Example 5.3.3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.3 Beta distribution and Jacobi Chaos\n",
    "\n",
    "$$ f(k;\\alpha,\\beta) = \\frac{(1-k)^{\\alpha} (1+k)^{\\beta}}{2^{\\alpha+\\beta+1} B(\\alpha+1,\\beta+1)} = Beta (k, \\beta+1, \\alpha+1, loc =-1, scale =2)$$\n",
    "\n",
    "When $\\alpha=\\beta=0$, $k\\sim U(-1,1)$;\n",
    "\n",
    "When $\\alpha =1, \\beta =3$, \n",
    "$$ f(k; 1, 3) = \\frac{(1-k)(1+k)^3}{32 B(2,4)} = \\frac{5(1-k)(1+k)^3}{8}$$\n",
    "\n",
    "[Wiki - Beta Distribution](https://en.wikipedia.org/wiki/Beta_distribution)\n",
    "\n",
    "$$ \\zeta \\sim Beta (k, \\beta+1, \\alpha+1, loc =-1, scale =2)$$\n",
    "[Beta in Python](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.beta.html)\n",
    "\n",
    "When $\\alpha = \\beta =0$, Jacobi Chaos is [Legendre-chaos](https://en.wikipedia.org/wiki/Legendre_polynomials)\n",
    "\n",
    "**Legendre Polynomial: ($\\alpha = \\beta = 0$)**\n",
    "$$\n",
    "\\begin{align*}\n",
    "P_0 &= 1\\\\\n",
    "P_1 &= x\\\\\n",
    "P_2 &= \\frac{1}{2}(3x^2 - 1)\\\\\n",
    "P_3 &= \\frac{1}{2}(5x^3 - 3x)\\\\\n",
    "P_4 &= \\frac{1}{8}(35x^4 - 30x^2 + 3)\\\\\n",
    "\\cdots\n",
    "\\end{align*}\n",
    "$$\n",
    "Corresponding Hypergeometric orthogonal polynomial\n",
    "$$ P_n^{(\\alpha,\\beta)}(x) = \\frac{(\\alpha+1)_n}{n!}\\  _2F_1(-n,n+\\alpha+\\beta+1;\\alpha+1;\\frac{1-x}{2})$$\n",
    "\n",
    "No package for Jacobi chaos in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7486874999999997\n",
      "0.7486875000000002\n"
     ]
    }
   ],
   "source": [
    "k=0.1\n",
    "\n",
    "print(beta.pdf(k,4,2,loc=-1,scale=2))\n",
    "\n",
    "print(5*(1-k)*(1+k)**3/8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.polynomial.legendre as Le   #$\\zeta \\sim U(-1,1)$, when $\\alpha=\\beta=0$, Jacobi=Legendre\n",
    "from math import factorial\n",
    "from scipy.stats import beta\n",
    "from scipy.special import gamma  #gamma function\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 Jacobi(params):\n",
    "    '''\n",
    "    The first 4 (degree from 0 to 4) Meixner polynomial\n",
    "    Follow definition on P642\n",
    "    '''\n",
    "    n = params[0]  #degree\n",
    "    a = params[1]  #parameter alpha value\n",
    "    b = params[2]  #parameter beta value\n",
    "    if n==0:\n",
    "        return lambda u: 1\n",
    "    elif n==1:\n",
    "        return lambda u: (a+1) - (a+b+2)*(1-u)/2 \n",
    "    elif n==2:\n",
    "        return lambda u: (a+1)*(a+2)/2 - (a+2)*(a+b+3)*(1-u)/2 + (a+b+3)*(a+b+4)*(1-u)**2/8\n",
    "    elif n==3:\n",
    "        return lambda u: (a+1)*(a+2)*(a+3)/6 - (a+2)*(a+3)*(a+b+4)*(1-u)/4 + (a+3)*(a+b+4)*(a+b+5)*(1-u)**2/8 - (a+b+4)*(a+b+5)*(a+b+6)*(1-u)**3/48 \n",
    "    else: #this actually means n=4\n",
    "        return lambda u: (a+1)*(a+2)*(a+3)*(a+4)/24 - (a+2)*(a+3)*(a+4)*(a+b+5)*(1-u)/12 + (a+3)*(a+4)*(a+b+5)*(a+b+6)*(1-u)**2/16 - (a+4)*(a+b+5)*(a+b+6)*(a+b+7)*(1-u)**3/48 + (a+b+5)*(a+b+6)*(a+b+7)*(a+b+8)*(1-u)**4/384"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(params):\n",
    "    c = params[0]\n",
    "    a = params[1]\n",
    "    b = params[2]\n",
    "    if a==1 and b==1:\n",
    "        return lambda x: x*(a+b+1)\n",
    "    else:\n",
    "        return lambda x: x*c    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Phi(n):\n",
