lengths.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean= 29.9530095923 \tmean max= 82.669091423\n"
     ]
    },
    {
     "data": {
      "image/png": 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mz1mgjpOA89r584AXt/MvAi6sqvurahuwFdicZAp4ZFVd0653fs82kiRJ0sTo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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f756b2e6d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "batch_size=50\n",
    "\n",
    "# 1000 times the batch size\n",
    "batch_lengths = np.random.gamma(3,10,size=(1000,batch_size))\n",
    "\n",
    "batch_means = batch_lengths.mean(axis=-1)\n",
    "batch_maxima = batch_lengths.max(axis=-1)\n",
    "\n",
    "limits = min(batch_lengths.ravel()),max(batch_lengths.ravel())\n",
    "\n",
    "plt.figure(figsize=[12,4])\n",
    "plt.xlim(*limits)\n",
    "plt.subplot(1,3,1)\n",
    "plt.hist(batch_lengths.ravel());\n",
    "plt.title('length')\n",
    "plt.subplot(1,3,2)\n",
    "plt.xlim(*limits)\n",
    "plt.hist(batch_means);\n",
    "plt.title('mean over batch')\n",
    "plt.subplot(1,3,3)\n",
    "plt.xlim(*limits)\n",
    "plt.hist(batch_maxima);\n",
    "plt.title('max over batch')\n",
    "\n",
    "print \"mean=\",np.mean(batch_lengths), \"\\tmean max=\", np.mean(batch_maxima)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}