week_6_calculus.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part I. One-sided finite differences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function, `deriv`, which computes a derivative of its argument at a given point, $x$, using a one-sided finite difference rule with a given step side $h$, with the approximation order of $O(h^2)$. \n",
    "**Below two-point methos is refered as 'deriv2', sorry.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def deriv2(f, x, h):\n",
    "    \"\"\" Compute a derivative of `f` at point `x` with step size `h`.\n",
    "    \n",
    "    Compute the derivative using the one-sided rule of the approximation order of $O(h)$.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    f : callable\n",
    "        The function to differentiate\n",
    "    x : float\n",
    "        The point to compute the derivative at.\n",
    "    h : float\n",
    "        The step size for the finite different rule.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    fder : derivative of f(x) at point x using the step size h.\n",
    "    \"\"\"\n",
    "    x1 = x + h\n",
    "    dx = x1 - x\n",
    "    df = f(x1) - f(x)\n",
    "    return df/dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deriv3(f, x, h):\n",
    "    x1 = x + h \n",
    "    x2 = x1 + h\n",
    "    dx_1 = x1 - x #here we agree steps\n",
    "    dx_2 = x2 - x\n",
    "    up = -3*f(x)+4*f(x+h)-f(x+h+h)\n",
    "    #print(h, 4*dx_1 - dx_2, dx_1, dx_2)\n",
    "    return up/(4*dx_1 - dx_2)\n",
    "deriv3 = np.vectorize(deriv3)\n",
    "deriv2 = np.vectorize(deriv2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test I.1\n",
    "\n",
    "Test your function on a simple test case: differentiate $f(x) = x^3$ at $x=0$. Comment on whether your results are consistent with the expected value of $f'(x) = 0$ and on an expected scaling with $h\\to 0$.\n",
    "\n",
    " (10% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01 -- -0.0002\n",
      "0.001 --  -2e-06\n",
      "0.0001 --  -2e-08\n",
      "1e-05 --  -2e-10\n",
      "1e-07 --  -2e-14\n",
      "1e-14 --  -2e-28\n",
      "1e-20 --  -2e-40\n"
     ]
    }
   ],
   "source": [
    "x = 0\n",
    "for h in [1e-2, 1e-3, 1e-4, 1e-5, 1e-7,1e-14, 1e-20]:\n",
    "    err = deriv3(lambda x: x**3, x, h)\n",
    "    print(\"%2.g -- %7.4g\" % (h, err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hmm, all is good?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test I.2\n",
    "\n",
    "Now use a slightly more complicated function, $f(x) = x^2 \\log{x}$, evaluate the derivative at $x=1$ using your one-sided rule and a two-point one-sided rule. Roughly estimate the value of $h$ where the error stops decreasing, for these two schemes. \n",
    "(15% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import log\n",
    "import numpy as np\n",
    "def f(x):\n",
    "    return x**2 * log(x)\n",
    "    \n",
    "def fder(x):\n",
    "    return x * (2.*log(x) + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary error for one point:\n",
    "$$\n",
    "    e \\sim f'' h + \\frac{e_f}{h}\\cdot(\\sim h)\n",
    "$$\n",
    "Corollary $h_{opt}$ is supposed to be approched when 'mashine eps' is got. Moreover $err$ is decrising with $h$.\n",
    "What about two-point, we are expect same point, but we have to agree 'real steps'.\n",
    "Thus \n",
    "$$\n",
    "h_{opt}^{(1)}\\sim 10^{-16}\\;\n",
    "h_{opt}^{(2)}\\sim 10^{-8}\n",
    "$$\n",
    "**Notice!** That is due to $f(x+h) \\sim h $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = np.logspace(-15, -2, 17)\n",
    "err3 = abs(fder(1) - deriv3(f, 1 , h))\n",
    "err2 = abs(fder(1) - deriv2(f,1 , h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f34c4a96210>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "plt.plot(h, err3, 'o', label='Three point')\n",
    "plt.plot(h, err2, 'o',label='Two point')\n",
    "plt.grid()\n",
    "plt.title(r'Error of evaluation of $f =x^2\\ln x$ at $x=1$')\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test I.3 \n",
    "\n",
    "Now try differentiating $x^2 \\log(x)$ at $x=0$. Use the three-point one-sided rule. Note that to evaluate the function at zero, you need to special-case this value. Check the scaling of the error with $h$, explain your results. \n",
    "(25% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.010000 -- -0.01386\n",
      "0.001000 -- -0.001386\n",
      "0.000100 -- -0.0001386\n",
      "0.000010 -- -1.386e-05\n"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    if x < 1e-50:\n",