    "    #define H_n\n",
    "    coeffs = [0]*(n+1)\n",
    "    coeffs[n] = 1\n",
    "    return coeffs\n",
    "\n",
    "def inner2_le(params):\n",
    "    n = params[0]\n",
    "    a = params[1]  #store the value of alpha from beta distr\n",
    "    b = params[2]  #store the value of beta from beta distr\n",
    "    return gamma(n+a+1)*gamma(n+b+1)/((2*n+a+b+1)*gamma(n+a+b+1)*factorial(n))\n",
    "\n",
    "def product3_le(i,j,l,params):\n",
    "    #compute \\Phi_i*\\Phi_j*\\Phi_l\n",
    "    a = params[0]\n",
    "    b = params[1]\n",
    "    if a==0 and b==0:\n",
    "        return lambda x: Le.legval(x, Le.legmul(Le.legmul(Phi(i),Phi(j)),Phi(l))) \n",
    "    else: #actually this means a=1, b=3\n",
    "        return lambda x: Jacobi([i]+params)(x)*Jacobi([j]+params)(x)*Jacobi([l]+params)(x)\n",
    "\n",
    "def inner3_le(P,i,j,l,params):\n",
    "    #compute <\\Phi_i\\Phi_j\\Phi_l>\n",
    "    a = params[0]\n",
    "    b = params[1]\n",
    "    if a==0 and b==0:\n",
    "        #Set up Gauss-Legendre quadrature, weighting function is 1\n",
    "        m=(P+1)**2\n",
    "        x, w=Le.leggauss(m)        #x is point, w is the corresponding weight\n",
    "        inner=sum([product3_le(i,j,l,params)(x[idx]) * w[idx] for idx in range(m)])\n",
    "        return inner/2       ##because of the weight\n",
    "    else:\n",
    "        nsample = 1000\n",
    "        rv = beta.rvs(b+1, a+1, loc=-1, scale=2, size=nsample, random_state=None)\n",
    "        inner = np.mean(product3_le(i,j,l,params)(rv))*gamma(a+1)*gamma(b+1)/gamma(a+b+2)   \n",
    "        return inner\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_system_le(y, t, P, params):   \n",
    "    #P indicates the highest degree\n",
    "    a = params[0]\n",
    "    b = params[1]\n",
    "    dydt = np.zeros(P+1) \n",
    "    for l in range(len(dydt)):\n",
    "        dydt[l] = -(sum(sum(inner3_le(P,i,j,l,params)*ki_le[i]*y[j] for j in range(P+1)) for i in range(P+1)))/inner2_le((l,a,b))\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#h = unif_icdf([-1,1])                          #index k follows uniform distr\n",
    "P = 4\n",
    "params = [0, 0]\n",
    "ki_le = [0,1]+[0]*(P-1)\n",
    "sol_le = odeint(ode_system_le, [1.0]+[0.0]*P, np.linspace(0,1,101), args=(P, params)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "/* 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 0x1a16073b38>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.ylim([-1.2,1.2])\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_le[:,i],label=i)\n",
    "\n",
    "plt.axhline(y=1.0, color='r', linestyle='-.',label='Deterministic')\n",
    "plt.legend(prop={'size': 8})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error plot when $\\alpha=\\beta=0$\n",
    "\n",
    "$$\n",
    "\\bar{y}_{exact}(t) = \\frac{\\hat{y_0}}{2t}(e^{t} - e^{-t}) \\ \\ \\ \\ \\ \\ \\ \\ \\bar{y}(t) = y_0\n",
    "$$\n",
    "So \n",
    "$$\n",
    "\\epsilon_{mean}(t) = \\left| \\frac{\\bar{y}(t) - \\bar{y}_{exact}(t)}{\\bar{y}_{exact}(t)}\\right|\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_{exact}(t) = \\frac{1-e^{-2}}{2} \\ \\ \\ \\ \\ \\ \\ \\ \\sigma(t) = a_1y_1^2 +a_2y_2^2+a_3y_3^2+a_4y_4^2\n",
    "$$\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 $\\alpha=\\beta=0$\n",
