tanutarou/mcmc.ipynb

## mcmc.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import math\n",
    "import itertools\n",
    "import copy\n",
    "import seaborn as sns\n",
    "sns.set(context='paper', style='darkgrid', rc={'figure.facecolor':'white'}, font_scale=1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## メトロポリス法\n",
    "### 完全グラフの2変数相互作用を持つ確率分布(2.1 p.8)\n",
    "$$\n",
    "P(\\bf{x}) = \\frac{\\exp(\\sum_{i<j} \\theta x_i x_j)}{Z}\n",
    "$$\n",
    "$\\theta$: 相互作用の強さ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_p(theta, x):\n",
    "    def calc_non_normalized_p(theta, x):\n",
    "        \"\"\" 正規化されていないpを返す \"\"\"\n",
    "        E = 0\n",
    "        for (x1, x2) in itertools.combinations(x,2):\n",
    "            E += x1 * x2\n",
    "        E *= theta\n",
    "        return np.exp(E)\n",
    "    \n",
    "    def calc_z(theta, x, n):\n",
    "        \"\"\" 分配関数の計算 \"\"\"\n",
    "        if len(x) == n:\n",
    "            return calc_non_normalized_p(theta, x)\n",
    "        ret = 0\n",
    "        for i in [-1, 1]:\n",
    "            x.append(i)\n",
    "            ret += calc_z(theta, x, n)\n",
    "            x.pop()\n",
    "        return ret\n",
    "    \n",
    "    z = calc_z(theta, [], len(x))\n",
    "    return calc_non_normalized_p(theta, x) / z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p(1,1,1) = 0.21294837787583085\n"
     ]
    }
   ],
   "source": [
    "print(\"p(1,1,1) = {}\".format(calc_p(0.2, [1, 1, 1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_r(theta, x, idx):\n",
    "    \"\"\" 候補の確率と現在の状態の確率の比を計算する関数 \"\"\"\n",
    "    return np.exp(-2 * theta * x[idx] * (sum(x) - x[idx]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mcmc_metro(calc_r, init, max_iter, burn_in, theta=0.2):\n",
    "    \"\"\" \n",
    "    メトロポリス法によるMCMC\n",
    "    calc_r : 候補の確率と現在の状態の確率の比を計算する関数\n",
    "    init : 初期状態\n",
    "    max_iter : 繰り返し回数\n",
    "    burn_in : 捨てる初期サンプル数\n",
    "    theta : 相互作用の強さ\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    x = init\n",
    "    for i in range(max_iter):\n",
    "        # 次の候補の生成\n",
    "        select = np.random.randint(len(x))\n",
    "        \n",
    "        # 候補の確率と現在の状態の確率の比の計算\n",
    "        r = calc_r(theta, x, select)\n",
    "        if np.random.rand() < r:\n",
    "            # aceptなら状態を変更する\n",
    "            x[select] = -x[select]\n",
    "        \n",
    "        # サンプル列に追加\n",
    "        samples.append(copy.deepcopy(x))\n",
    "    return samples[burn_in:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean x0 : 0.10888888888888888\n",
      "mean x1 : 0.12066666666666667\n",
      "mean x2 : 0.12933333333333333\n"
     ]
    }
   ],
   "source": [
    "init = np.array([1, 1, 1])\n",
    "samples = np.array(mcmc_metro(calc_r, init, 10000, 1000, 0.8))\n",
    "samples = samples.transpose()\n",
    "for i in range(len(init)):\n",
    "    print(\"mean x{} : {}\".format(i, samples[i].mean()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mean_x_plot(samples, idx):\n",
    "    \"\"\" 1変数期待値のplot \"\"\"\n",
    "    div = 10\n",
    "    itr = []\n",
    "    means = []\n",
    "    for i in range(div, len(samples[idx]), div):\n",
    "        itr.append(i)\n",
    "        means.append(samples[idx][:i].mean())\n",
    "    plt.ylim([-1, 1])\n",
    "    plt.ylabel(\"mean x\")\n",
    "    plt.xlabel(\"number of iteration\")\n",
    "    plt.plot(itr, means, label=\"mean x{}\".format(idx))\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