    "        # the limit of $x^2 log(x)$ at $x-> 0$ is zero, even though log(x) is undefined at x=0\n",
    "        return 0\n",
    "    else:\n",
    "        return x**2 * log(x)\n",
    "    \n",
    "def fder(x):\n",
    "    if x == 0:\n",
    "        return 0.0\n",
    "    else:\n",
    "        return x*(2*log(x) + 1)\n",
    "\n",
    "x = 0\n",
    "for h in [1e-2, 1e-3, 1e-4, 1e-5]:\n",
    "    err = deriv3(f, x, h) - fder(x)\n",
    "    print(\"%5f -- %7.4g\" % (h, err))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = np.logspace(-48, -2, 20)\n",
    "err3 = abs(fder(x) - deriv3(f, x , h))\n",
    "err2 =abs(fder(x) - deriv2(f, x , h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.230792677615\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "plt.plot(h, err3, '.', label='Three point')\n",
    "plt.plot(h, err2, '.',label='Two point')\n",
    "plt.grid()\n",
    "plt.title(r'Error of evaluating the derivation of $f =x^2\\ln x$ at $x=0$')\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see strange result, but it is easy to explain, first get derivations:\n",
    "$$\n",
    "f^{(0)}(0) = x^2 \\ln x\\;\n",
    "f^{(1)}(0) = 2x \\ln x + x;\n",
    "f^{(2)}(0) = 2 \\ln x + 3= \\infty;\n",
    "$$\n",
    "Thus there is not Teylor series.\n",
    "End $\\boxed{err\\sim h\\ln h}$ in two-poind case.\n",
    "What about 3-point, $$err\\sim \\frac{h^2\\ln h  - h^2 \\ln(2h)}{h}\\boxed{\\sim h}$$\n",
    "And at the plot we can see this different"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.230792677615\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$\\\\frac{err_{2}}{err_{3}}\\\\sim \\\\ln h$')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(h, err2/err3,'.')\n",
    "plt.grid()\n",
    "plt.xscale('log')\n",
    "plt.title(r'$\\frac{err_{2}}{err_{3}}\\sim \\ln h$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check dual numbers :)\n",
    "I have released dual number here https://github.com/ev-br/CP2020/pull/11\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "-9.210340371976183e-198\n"
     ]
    }
   ],
   "source": [
    "import Dual_numbers as d\n",
    "#Test I.2\n",
    "x = d.Dual(1, 1)\n",
    "print((x**2*d.ln(x)).g)\n",
    "#Test I.3\n",
    "x = d.Dual(1e-200, 1)\n",
    "print((x**2*d.ln(x)).g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part II. Midpoint rule "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function which computes a definite integral using the midpoint rule up to a given error, $\\epsilon$. Estimate the error by comparing the estimates of the integral at $N$ and $2N$ elementary intervals. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def midpoint_rule(f, a, b, eps):\n",
    "    \"\"\" Calculate the integral of f from a to b using the midpoint rule.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    func : callable\n",
    "        The vectorizated function to integrate.\n",
    "    a : float\n",
    "        The lower limit of integration.\n",
    "    b : float\n",
    "        The upper limit of integration.\n",
    "    eps : float\n",
    "        The target accuracy of the estimate.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    integral : float\n",
    "        The estimate of $\\int_a^b f(x) dx$.\n",
    "    n : int\n",
    "        The number of intervals on segment.\n",
    "    \"\"\"\n",
    "    n = 4\n",
    "    h = (b-a) / n\n",
    "    x = np.linspace(a+h/2, b-h/2, n)\n",
    "    i = h * f(x).sum()\n",
    "    delta = np.inf\n",
    "    \n",
    "    while (delta > eps):\n",
    "        n *= 2\n",
    "        h /= 2\n",
    "        x  = np.linspace(a+h/2, b-h/2, n)\n",
    "        i2 = h * f(x).sum()\n",
    "        delta = abs(i-i2)\n",
    "        i = i2   \n",
    "    return i, n # I've changed signature of function for usability it to task below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
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     "output_type": "display_data"
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\" width=\"639.230792677615\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "NameError",
     "evalue": "name 'n' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-5eb0d3aebc5b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# What was this code supposed to do?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0merr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'log'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'n' is not defined"
     ]
    }
   ],
   "source": [
    "# What was this code supposed to do?\n",
    "plt.figure()\n",
