{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from scipy.special import gammaln\n",
      "\n",
      "outcomes = np.zeros((10001, 3), int)\n",
      "outcome_to_index = {'W': 0, 'B': 1, 'D': 2}\n",
      "for game, line in enumerate(open('data/chess_outcomes.txt')):\n",
      "    outcome = line.strip()\n",
      "    index = outcome_to_index[outcome]\n",
      "    outcomes[game + 1][index] = 1\n",
      "    \n",
      "counts_up_to = outcomes.cumsum(axis=0)\n",
      "\n",
      "def compute_prior(w, b):\n",
      "    if 0 < w < 1 and \\\n",
      "       0 < b < 1 and \\\n",
      "       w + b < 1:\n",
      "        return 1. # the factor of 2 is taken care of by the Bayes denominator\n",
      "    else:\n",
      "        return 0.\n",
      "\n",
      "def compute_log_evidence_factor(w, b, W, B, D):\n",
      "    return W * np.log(w) + B * np.log(b) + D * np.log(1 - w - b)\n",
      "\n",
      "def compute_log_denominator(W, B, D):\n",
      "    return gammaln(W + 1) + gammaln(B + 1) + gammaln(D + 1) - gammaln(W + B + D + 3)\n",
      "\n",
      "def compute_p(w, b, W, B, D):\n",
      "    prior = compute_prior(w, b)\n",
      "    if prior == 0.:\n",
      "        p = 0.\n",
      "    else:\n",
      "        log_evidence_factor = compute_log_evidence_factor(w, b, W, B, D)\n",
      "        log_bayes_denominator = compute_log_denominator(W, B, D)\n",
      "        p = np.exp(log_evidence_factor - log_bayes_denominator) * prior\n",
      "    return p\n",
      "\n",
      "compute_p = np.vectorize(compute_p)\n",
      "\n",
      "n = 200  # Number of grid points on each axis\n",
      "w, w_step = np.linspace(0, 1., num=n, retstep=True)\n",
      "b, b_step = np.linspace(0, 1., num=n, retstep=True)\n",
      "ww, bb = np.meshgrid(w, b)\n",
      "\n",
      "def get_p(num_games):\n",
      "    W, B, D = counts_up_to[num_games]\n",
      "    p = compute_p(ww, bb, W, B, D)\n",
      "    return p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 121
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ns = range(10) + range(10, 100, 10) + range(100, 1000, 100) + range(1000, 10001, 1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 123
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time ps = [get_p(n) for n in ns]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 31.1 s, sys: 8 ms, total: 31.2 s\n",
        "Wall time: 31.2 s\n"
       ]
      }
     ],
     "prompt_number": 124
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "from matplotlib import animation\n",
      "from JSAnimation import IPython_display\n",
      "\n",
      "fig, ax = plt.subplots()\n",
      "\n",
      "im = ax.imshow(get_p(0), extent=[0, 1, 0, 1], origin='lower')\n",
      "ax.set_xlabel('w')\n",
      "ax.set_ylabel('b')\n",
      "fig.colorbar(im)\n",
      "\n",
      "def animate(i):\n",
      "    im.set_array(ps[i])\n",
      "    im.autoscale()\n",
      "    ax.set_title('Posterior after {0:5d} games'.format(ns[i]))\n",
      "    return [im]\n",
      "\n",
      "animation.FuncAnimation(fig, animate, frames=len(ns), interval=400)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Define the Animation class */\n",
        "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
        "    this.img_id = img_id;\n",
        "    this.slider_id = slider_id;\n",
        "    this.loop_select_id = loop_select_id;\n",
        "    this.interval = interval;\n",
        "    this.current_frame = 0;\n",
        "    this.direction = 0;\n",
        "    this.timer = null;\n",
        "    this.frames = new Array(frames.length);\n",
        "\n",
        "    for (var i=0; i<frames.length; i++)\n",
        "    {\n",
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        "    this.set_frame(this.current_frame);\n",
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        "        var button = button_group[i];\n",
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        "    document.getElementById(this.slider_id).value = this.current_frame;\n",
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        "\n",
        "  Animation.prototype.next_frame = function()\n",
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        "\n",
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        "    this.interval /= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
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        "\n",
        "  Animation.prototype.faster = function()\n",
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        "    this.interval *= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_forward = function()\n",
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        "    this.current_frame += 1;\n",
        "    if(this.current_frame < this.frames.length){\n",
        "      this.set_frame(this.current_frame);\n",
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        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.first_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.last_frame();\n",
        "        this.reverse_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.last_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
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        "  Animation.prototype.anim_step_reverse = function()\n",
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        "    if(this.current_frame >= 0){\n",
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        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.last_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.first_frame();\n",
        "        this.play_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.first_frame();\n",
        "      }\n",
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        "  }\n",
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        "  Animation.prototype.pause_animation = function()\n",
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        "    if (this.timer){\n",
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        "      this.timer = null;\n",
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        "    this.direction = 1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
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        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
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        "  <form action=\"#n\" name=\"_anim_loop_selectLERUUOKNUVVJNGSP\" class=\"anim_control\">\n",
        "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
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        "  </form>\n",
        "</div>\n",
        "\n",
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_imgLERUUOKNUVVJNGSP\";\n",
        "    var slider_id = \"_anim_sliderLERUUOKNUVVJNGSP\";\n",
        "    var loop_select_id = \"_anim_loop_selectLERUUOKNUVVJNGSP\";\n",
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        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
        "        animLERUUOKNUVVJNGSP = new Animation(frames, img_id, slider_id, 400, loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 126,
       "text": [
        "<matplotlib.animation.FuncAnimation at 0xd84c38c>"
       ]
      }
     ],
     "prompt_number": 126
    }
   ],
   "metadata": {}
  }
 ]
}