Example 5.3.5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.5 Binomial distribution and Krawtchouk-chaos\n",
    "\n",
    "$$ f(k; p, N) = \\binom{N}{k} p^k (1-p)^{N-k}$$\n",
    "\n",
    "When $p=0.5, N=5$, then $k\\sim B(5, 0.5)$; when $p=0.2, N=5$, then $k\\sim B(5, 0.2)$; \n",
    "\n",
    "\n",
    "$$ \\zeta \\sim B(5, 0.5) \\text{ or } B(5, 0.2)$$\n",
    "\n",
    "Krawtchouk Polynomial (Different from polynomials in Wiki)\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "K_0(x; p, N) &= 1\\\\\n",
    "K_1(x; p, N) &= 1-\\frac{x}{Np}\\\\\n",
    "K_2(x; p, N) &= 1-\\frac{2x}{Np}+\\frac{x^2-x}{p^2(N^2-N)}\\\\\n",
    "K_3(x; p, N) &= 1-\\frac{3x}{Np}+\\frac{3(x^2-x)}{p^2(N^2-N)}+\\frac{(-1)(-x^3+3x^2-2x)}{p^3(-N^3+3N^2-2N)}\\\\\n",
    "K_4(x; p, N) &= 1-\\frac{4x}{Np}+\\frac{6(x^2-x)}{p^2(N^2-N)}+\\frac{-4(-x^3+3x^2-2x)}{p^3(-N^3+3N^2-2N)}+\\frac{x^4-6x^3+11x^2-6x}{p^4(N^4-6N^3+11N^2-6N)}\\\\\n",
    "\\cdots\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "$$ K_n(x; p, N) =\\ _2F_1(-n,-x;-N;\\frac{1}{p})$$\n",
    "\n",
    "[Binom in Python](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-11.408000000000001"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-0.768-1.44-3.2-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import binom\n",
    "from math import factorial\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Krawt(params):\n",
    "    '''\n",
    "    The first 4 (degree from 0 to 4) Krawtchouk polynomial\n",
    "    Follow definition on P641\n",
    "    '''\n",
    "    n = params[0]  #degree\n",
    "    p = params[1]  #parameter value\n",
    "    N = params[2]  #parameter value\n",
    "    if n==0:\n",
    "        return lambda u: 1\n",
    "    elif n==1:\n",
    "        return lambda u: 1-u/(N*p)\n",
    "    elif n==2:\n",
    "        return lambda u: 1-2*u/(N*p)+(u**2-u)/(p**2*(N**2-N))\n",
    "    elif n==3:\n",
    "        return lambda u: 1-3*u/(N*p)+3*(u**2-u)/(p**2*(N**2-N))+(-1)*(-u**3+3*u**2-2*u)/(p**3*(-N**3+3*N**2-2*N))\n",
    "    else: #this actually means n=4\n",
    "        return lambda u: 1-4*u/(N*p)+6*(u**2-u)/(p**2*(N**2-N))+(-4)*(-u**3+3*u**2-2*u)/(p**3*(-N**3+3*N**2-2*N))+(u**4-6*u**3+11*u**2-6*u)/(p**4*(N**4-6*N**3+11*N**2-6*N))\n",
    "\n",
    "def factorial_rev(params):\n",
    "    '''\n",
    "    define Pochhammer symbol (a)_n\n",
    "    '''\n",
    "    a=params[0]\n",
    "    n=params[1]\n",
    "    y=1\n",
    "    if n == 0:\n",
    "        return 1\n",
    "    else:\n",
    "        for i in range(n):\n",
    "            y*=a+i\n",
    "        return y\n",
    "    \n",
    "############# Charlier Chaos ###############\n",
    "def inner2_kr(params):\n",
    "    '''\n",
    "    n is the degree of Krawtchouk polynomial\n",
    "    p is the parameter of binomial\n",
    "    N is the parameter of binomial\n",
    "    '''\n",
    "    n = params[0]\n",
    "    p = params[1]\n",
    "    N = params[2]\n",
    "    return (-1)**n*factorial(n)*((1-p)/p)**n/factorial_rev((-1*N,n))\n",
    "\n",
    "\n",
    "def product3_kr(i,j,l,params):\n",
    "    #compute \\Phi_i*\\Phi_j*\\Phi_l\n",
    "    p = params[0]\n",
    "    N = params[1]\n",
    "    return lambda x: Krawt((i,p,N))(x)*Krawt((j,p,N))(x)*Krawt((l,p,N))(x)\n",
    "\n",
    "def inner3_kr(i,j,l,params):\n",
    "    #compute <\\Phi_i\\Phi_j\\Phi_l>\n",
    "    inner = 0 \n",
    "    p = params[0]\n",
    "    N = params[1]\n",
    "    for k in range(N+1):\n",
    "        inner += factorial(N)*(p**k)*((1-p)**(N-k))*product3_kr(i,j,l,params)(k)/(factorial(k)*factorial(N-k))\n",
    "    \n",
    "    return inner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_system_kr(y, t, P, params):   \n",
    "    #P indicates the highest degree\n",
    "    p = params[0]\n",
    "    N = params[1]\n",
    "    \n",
    "    dydt = np.zeros(P+1) \n",
    "    for l in range(len(dydt)):\n",
    "        dydt[l] = -(sum(sum(inner3_kr(i,j,l,params)*ki_kr[i]*y[j] for j in range(P+1)) for i in range(P+1)))/inner2_kr((l,p,N))\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = 4\n",
    "params = [0.5, 5]\n",
    "\n",
    "ki_kr = [2.5,-2.5]+[0]*(P-1)\n",