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CEsfZ8LvdgCQOIYQASRxnxVdds3SAJtvTCiGEJI6z4a6oaapS1C69rJcQQpwVSRxnweuq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\nVO3sahwAxn4DKYyw4NidS0CBMFssack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zEcXFxRQVFaHRaPDy8iItLY3q6mr27NkDwNdf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\nSOEQQghhESkcQgghLPJf5/5I9JXzvS4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28332cac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1変数期待値のtrace\n",
    "init = np.array([1, 1, 1])\n",
    "samples = np.array(mcmc_metro(calc_r, init, 10000, 1000, 0.8))\n",
    "samples = samples.transpose()\n",
    "for i in range(3):\n",
    "    mean_x_plot(samples, i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mean_xx_plot(samples, i1, i2):\n",
    "    \"\"\" 2変数期待値のplot \"\"\"\n",
    "    div = 10\n",
    "    itr = []\n",
    "    means = []\n",
    "    for i in range(div, len(samples[i1]), div):\n",
    "        itr.append(i)\n",
    "        xx = samples[i1][:i] * samples[i2][:i]\n",
    "        means.append(xx.mean())\n",
    "    plt.ylim([-1, 1])\n",
    "    plt.ylabel(\"mean x\")\n",
    "    plt.xlabel(\"number of iteration\")\n",
    "    plt.plot(itr, means, label=\"mean x{} * x{}\".format(i1, i2))\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta = 0.2\n"
     ]
    },
    {
     "data": {
      "image/png": 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xOIsAhQizjSYRDYkIDUXXSnoBNEpi8+penB4XTq8Hl9uDW/NgMukYVB2z0UCh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\nRkYQohVCCHGxoBSO9PR0YmJ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ccMMNjB07ltTUVObNm0d6ejomk4l58+bxm9/8hlOnTpGQ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\nBEQKhxBCiIBI4RBCCBEQKRxCCCEC8v8B484uI5m/D3cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282fb9ac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta = 0.4\n"
     ]
    },
    {
     "data": {
      "image/png": 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QQjQ+tRaODz74gLVr1xIbG3sq4hFCCNHI1XqOw+VyERMjVxYJIYSoVGuPo3Pn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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2865abe828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta = 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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Y1NRUXC7XxYhHCCFEA1djW/Xu3btXLKgoAOi6jqIo7Nu3r/6jqwPSVr3uSD58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\nl/Hss4t54423iIpqh6oayM0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TWFgYdrvd+3rAgAFs2LCB/Px8AEpLSzl06FCl6xYXF9O6\ndWsURWHz5s0+7b5DQ0N9tnuua6+91nvqbe/evRQUFHi/MVI0bzLiEE3GVVddRe/evRk+fDixsbH0\n6NGjVttp3bo1n3/+Oc888wzh4eE899xzAIwbN47s7GwmTJgAgMlkYu7cubRt27ba7fXo0YM777yT\nyZMnA3DNNddw6623+hVTYmIiM2bMYPTo0dx5553cfPPNTJkyhSlTpnCmT+mMGTPo1KnTeetOnz6d\nRx99lDfffJM+ffpwySWXeOdNnjyZWbNmERQUxJo1a3zWe/zxx5k3bx7vv/8+JpOJZ5991mekIZov\n6Y4rhBDCL3KqSgghhF+kcAghhPCLFA4hhBB+kcIhhBDCL1I4hBBC+EUKhxBCCL9I4RBCCOEXKRxC\nCCH88v8DXSGodGvL+EEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2833873f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2変数期待値のtrace\n",
    "for theta in [0.2, 0.4, 0.8]:\n",
    "    print(\"theta = {}\".format(theta))\n",
    "    samples = np.array(mcmc_metro(calc_r, init, 10000, 1000, theta))\n",
    "    samples = samples.transpose()\n",
    "    \n",
    "    # 理論線\n",
    "    plt.axhline((2*np.exp(3*theta) - 2*np.exp(-theta)) / (2*np.exp(3*theta) + 6*np.exp(-theta)), 0, len(samples), c=\"k\", label=\"ideal\")\n",
    "    # トレースのプロット\n",
    "    for (i1, i2) in itertools.combinations(list(range(len( samples ))), 2):\n",
    "        mean_xx_plot(samples, i1, i2)\n",
    "    plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### イジングモデル(2.3 p.16)\n",
    "$$\n",
    "P(\\bf{x}) = \\frac{exp \\left(\\theta \\sum_{(i,j) \\in G} x_i x_j \\right)}{Z}\n",
    "$$\n",
    "グラフG : $L \\times L$格子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_r_ising(theta, x, idx):\n",
