCqZaZcEIgggTgbgLONp6/w3TqNq1+/mXav0JfHWIKjTIcXOmHSgwAEIACBBgi4EXjuubZ301VBwMtsds6JJwbzAxuIymMIQCAgEPUhYF+Zu0qosVa08/VMfzb91vQa03tN3zN9y/QIU3cBc6tpMeUmS9zVl/76ghAEAhCAAARKTeCUU4Lh4P79g6FhHw6+1T7+fb4gAgEIZCQQdQNwQyv9kFAN3OBzGWjaz/Rh06VNzzNdztR9/W1vOtYUgQAEIACBpBM4+ujACDzkkGCRiBuB7ibGVw4jEIBAvQSsHx3Jg0B1DyB+APMgSFQIQAAChSDw6KPSvvtKc+YEDqMffNC8trYoRMqkkUAC+AE0l5oJbNdSVIk5gKWgTB4QgAAEsiWwxx7SE08ERp8fd9klWCGcbXzCQaDCCGAA5tbgPv+vq2n33KITCwIQgAAECk6gTx/pf/8LhoRfeEHaYQfpt98Kng0JQiAJBDAAk9CK1AECEIAABAICW20lvfiitLjt1Dl0qNS7t/Trr9CBAATSCGAApgHhEgIQgAAEYk5gs82kV16RllxSevttaYstpB9/jHmlKD4ECksAAzA3nswBzI0bsSAAAQiUhsBf/xr0AC67rPTBB1KvXtL335cmb3KBQAwIYADm1kjMAcyNG7EgAAEIlI7AOutIr74qrbCCue4fJfXoYU7C8BJWugYgpygTwACMcutQNghAAAIQyI9Aly7Sa69JK64offVVYAR++WV+aRIbAgkggAGYgEakChCAAAQgkIGAG3/eE7jaatK4cYER+OmnGSLwCALJJ4ABmPw2poYQgAAEINChQ2AErr22NHGi1LOn9P77cIFAxRLAAMyt6VkEkhs3YkEAAhAoH4F27YKFIRvaLqM//RSsDn7rrfKVh5whUEYCGIC5wWcRSG7ciAUBCECgvASWWkp6+WXJXcVMmSJtvXVgFJa3VOQOgZITwAAsOXIyhAAEIACBshJo00bynULcafT06dJ22wXXZS0UmUOgtAQwAEvLm9wgAAEIQCAKBFq1kp55RvLt42bOlHbaKdhLOAplowwQKAEBDMASQCYLCEAAAhCIIIFFFpEef1zaYw/pjz+C4wMPRLCgFAkChSeAAVh4pqQIAQhAAAJxIdC8ueRG30EHSXPnSvvvL915Z1xKTzkhkDMBDMDc0LEKODduxIIABCAQPQLNmkl33y0dfbRUVSUdfrh0/fXRKyclgkABCWAA5gaTVcC5cSMWBCAAgWgSWMi+Dm+yj/ZTTgnKd8IJ0mWXRbOslAoCBSCAAVgAiCQBAQhAAAIJINCkifSvf0nnnx9U5qyzpHPOCXoFE1A9qgCBMAEMwDANziEAAQhAoLIJuBF4wQXSFVcEHC65RDr5ZIzAyn4rEll7DMBENiuVggAEIACBvAicfrp0441BEtddJx11lDRvXl5JEhkCUSKAARil1qAsEIAABCAQHQLH2Ho/Xxzi8wNvvz1YKTxnTnTKR0kgkAcBDMA84BEVAhCAAAQSTuDgg6X775eaNpXuu0/ae29p9uyEV5rqVQIBDMDcWhk3MLlxIxYEIACB+BFwo++xx6SFFw6OfftKM2bErx6UGAIhAhiAIRiNOMUNTCNgERQCEIBA7AnsvHOwddyii0rPPRdsITdtWuyrRQUqlwAGYOW2PTWHAAQgAIHGEOjdW3rhBWmxxaTBg6VttpGmTGlMCoSFQGQIYABGpikoCAQgAAEIRJ7A5ptLr7wiLbGE9Oab0pZbSpMnR77YFBAC6QQwANOJcA0BCEAAAhDIRKB7d2noUGmZZaSRI6VevaSJEzPF4BkEIkcAAzByTUKBIAABCEAg8gTWXVcaNkxafnnp008l7xkcNy7yxaaAEEgRwABMkeAIAQhAAAIQaAyBNdaQXn1V6tRJ+r//k3r0kL76qjEpEBYCZSOAAVg29GQMAQhAAAKxJ7DyytJrr0mrriqNHRv0BH72WeyrRQWSTwADMPltTA0hAAEIQKCYBP7yl6AncK21pO++k3r2lD78sJg5kjYE8iaAAZg3QhKAAAQgAIGKJ9C+fbAwZP31pR9/DBaGvPNOxWMBQHQJNIlu0SJdMt8JxNUN6C5TzA9U69atI11gCgcBCEAAAiUg4H4Bt98+cBHj/gJ9L2EfJq5P2raVOnas7yn3i0Rg6tSpatOmjafuf6YWKZtIJ4sBmF/zuNVn9h8GYH4YiQ0BCEAgQQR8hxDfOcSdRTckiywijR6NEdgQpwI/xwAMerAKjJXkIAABCEAAAhVMwHv+/vc/adNNG4YwcyaOpBumRIgiEGAOYBGgkiQEIAABCFQ4Ad8z+OqrKxwC1Y8yAQzAKLcOZYMABCAAgfgSaN48vmWn5IkngAGY+CamghCAAAQgAAEIQKA2AQzA2jy4ggAEIAABCEAAAokngAGY+CamghCAAAQgAAEIQKA2AQzA2jy4ggAEIAABCEAAAokngAGY+CamghCAAAQgUBYC7uTZ/fxlEn/u