    "sol_kr = odeint(ode_system_kr, [1.0]+[0.0]*P, np.linspace(0,1,101), args=(P, params)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def y_determ_kr(x):\n",
    "    return np.e**(-2.5*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = red> \n",
    "-  **There is no $y_4$ plot in the paper.**\n",
    "-  **The following plot is different from the paper.**\n",
    "-  **First plot different, but I got the second error plot correct. Interesting!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(1)\n",
    "plt.ylim([-0.2,1])\n",
    "plt.xlim([0,1])\n",
    "\n",
    "x= np.linspace(0,1,101)\n",
    "\n",
    "for i in range(P+1):\n",
    "    plt.plot(x,sol_kr[:,i],label=i)\n",
    "\n",
    "plt.plot(x, y_determ_kr(x), color='r', linestyle='-.',label='Deterministic')\n",
    "plt.legend(prop={'size': 8})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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",
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       "\n",
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       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a1d63e6d8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.ylim([-0.2,1])\n",
    "plt.xlim([0,1])\n",
    "\n",
    "x= np.linspace(0,1,101)\n",
    "\n",
    "for i in range(P+1):\n",
    "    plt.plot(x,sol_kr[:,i],label=i)\n",
    "\n",
    "plt.plot(x, y_determ_kr(x), color='r', linestyle='-.',label='Deterministic')\n",
    "plt.legend(prop={'size': 8})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error plot\n",
    "$$\n",
    "\\bar{y}_{exact}(t) = \\hat{y_0} (1-p+pe^{-t})^N \\ \\ \\ \\ \\ \\ \\ \\ \\bar{y}(t) = y_0\n",
    "$$\n",
    "So \n",
    "$$\n",
    "\\epsilon_{mean}(t) = \\left| \\frac{\\bar{y}(t) - \\bar{y}_{exact}(t)}{\\bar{y}_{exact}(t)}\\right|\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_{exact}(t) = \\hat{y_0}^2(1-p+pe^{-2t})^N -\\hat{y_0}^2(1-p+pe^{-t})^{2N}  \\ \\ \\ \\ \\ \\ \\ \\ \\sigma(t) = a_1y_1^2 +a_2y_2^2+a_3y_3^2+a_4y_4^2\n",
    "$$\n",
    "The coefficients $(a_1, a_2, a_3, a_4)$ in $\\sigma(t)$ can be obtained by code below.\n",
    "\n",
    "So\n",
    "$$\n",
    "\\epsilon_{variance}(t) = \\left| \\frac{\\sigma(t) - \\sigma_{exact}(t)}{\\sigma_{exact}(t)} \\right|= \\ldots\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = red>This is $p=0.5, N=5$\n",
    "$\\downarrow$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcoeff_535_1 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_535_1[0,:]=2.5*np.ones(4)\n",
    "allcoeff_535_1[1,:]=-2.5*np.ones(4)\n",
    "y_535_1 = np.zeros((5,4))   #row 0 stores y0 for each P from 1-4; row 1 stores y1 for P from 1-4;...\n",
    "\n",
    "params = [0.5, 5]\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_kr = allcoeff_535_1[:,i]\n",
    "    y_mid=odeint(ode_system_kr, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, params))[1,:]\n",
    "    y_535_1[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "-2.7755575615628914e-17\n",
      "-8.326672684688674e-17\n",
      "2.7755575615628914e-17\n",
      "-6.938893903907228e-17\n",
      "-6.938893903907228e-17\n",
      "-6.938893903907228e-17\n",
      "-6.938893903907228e-17\n",
      "-6.938893903907228e-17\n"
     ]
    }
   ],
   "source": [
    "for i in range(9):\n",
    "    #to compute $\\bar{y}(t)$\n",
    "    print(binom.expect(Krawt((i,0.5,5)), args=(5, 0.5), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.19999999999999996\n",
      "0.09999999999999998\n",
      "0.09999999999999999\n",
      "0.20000000000000007\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (Krawt((n,0.5,5))(u))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    #to compute $\\sigma^2(t)$\n",
    "    print(binom.expect(g(i), args=(5, 0.5), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 0.5\n",
    "N = 5\n",
    "\n",
    "mean_535_1 = y_535_1[0,:]\n",
    "mean_exact_535_1 = (1-p+p*np.e**(-1))**N\n",
    "error_mean_535_1=np.abs((mean_535_1 - mean_exact_535_1)/mean_exact_535_1)\n",
    "\n",
    "\n",
    "sigma2_535_1=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_535_1[i]=0.2*y_535_1[1,i]**2+0.1*y_535_1[2,i]**2+0.1*y_535_1[3,i]**2+0.2*y_535_1[4,i]**2\n",
    "    \n",
    "sigma2_exact_535_1 = (1-p+p*np.e**(-2))**N - (1-p+p*np.e**(-1))**(2*N)\n",