    "    L = int(np.sqrt(len(x)))\n",
    "    assert int(L*L) == len(x)\n",
    "    \n",
    "    adjs = [idx+1, idx-1, idx+L, idx-L]\n",
    "    \n",
    "    sum_adj = 0\n",
    "    for a in adjs:\n",
    "        if a >= 0 and a < len(x):\n",
    "            sum_adj += x[a]\n",
    "    return np.exp(-2 * theta * x[idx] * sum_adj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mTp3KLbfcwtSpU7nzzjuJi4tzSRk7H7fgV2ypeV0tu+GhaV3B5Zwb2hvINFnI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\niEh2DBciIpLd/wFk/T82o2wQ2gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2833176e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1変数期待値のtrace\n",
    "L = 5\n",
    "init = [1 for i in range(L*L)]\n",
    "samples = np.array(mcmc_metro(calc_r_ising, init, 100000, 2000, 0.5))\n",
    "samples = samples.transpose()\n",
    "for i in range(3):\n",
    "    mean_x_plot(samples, i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "scrolled": true
   },
   "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",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the 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",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"431.818172458775\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# イジングモデルのアニメーション\n",
    "%matplotlib nbagg\n",
    "from matplotlib import animation\n",
    "L = 20\n",
    "theta = 0.50\n",
    "init = [1 - 2*np.random.randint(0, 2)  for i in range(L*L)]\n",
    "samples = np.array(mcmc_metro(calc_r_ising, init, 10000, 2000, theta))\n",
    "\n",
    "# animation \n",
    "fig = plt.figure()\n",
    "plt.axes().set_aspect('equal')\n",
    "ims = []\n",
    "for sample in samples[::20]:\n",
    "    sample = np.reshape(sample, [L, L])\n",
    "    ims.append((plt.pcolor(np.arange(L), np.arange(L), sample, cmap=plt.cm.Blues),))\n",
    "\n",
    "ani = animation.ArtistAnimation(fig, ims, interval=5,  blit=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 2変量正規分布 (2.4 p.19)\n",
    "$$\n",
    "p(x_1, x_2) = \\frac{1}{Z} \\exp \\left(- \\frac{x_1^2 - 2b x_1 x_2 + x_2^2}{2} \\right)\n",
    "$$\n",
    "b : x1とx2の相関の強さ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mcmc_metro_continuous(calc_r, init, max_iter, burn_in, theta=0.2):\n",
    "    \"\"\" \n",
    "    メトロポリス法によるMCMC(連続変数ver)\n",
    "    calc_r : 候補の確率と現在の状態の確率の比を計算する関数\n",
    "    init : 初期状態\n",
    "    max_iter : 繰り返し回数\n",
    "    burn_in : 捨てる初期サンプル数\n",
    "    theta : 相互作用の強さ\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    x = init\n",
    "    for i in range(max_iter):\n",
    "        # 次の候補の生成\n",
    "        delta = np.random.normal(0, 1, (len(x)))\n",
    "        \n",
    "        # 候補の確率と現在の状態の確率の比の計算\n",
    "        r = calc_r(theta, x, delta)\n",
    "        if np.random.rand() < r:\n",
    "            # aceptなら状態を変更する\n",
    "            x += delta\n",
    "        \n",
    "        # サンプル列に追加\n",
    "        samples.append(copy.deepcopy(x))\n",
    "    return samples[burn_in:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_unormalized_p(x):\n",
    "    \"\"\" 2変量正規分布の正規化されていない値 \"\"\"\n",
    "    return np.exp(-(x[0]**2 - 2*b*x[0]*x[1] + x[1]**2)/2)\n",
    "\n",
    "def calc_r_mul_normal(b, x, delta):\n",
    "    \"\"\" 2変量正規分布の次状態と現在の状態の確率の比を返す \"\"\"\n",
    "    nx = x + delta\n",
