{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import time\n",
      "\n",
      "from our_random import test"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "seed = .123\n",
      "def rand():\n",
      "    \"\"\"Our very own random number generator.\"\"\"\n",
      "    \n",
      "    # The seed is always a number between 0 and 1.\n",
      "    global seed\n",
      "    \n",
      "    # Get the time as a floating point number in seconds, multiply it by the seed\n",
      "    # (after adding 1.0 to the seed so we never multiple by 0), and get the 10\n",
      "    # digits after the decimal as a string in reverse order (so the quickest\n",
      "    # changing digit is first.\n",
      "    tmp = time.time() * (1.0 + seed)\n",
      "    tmp = tmp - int(tmp)\n",
      "    digits = ''.join(reversed(\"{:.10f}\".format(tmp)[2:]))\n",
      "    \n",
      "    # Prepend '0.' to the digits as our random number and save it as the seed for\n",
      "    # next time.\n",
      "    result = float('0.' + str(digits))\n",
      "    seed = result\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Number of random numbers to generate for each test.\n",
      "NUM_TEST_SAMPLES = 1000000\n",
      "\n",
      "# Do a single test of our random number generator and plot a histogram.\n",
      "numbers = np.array([rand() for _ in xrange(NUM_TEST_SAMPLES)])\n",
      "NUM_BINS = 100\n",
      "plt.hist(numbers, bins=NUM_BINS)\n",
      "plt.axhline(y=(NUM_TEST_SAMPLES / float(NUM_BINS)), color='red')\n",
      "print 'pvalue', test(numbers)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "pvalue "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0510114145228\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kIowDAEAmwjgAAGQijAMAQCbCOAAAZCKMAwBAJsI4AABkIowDAEAmwjgAAGQi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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa4d828c>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Define some functions to test our random number generator as well as\n",
      "# numpy's generator. For each generator, we call the provided test\n",
      "# function 'NUM_EXPERIMENTS' times with 'NUM_TEST_SAMPLES' random\n",
      "# samples and then summarize the results.\n",
      "\n",
      "NUM_EXPERIMENTS = 100\n",
      "\n",
      "def test_our_random():\n",
      "    \"\"\"Get the p-value for a single test of our generator.\"\"\"\n",
      "    return test([rand() for _ in xrange(NUM_TEST_SAMPLES)])\n",
      "\n",
      "def test_numpy_random():\n",
      "    \"\"\"Get the p-value for a single test of numpy's generator.\"\"\"\n",
      "    return test(np.random.random(NUM_TEST_SAMPLES))\n",
      "\n",
      "def get_pvals(test_func):\n",
      "    \"\"\"Return an array of p-values from the given test function.\"\"\"\n",
      "    pvals = np.array([test_func() for _ in xrange(NUM_EXPERIMENTS)])\n",
      "    return pvals\n",
      "\n",
      "def summarize_results(name, pvals):\n",
      "    \"\"\"Print a summary of the results from an array of p-values.\"\"\"\n",
      "    print \"{} results:\".format(name)\n",
      "    print \"  mean: {}\".format(np.mean(pvals))\n",
      "    print \"  std: {}\".format(np.std(pvals))\n",
      "    print \"  pvals: {}\".format(\" \".join(\"{:.2f}\".format(pval) for pval in pvals))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Summarize numpy's results.\n",
      "numpy_pvals = get_pvals(test_numpy_random)\n",
      "summarize_results('numpy', numpy_pvals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "numpy results:\n",
        "  mean: 0.552962303605\n",
        "  std: 0.29984188423\n",
        "  pvals: 0.98 0.99 0.48 0.64 0.98 0.42 0.97 0.78 0.89 0.05 0.98 0.88 0.79 0.61 0.70 0.62 0.15 0.61 0.04 0.94 0.86 0.21 0.98 0.69 0.90 0.70 0.09 0.37 0.31 0.73 0.34 0.31 0.70 0.96 0.48 0.31 0.76 0.12 0.08 0.74 0.21 0.57 0.62 0.99 0.16 0.97 0.61 0.46 0.76 0.63 0.83 0.01 0.49 0.70 0.98 0.18 0.64 0.16 0.33 0.84 0.43 0.41 0.72 0.44 0.92 0.44 0.28 0.90 0.81 0.64 0.09 0.01 0.24 0.31 0.71 0.75 0.69 0.84 0.96 0.01 0.53 0.17 0.78 0.58 0.47 0.85 0.47 0.06 0.97 0.48 0.79 0.30 0.18 0.05 0.17 0.81 0.40 0.71 0.44 0.21\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Summarize our results. Takes quite a few minutes to run.\n",
      "our_pvals = get_pvals(test_our_random)\n",
      "summarize_results('our', our_pvals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "our results:\n",
        "  mean: 0.503211314223\n",
        "  std: 0.284857700816\n",
        "  pvals: 0.65 0.85 0.08 0.83 0.41 0.85 0.83 0.57 0.04 0.85 1.00 0.28 0.04 0.73 0.07 0.78 0.47 0.19 0.44 0.71 0.04 0.05 0.08 0.85 0.58 0.09 0.53 0.27 0.83 0.48 0.37 0.45 0.37 0.13 0.46 0.08 0.74 0.86 0.21 0.99 0.54 0.25 0.31 0.78 0.53 0.59 0.67 0.38 0.19 0.05 0.85 0.54 0.84 0.52 0.22 0.53 0.98 0.95 0.74 0.86 0.56 0.17 0.20 0.00 0.26 0.65 0.23 0.75 0.27 0.74 0.88 0.82 0.62 0.62 0.54 0.94 0.38 0.44 0.29 0.13 0.45 0.65 0.68 0.19 0.32 0.71 0.32 0.23 0.92 0.26 0.26 0.93 0.65 0.43 0.57 0.42 0.93 0.05 0.65 0.77\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}