4RAIlJhAsxLnR3YQgAAEIACByiDgO3y4k+fJk+uvLzuB1M+GJ0UlgAFYVLwkDgEIQAACFU3AjUC2eqvoVyCqlWcIOKotQ7kgAAEIQAACEIBAkQhgAOYG9hiLNsp0eG7RiQUBCEAAAhCAAATKRwADMDf2N1m0rqbdc4tOLAhAAAIQgAAEIFA+AhiA5WNPzhCAAAQgAAEIQKAsBDAAy4KdTCEAAQhAAAIQgED5CGAAlo89OUMAAhCAAAQgAIGyEMAALAt2MoUABCAAAQhAAALlI4ABWD725AwBCEAAAhCAAATKQgADsCzYyRQCEIAABCAAAQiUjwA7gRSA/dSpUwuQCklAAAIQgAAEIFAKAnxvS01KATrBeXS2un2T4PpRNQhAAAIQgECSCaxolRuT5ArWVzd6AOsjk939n2uCdbDjb9lFIVSRCCxu6Y43pS2KBLgRydIWjYBVgqC0RwkgZ5kFbZElqBIES7VF6nu8BFlGKwsMwMK0hxt/jAMXhmW+qdAW+RIsXHzaonAsC5ES7VEIioVJg7YoDEdSyYMAi0DygEdUCEAAAhCAAAQgEEcCGIBxbDXKDAEIQAACEIAABPIg0DSPuEQNCMy1w1BTPyLlJUBblJd/OHfaIkyj/Oe0R/nbIFUC2iJFovxH2qL8bUAJIAABCEAAAhCAAAQgAIH/b+9OQuQowzAAx4tRFLwoLmhcUERF3BI0gkZED97USzyJGAgoXvQU0UMuMZegEU3Eg+BF8CIoIoIbI4oiKqi4BC8ZCMYNQcSDitv7QQ8UxWRwhPx/D/V88DJV1d35/n4q01NdVV1NgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIEDg6Avfmn62vgfst+Ti5LlHtBa5Py5eTw8k/ya2J6iPwYNp+mNRFbn9IXkwuTFR7gXvS8rOkLlBfeT+5JVH9Ber3pF6r9vYfyiRHsDPPuvyH+W6KEq4D+P/W+tY8rH55dyVXJO8kryYbEtVW4IS0+zS5r21b3ZYR2JJl+5JrkpuT+qah15JaR6qtQH0t4o5k4yxv5edLySWJ6iewKa23J7VxrvoJfJHWpw9yab+h6LzWBD7IgJ8aDfqrzO8eLTPbVqDe0dkD2NZ8pW6n5MZaJ7WXVvUXqO883dZ/GJMdwYl55l8nNyULiT2AQehQO9Pzkw59566lPYCrXyXH5iFXJbVnY1g1f+1wgWkCExc4afb8J/tl63Oy/uuC/3cktSe2DgWrPgK1d/yV5I0+7XUdCFyQ6Tpt6GDyfHJeMrmqQzRqdQIn5+71gvr96GE1f9pomVkCUxU4Jk/80eTd5POpInR+3nVYqzb4jkt+TW5LvkxUe4HaAL8y2dS+tY4jgTqCd2dSe2NPTR5O3kvq9IifEkXgiAJn5JY6rLV5dI+HMn9gtMxsWwGHgNt6r9St9nYsJmeudCe3HVWBOlpxflLnAdbpKT8mFyeqrcBZaVc7CC4btF3ItEPAA5COk7VnvD4E8kDHMWi9RgTqRfXPpN5ND+vxzLw9XGC6uYANwObkyzZ8IksPJecue6uFvQTq0OPTvZpPuG+dl1yvTfV3Yyk1//dsvo4oqb4Cr6f9+Lz+viNq0N05gKtH/iMPqcu+1Kcch1XztRtZEZiqQB32fTK5PbkxOZio+RGo9bN+foYzmZG8mWdah+MvH+SjTD83m/8rP1U/gfqduCj5tt8QdF5LAlsz2NoQvDup/ziPJXWOzdmJaitQn6xbemGtd9X3z+Y3tB2GbhHYn/ycbEnqfNilHJ9p1VbgkbSra5Oek9TGx66kNjTGb1yzSHUQWEjPvR36arlu3Z4g1GtUHaG4OqnryP6S+PsdBPXfBOpC0IvJ70ntEXSpiyB0qBvSszb8xnk2y1RbgfE6WJq/q+0wdIvAM8liUq9PdVHuOvxr4y8Ic1ILGYcNwD4roz71ezipnTjfJC8kzo0NgiJAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgACB+RT4F/kiFLal521eAAAAAElFTkSuQmCC\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a17592e48>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.xlim([0,5])\n",
    "\n",
    "plt.title('Error Convergence of Mean and Variance')\n",
    "plt.semilogy([1,2,3,4],error_mean_531,'-rs',label='mean')\n",
    "plt.semilogy([1,2,3,4],error_var_531,'-bs',label='variance')     \n",
    "\n",
    "plt.legend()"
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}