    "    r = calc_unormalized_p(nx) / calc_unormalized_p(x)\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282f87ecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.25\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28332cfe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2831d54c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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q6MYU2Ii+t5IYEymXCW15nOcVqnpERC4AXhaR7aq6t4hNNEObl/6OLgJeEJFl\nqnoy6EYFqSRCxOcJbSVjqPNU1SPpfw+LyEvAMiCMIXKEvn/BZgLvBNSWgsr6jnan/ygsBN4OtlUF\n4/a9Dfk7FdrLmWFMaAsFEZkgIlXpnycBjUBzsK0asW1Ag4hMF5GJpK6rNwbcJs9EpEZExqZ/ngEs\nAfYH26rCyQSkiFwsInHgFvL4nQrFPJH0hLbrgVrgA+CbqvprEVlI6s5NNfAy8N9UNRlcS0dOROYD\nz6ZfVgBrVfXhAJvkSXpC4QOkzuVvVfWRgJvkmYh8AXgESABJ4H+q6i+DbdXIicgLpAbBJwCdpG5M\njAX+mdQt3idU9a+G+pxQhIgxpnSF9nLGGFMaLESMMZ5YiBhjPLEQMcZ4YiFijPHEQsQY44mFiDHG\nEwsRY4wn/x+33mmR9LRIQAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2832b649b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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8NuAUPlvhseDSifmA2+3my09sCwRmdbkG2NnSww8eWBnXdYziQxbVluI6PcDR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\nBCEpREQEQUgKERFBEJLi/wNAtTPZtyjQRAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2831ba0c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# サンプリングの散布図の描画\n",
    "init = [5, 5]\n",
    "bs = [0.0, 0.25, 0.5, 0.75, 1.0]\n",
    "for b in bs:\n",
    "    print(\"b = {}\".format(b))\n",
    "    samples = np.array(mcmc_metro_continuous(calc_r_mul_normal, init, 10000, 2000, b))\n",
    "    plt.axes().set_aspect('equal')\n",
    "    plt.scatter(samples[:, 0], samples[:, 1])\n",
    "    plt.xlim([-10, 10])\n",
    "    plt.ylim([-10, 10])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_r_mul_normal_constrain(b, x, delta):\n",
    "    nx = x + delta\n",
    "    # 制約条件に満たない場合はreject\n",
    "    if nx[1] < 0.5*nx[0]**2 + 3:\n",
    "        return 0\n",
    "    \n",
    "    r = calc_unormalized_p(nx) / calc_unormalized_p(x)\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282fa5b9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.25\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282f9fa7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282f951828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282fa76400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f283324f278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 制約付きの場合のサンプリングの散布図の描画\n",
    "init = [2, 8]\n",
    "bs = [0.0, 0.25, 0.5, 0.75, 1.0]\n",
    "for b in bs:\n",
    "    print(\"b = {}\".format(b))\n",
    "    samples = np.array(mcmc_metro_continuous(calc_r_mul_normal_constrain, init, 10000, 2000, b))\n",
    "    # サンプルのplot\n",
    "    plt.axes().set_aspect('equal')\n",
    "    plt.scatter(samples[:, 0], samples[:, 1])\n",
    "    plt.xlim([-10, 10])\n",
    "    plt.ylim([-10, 10])\n",
    "    # 制約条件のplot\n",
    "    xs = np.linspace(-10, 10, 100)\n",
    "    ys = [0.5*(x**2) + 3 for x in xs]\n",
    "    plt.plot(xs, ys, c=\"r\")\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ギブス・サンプラー\n",
    "### 2変量正規分布 (2.5 p.23)\n",
    "$$\n",
    "p(x_1, x_2) = \\frac{1}{Z} \\exp \\left(- \\frac{x_1^2 - 2b x_1 x_2 + x_2^2}{2} \\right)\n",
    "$$\n",
    "b : x1とx2の相関の強さ\n",
    "\n",
    "条件付き確率:\n",
    "$$\n",
    "p(x_1 | x_2) = \\frac{1}{\\sqrt{2\\pi}} \\exp \\left( - \\frac{(x_1 - bx_2)^2}{2} \\right)\n",
    "$$\n",
    "$$\n",
    "p(x_2 | x_1) = \\frac{1}{\\sqrt{2\\pi}} \\exp \\left( - \\frac{(x_2 - bx_1)^2}{2} \\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mcmc_gibbs_normal(init, max_iter, burn_in, b=0.8):\n",
    "    \"\"\" \n",
    "    ギブスサンプリングによるMCMC(2変量正規分布)\n",
    "    init : 初期状態\n",
    "    max_iter : 繰り返し回数\n",
    "    burn_in : 捨てる初期サンプル数\n",
    "    b : 相関の強さ\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    x = init\n",
    "    for i in range(max_iter):\n",
    "        # 交互に条件付き確率からのサンプリング\n",
    "        if i % 2 == 0:\n",
    "            x[0] = np.random.normal(b*x[1], 1)\n",
    "        else:\n",
    "            x[1] = np.random.normal(b*x[0], 1)\n",
    "        \n",
    "        # サンプル列に追加\n",