    "error_var_535_1=np.abs((sigma2_535_1-sigma2_exact_535_1)/sigma2_exact_535_1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = red>This is $p=0.2, N=5$\n",
    "$\\downarrow$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcoeff_535_2 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_535_2[0,:]=np.ones(4)\n",
    "allcoeff_535_2[1,:]=-1*np.ones(4)\n",
    "y_535_2 = np.zeros((5,4))   #row 0 stores y0 for each P from 1-4; row 1 stores y1 for P from 1-4;...\n",
    "\n",
    "params = [0.2, 5]\n",
    "\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_kr = allcoeff_535_2[:,i]\n",
    "    y_mid=odeint(ode_system_kr, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, params))[1,:]\n",
    "    y_535_2[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.49751271, 0.50834881, 0.50874182, 0.50874851],\n",
       "       [0.31479488, 0.36538522, 0.3680706 , 0.36813058],\n",
       "       [0.        , 0.0981402 , 0.1063029 , 0.10654951],\n",
       "       [0.        , 0.        , 0.01478985, 0.0154121 ],\n",
       "       [0.        , 0.        , 0.        , 0.00109727]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_535_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999999999999997\n",
      "-1.1145598333150986e-16\n",
      "-8.239936510889834e-17\n",
      "-3.5041414214731503e-16\n",
      "-7.494005416219807e-16\n",
      "-7.494005416219807e-16\n",
      "-7.494005416219807e-16\n",
      "-7.494005416219807e-16\n",
      "-7.494005416219807e-16\n"
     ]
    }
   ],
   "source": [
    "for i in range(9):\n",
    "    #to compute $\\bar{y}(t)$\n",
    "    print(binom.expect(Krawt((i,0.2,5)), args=(5, 0.2), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "1.7999999999999998\n",
      "3.8800000000000003\n",
      "9.672\n",
      "26.958400000000008\n",
      "82.05600000000003\n",
      "268.4560000000001\n",
      "933.1920000000003\n"
     ]
    }
   ],
   "source": [
    "def gdd(params):\n",
    "    n = params\n",
    "    return lambda u:u**n\n",
    "\n",
    "for i in range(1,9):\n",
    "    #to compute $\\sigma^2(t)$\n",
    "    print(binom.expect(gdd(i), args=(5, 0.2), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.380672"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "11.408*0.192*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7999999999999999\n",
      "1.5999999999999994\n",
      "6.399999999999998\n",
      "51.199999999999996\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (Krawt((n,0.2,5))(u))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    #to compute $\\sigma^2(t)$\n",
    "    print(binom.expect(g(i), args=(5, 0.2), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.38699344845837064\n"
     ]
    }
   ],
   "source": [
    "def g(u):\n",
    "    return np.e**(-2*u)\n",
    "\n",
    "print(binom.expect(g, args=(5, 0.2), loc=0, lb=None, ub=None, conditional=False))\n",
    "\n",
    "def f(u):\n",
    "    return np.e**(-u)\n",
    "\n",
    "print(binom.expect(g, args=(5, 0.2), loc=0, lb=None, ub=None, conditional=False))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 0.2\n",
    "N = 5\n",
    "\n",
    "mean_535_2 = y_535_2[0,:]\n",
    "mean_exact_535_2 = (1-p+p*np.e**(-1))**N\n",
    "error_mean_535_2=np.abs((mean_535_2 - mean_exact_535_2)/mean_exact_535_2)\n",
    "\n",
    "\n",
    "sigma2_535_2=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_535_2[i]=0.8*y_535_2[1,i]**2+1.6*y_535_2[2,i]**2+6.4*y_535_2[3,i]**2+51.2*y_535_2[4,i]**2\n",
    "    \n",
    "sigma2_exact_535_2 = (1-p+p*np.e**(-2))**N - (1-p+p*np.e**(-1))**(2*N)\n",
    "error_var_535_2=np.abs((sigma2_535_2-sigma2_exact_535_2)/sigma2_exact_535_2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a12f1bf98>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure(2)\n",
    "plt.xlim([0,5])\n",
    "plt.semilogy([1,2,3,4],error_mean_535_2,'-bs',label='mean $p=0.2, N=5$')\n",
    "plt.semilogy([1,2,3,4],error_var_535_2,'-rs',label='variance $p=0.2, N=5$')     \n",
    "plt.semilogy([1,2,3,4],error_mean_535_1,'-.b^',label='mean$ p=0.5, N=5$')\n",
    "plt.semilogy([1,2,3,4],error_var_535_1,'-.r^',label='variance $p=0.5, N=5$')     \n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}