{
 "metadata": {
  "name": "Random function with wrapper to check for trivial cases"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Functions that return random number are many times the computational bottlenecks of my programs.\n",
      "On top of that, I like to write generic but sometimes the result is that I call a random function that has a trivial domain, \n",
      "that is, there is only one value it can even possible return.\n",
      "I wondered if *NumPy* knows how to handle that, but it turns out it doesn't. I'll show you.\n",
      "\n",
      "First I define a function that returns a discrete uniform number between 0 and *n*:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import random_integers\n",
      "from timeit import timeit\n",
      "def uniform(n):\n",
      "    return random_integers(0,n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next I define a *smart* function that returns discrete uniform, but first checks that the domain is not trivial, an dif it is, it returns the trivial value:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def smart_uniform(n):\n",
      "    if n==0: \n",
      "        return 0\n",
      "    else: \n",
      "        return random_integers(0,n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def trivial():\n",
      "    return 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now I define a factory function that for a given function (which will be either *uniform* or *smart_uniform*) returns two versions - one with a range limit 0 and one with a range limit 1, both given as the first argument. This is used by the *timeit* function timer later on."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def function_factory(func):\n",
      "    def f0():\n",
      "        return func(0)\n",
      "    def f1():\n",
      "        return func(1)\n",
      "    return f0,f1\n",
      "\n",
      "uniform0,uniform1 = function_factory(uniform)\n",
      "smart_uniform0,smart_uniform1 = function_factory(smart_uniform)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now I use the *timeit* function timer to time how long each function calls takes. *timeit* is nice, it calls the function many times and calculates the average time. But as far as I know it doesn't take arguments, which is why I needed the above function factory.\n",
      "\n",
      "As you can see, the uniform functions take roughly the same time, although *uniform 0* is trivial and always returns 0.\n",
      "The smart function for the trivial case does take less time than the regular version - \n",
      "because it doesn't do the random draws - but still takes longer than the trivial version, probably because of the *if* calls.\n",
      "\n",
      "The bad news are that the non-trivial smart uniform function takes much longer than the regular version, which means this is not a good implementation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"trivial 0:\",timeit(trivial)\n",
      "print \"uniform 0:\",timeit(uniform0)\n",
      "print \"uniform 1:\",timeit(uniform1)\n",
      "print \"smart uniform 0:\",timeit(smart_uniform0)\n",
      "print \"smart uniform 1:\",timeit(smart_uniform1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "trivial 0: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.380914433709\n",
        "uniform 0: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.632382798\n",
        "uniform 1: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.66399043729\n",
        "smart uniform 0: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.00784697256\n",
        "smart uniform 1: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2.23995387685\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}