    "        samples.append(copy.deepcopy(x))\n",
    "    return samples[burn_in:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282fae4d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.25\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f282d741748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2832f93eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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KV0WoZk+cQeQNYI2ZLQdOkh/v+GbxZKGQN2Z2JbAHuBP4aoztmRNKU933D/+SFjLkCNhc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2832a33588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b = 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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VyVZ8SleLqiDoLt4q47RCFNDVoiowGkSqVOYCMQ0eKijanVFK+aJBRCnliwYR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\nypf/D0I2mttUHdXZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28326f2b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# サンプリングの散布図の描画\n",
    "init = [5, 9]\n",
    "bs = [0.0, 0.25, 0.5, 0.75, 1.0]\n",
    "for b in bs:\n",
    "    print(\"b = {}\".format(b))\n",
    "    samples = np.array(mcmc_gibbs_normal(init, 1000, 0, b))\n",
    "    plt.axes().set_aspect('equal')\n",
    "    plt.scatter(samples[:, 0], samples[:, 1])\n",
    "    plt.xlim([-10, 10])\n",
    "    plt.ylim([-10, 10])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### イジングモデル(2.5 p.27)\n",
    "$$\n",
    "P(\\bf{x}) = \\frac{exp \\left(\\theta \\sum_{(i,j) \\in G} x_i x_j \\right)}{Z}\n",
    "$$\n",
    "グラフG : $L \\times L$格子\n",
    "\n",
    "条件付き確率\n",
    "$$\n",
    "P(x_i=1 | \\{ x_{j(\\neq i)} \\}) = \\frac{1 + \\tanh \\left( \\theta \\sum_{j \\in N(i)} x_j \\right)}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mcmc_gibbs_ising(init, max_iter, burn_in, theta=0.2):\n",
    "    \"\"\" \n",
    "    ギブスサンプリングによるMCMC(イジングモデル)\n",
    "    init : 初期状態\n",
    "    max_iter : 繰り返し回数\n",
    "    burn_in : 捨てる初期サンプル数\n",
    "    theta : 相関の強さ\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    x = init\n",
    "    L = int(np.sqrt(len(x)))\n",
    "    assert int(L*L) == len(x)\n",
    "    \n",
    "    for i in range(max_iter):\n",
    "        idx = np.random.randint(len(x))\n",
    "        adjs = [idx+1, idx-1, idx+L, idx-L]\n",
    "        sum_adj = 0\n",
    "        for a in adjs:\n",
    "            if a >= 0 and a < len(x):\n",
    "                sum_adj += x[a]\n",
    "        \n",
    "        p_1 = (1 + np.tanh(theta * sum_adj)) / 2\n",
    "        if  np.random.rand() < p_1:\n",
    "            x[idx] = 1\n",
    "        else:\n",
    "            x[idx] = -1\n",
    "        \n",
    "        # サンプル列に追加\n",
    "        samples.append(copy.deepcopy(x))\n",
    "    return samples[burn_in:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the 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",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# イジングモデルのアニメーション\n",
    "%matplotlib nbagg\n",
    "from matplotlib import animation\n",
    "L = 20\n",
    "theta = 0.90\n",
    "init = [1 - 2*np.random.randint(0, 2)  for i in range(L*L)]\n",
    "samples = np.array(mcmc_gibbs_ising(init, 10000, 2000, theta))\n",
    "\n",
    "# animation \n",
    "fig = plt.figure()\n",
    "plt.axes().set_aspect('equal')\n",
    "ims = []\n",
    "for sample in samples[::20]:\n",
    "    sample = np.reshape(sample, [L, L])\n",
    "    ims.append((plt.pcolor(np.arange(L), np.arange(L), sample, cmap=plt.cm.Blues),))\n",
    "\n",
    "ani = animation.ArtistAnimation(fig, ims, interval=5,  blit=True)\n",
    "plt.show()"
   ]
  }
 ],
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   "types_to_exclude": [
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