    "plt.plot(n, err)\n",
    "pl.grid()\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test II.1\n",
    "\n",
    "Test your midpoint rule on a simple integral, which you can calculate by paper and pencil.\n",
    "\n",
    "Compare the rate of convergence to the expected $O(N^{-2})$ scaling by studying the number of intervals required for a given accuracy $\\epsilon$.\n",
    "\n",
    "Compare the numerical results to the value you calculated by hand. Does the deviation agree with your estimate of the numerical error?\n",
    "(20% of the total grade)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let consider function\n",
    "$$\n",
    "f(x) = \\frac{1}{\\sqrt{1-x^2}}\\;\\implies \\int f d x + C\n",
    "= \\arcsin x\n",
    "$$\n",
    "Try to integrate it on segment \n",
    "$$\n",
    "\\int_{1/2}^{\\sqrt{3}/2} f(x) dx = \\frac{\\pi}{6}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 1/np.sqrt(1-x*x)\n",
    "f = np.vectorize(f, doc='Vectorized `f`')\n",
    "\n",
    "midpoint_rule = np.vectorize(midpoint_rule, excluded=['f','a','b'], doc='Vectorized `midpoint_rule` alone `eps`')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1/2\n",
    "b = np.sqrt(3)/2\n",
    "eps = np.logspace(-14, 0, 15)\n",
    "i_true = np.pi/6\n",
    "i, n = midpoint_rule(f, a, b, eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.230792677615\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Dependency on number N')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "err = np.abs(i_true - i)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(n, err, 'o--')\n",
    "plt.grid()\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of intervals')\n",
    "plt.ylabel('Error of estimate')\n",
    "plt.title('Dependency on number N')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.230792677615\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Agreement between deviation and $\\\\epsilon$')"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "err = np.abs(i_true - i)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(eps, np.abs(err-eps), 'o--')\n",
    "plt.grid()\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'Given accuracy $\\epsilon$')\n",
    "plt.ylabel(r'$|err - \\epsilon|$')\n",
    "plt.title(r'Agreement between deviation and $\\epsilon$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test II.2\n",
    "\n",
    "Now use your midpoint rule to compute the value of\n",
    "\n",
    "$$\n",
    "\\int_0^1\\! \\frac{\\sin{\\sqrt{x}}}{x}\\, dx\n",
    "$$\n",
    "\n",
    "up to a predefined accuracy of $\\epsilon=10^{-4}$.\n",
    "\n",
    "Note that the integral contains an integrable singularity at the lower limit. Do calculations two ways: first, do a straightforward computation; next, subtract the singularity. Compare the number of iterations required to achieve the accuracy of $\\epsilon$.\n",
    "\n",
    "(30% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(np.sqrt(x)) / x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "i_stupid = midpoint_rule(f, 0, 1, eps=1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sub_f(x):\n",
    "    return (np.sin(np.sqrt(x)) - np.sqrt(x)) / x\n",
    "#plt.plot(x,sub_f(x)+1/np.sqrt(x)-f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "i_sub = midpoint_rule(sub_f, 0, 1, eps=1e-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we have to take intergal of subtrahend:\n",
    "$$\n",
    "\\int_0^1 \\frac{1}{\\sqrt x} \\,dx = 2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8919572891351422\n",
      "1.892113005639548\n"
     ]
    }
   ],
   "source": [
    "#check congruency\n",
    "print(i_stupid[0])\n",
    "print(i_sub[0]+2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nuber of iteretion in \n",
      " stupid case 8388608 \n",
      " smart  case 32\n"
     ]
    }
   ],
   "source": [
    "print(f'Number of iteretion in \\n stupid case {i_stupid[1]} \\n smart  case {i_sub[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But if we look though this task, we can notice useful substitution:\n",
    "$$\n",
    "\\int_0^1\\! \\frac{\\sin{\\sqrt{x}}}{x}\\, dx = [x = t^2] = 2 \\int_0^1\\! \\frac{\\sin t}{t} \\, dt \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = midpoint_rule(lambda x: np.sinc(x / np.pi), 0, 1, eps=1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "estimate value = 1.8921906503147161 \n",
      " iteration = 32\n"
     ]
    }
   ],
   "source": [
    "print(f'estimate value = {i[0]*2} \\n iteration = {i[1]}')"
   ]
  }
 ],
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