    "$\\downarrow$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcoeff_533_0 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_533_0[1,:]=np.ones(4)\n",
    "y_533_0 = 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, 0]\n",
    "\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_le = allcoeff_533_0[:,i]\n",
    "    y_mid=odeint(ode_system_le, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, params))[1,:]\n",
    "    y_533_0[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "-3.51635587001176e-18\n",
      "9.020562075079397e-17\n",
      "3.2082226403008723e-16\n",
      "-2.5326962749261384e-16\n",
      "-2.5326962749261384e-16\n",
      "-2.5326962749261384e-16\n",
      "-2.5326962749261384e-16\n",
      "-2.5326962749261384e-16\n"
     ]
    }
   ],
   "source": [
    "for i in range(9):\n",
    "    #to compute $\\bar{y}(t)$\n",
    "    print(beta.expect(Jacobi((i,0,0)), args=(1,1), loc=-1, scale=2, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3333333333333333\n",
      "0.2\n",
      "0.1428571428571429\n",
      "0.11111111111111023\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (Jacobi((n,0,0))(u))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    print(beta.expect(g(i), args=(1, 1), loc=-1, scale=2, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "############# alpha = beta = 0  ################ \n",
    "mean_533_0 = y_533_0[0,:]\n",
    "mean_exact_533_0 = 1/2*(np.e - np.e**(-1))\n",
    "error_mean_533_0 = np.abs((mean_533_0 - mean_exact_533_0)/mean_exact_533_0)\n",
    "\n",
    "\n",
    "sigma2_533_0=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_533_0[i]=1/3*y_533_0[1,i]**2+1/5*y_533_0[2,i]**2+1/7*y_533_0[3,i]**2+1/9*y_533_0[4,i]**2\n",
    "    \n",
    "sigma2_exact_533_0 = 1/2-1/2*np.e**(-2)\n",
    "error_var_533_0 = np.abs((sigma2_533_0-sigma2_exact_533_0)/sigma2_exact_533_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error plot when $\\alpha=1,\\beta=3$\n",
    "\n",
    "$$\n",
    "\\bar{y}_{exact}(t) = \\frac{5\\hat{y_0}}{8}(-12e + 612 e^{-1}) \\ \\ \\ \\ \\ \\ \\ \\ \\bar{y}(t) = y_0\n",
    "$$\n",
    "So \n",
    "$$\n",
    "\\epsilon_{mean}(t) = \\left| \\frac{\\bar{y}(t) - \\bar{y}_{exact}(t)}{\\bar{y}_{exact}(t)}\\right|\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_{exact}(t) = 5\\hat{y_0}^2e^{-2} - \\frac{25}{64}\\hat{y_0}^2(-12e+612e^{-1})^2 \\ \\ \\ \\ \\ \\ \\ \\ \\sigma(t) = a_1y_1^2 +a_2y_2^2+a_3y_3^2+a_4y_4^2\n",
    "$$\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 $\\alpha=1,\\beta=3$\n",
    "$\\downarrow$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/zwj/anaconda3/lib/python3.6/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n",
      "  warnings.warn(warning_msg, ODEintWarning)\n"
     ]
    }
   ],
   "source": [
    "allcoeff_533_1 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_533_1[0,:]=1/3*np.ones(4)\n",
    "allcoeff_533_1[1,:]=1/3*np.ones(4)\n",
    "y_533_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 = [1, 3]\n",
    "\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_le = allcoeff_533_1[:,i]\n",
    "    y_mid=odeint(ode_system_le, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, params))[1,:]\n",
    "    y_533_1[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.67971666e-01,  9.99234457e-01,  9.99976844e-01,\n",
       "         9.88201315e-01],\n",
       "       [-3.18275458e-02, -7.32690220e-04, -4.60583490e-05,\n",
       "        -1.23452722e-02],\n",
       "       [ 0.00000000e+00, -6.54370491e-05,  4.58728490e-06,\n",
       "         5.52619983e-05],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  1.03499325e-05,\n",
       "         1.90219706e-04],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,\n",
       "         9.54801662e-04]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_533_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`beta.expect(func, args=(a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999999999999999\n",
      "5.551115123125783e-17\n",
      "2.7755575615628914e-17\n",
      "3.7643499428696714e-16\n",
      "-9.228728892196614e-16\n",
      "-9.228728892196614e-16\n",
      "-9.228728892196614e-16\n",
      "-9.228728892196614e-16\n",
      "-9.228728892196614e-16\n"
     ]
    }
   ],
   "source": [
    "for i in range(9):\n",
    "    #to compute $\\bar{y}(t)$\n",
    "    print(beta.expect(Jacobi((i,1,3)), args=(4,2), loc=-1, scale=2, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1428571428571426\n",
      "1.111111111111111\n",
      "1.0389610389610364\n",
      "0.9615384615384587\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (Jacobi((n,1,3))(u))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    print(beta.expect(g(i), args=(4, 2), loc=-1, scale=2, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "############# alpha = 1, beta = 3  ################ \n",
    "\n",
    "mean_533_1 = y_533_1[0,:]\n",
    "mean_exact_533_1 = 5/8*(-12*np.e +612*np.e**(-1))\n",
    "error_mean_533_1 = np.abs((mean_533_1 - mean_exact_533_1)/mean_exact_533_1)\n",
    "\n",
    "\n",
    "sigma2_533_1=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_533_1[i]=8/7*y_533_1[1,i]**2+10/9*y_533_1[2,i]**2+1.0389610389610364*y_533_1[3,i]**2+0.9615384615384587*y_533_1[4,i]**2\n",
    "    \n",
    "sigma2_exact_533_1 = 5*np.e**(-2) -25/64*(-12*np.e +612*np.e**(-1))**2\n",
    "error_var_533_1 = np.abs((sigma2_533_1-sigma2_exact_533_1)/sigma2_exact_533_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.90656886 0.9902277  0.99044444 0.98238702]\n",
      "120.32677253463385\n",
      "[0.99246578 0.99177051 0.99176871 0.99183567]\n",
      "[1.0000008  1.00000001 1.00000001 1.00000002]\n"
     ]
    }
   ],
   "source": [
    "print(mean_533_1)\n",
    "print(mean_exact_533_1)\n",
    "print(error_mean_533_1)\n",
    "print(error_var_533_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color = red> The error of mean plots when $\\alpha=\\beta=0$ is a little different since it is close to machine epsilon??, I am using lengendre package in python since $\\alpha=\\beta=0$.\n",
    "    \n",
    "### <font color = red> But when $\\alpha=1, \\beta=3$, the error plots are so strange, I am using the lengendre functions I defined by myself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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 0x1a153077f0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.xlim([0,5])\n",
    "plt.semilogy([1,2,3,4],error_mean_533_0,'-bs',label='mean,alpha=0,beta=0')\n",
    "plt.semilogy([1,2,3,4],error_var_533_0,'-rs',label='variance, alpha=0,beta=0') \n",
    "plt.semilogy([1,2,3,4],error_mean_533_1,'-.b^',label='mean, alpha=1,beta=3')\n",
    "plt.semilogy([1,2,3,4],error_var_533_1,'-.r^',label='variance, alpha=1,beta=3')  \n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}