{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Randomness : Monte Carlo techniques"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Finding the area\n",
      "\n",
      "Let us find the area of the disc. We know that a disc is given by the equation $x^2 + y^2 \\leq 1$. So if we generate $(x, y)$ uniform randomly on the $[-1, 1] \\times [-1, 1]$ square, the proportion of the points lying in the disc will give the area."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# I'll put all the imports here so that it is easy to reference what we\n",
      "# are importing\n",
      "\n",
      "import random\n",
      "\n",
      "# This is to plot points to show what is happening\n",
      "import matplotlib.pylab\n",
      "\n",
      "# This we need to make vectorized versions of Monte Carlo simulations.\n",
      "import numpy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = []\n",
      "y = []\n",
      "for i in range(1000) :\n",
      "    x.append(random.uniform(-1, 1))\n",
      "    y.append(random.uniform(-1, 1))\n",
      "plt = matplotlib.pylab.scatter(x, y)\n",
      "matplotlib.pylab.show(plt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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F8PmKU7p0tRz53KexZMlSNC0Bt3sQhnEnVavWzzb/S2bs2bOHmJiC2GylEMmD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\nBjf8HA6HU8b4f0Ja0poc39E5AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa0d566c>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def area_circle(N) :\n",
      "    i = 0\n",
      "    incircle = 0\n",
      "    areaofsquare = 2*2 # 2 = length of [-1, 1]\n",
      "    while i < N :\n",
      "        x = random.uniform(-1, 1)\n",
      "        y = random.uniform(-1, 1)\n",
      "        if x*x + y*y <= 1 :\n",
      "            incircle += 1\n",
      "        i += 1\n",
      "    area = (float(incircle)/N) * areaofsquare\n",
      "    return area"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print area_circle(1000000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3.141052\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Monte Carlo Simulations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What we did above was some kind of Monte Carlo simulation. We estimated the probability of a random point on the aforementioned square to lie on the circle. That probability turned out to be $\\pi$.\n",
      "\n",
      "However computations only seem to make sense when the number of iterations are large. Because of that, I explain how to do a numpy vectorized version of the code which will work faster. Though for the present examples it doesn't matter much, for huge simulations the vectorized version, if done properly, can save you a lot of time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def vect_area_circle(N) :\n",
      "    # Create a 2xN aarray of random numbers\n",
      "    r = numpy.random.random((2, N)) * 2 - 1\n",
      "    x = r[0, :]\n",
      "    y = r[1, :]\n",
      "    incircle = (x*x + y*y < 1)\n",
      "    no_incircle = numpy.sum(incircle)\n",
      "    return 4.0*float(no_incircle)/N"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print vect_area_circle(1000000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3.142084\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit      area_circle(1000000)\n",
      "%timeit vect_area_circle(1000000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 5.98 s per loop\n",
        "1 loops, best of 3: 358 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Simulations of probabilistic experiments"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider the very simple game where you throw a dice. You gain $n$ points if the dice shows $n$ eyes. The first person to achieve more than or equal to $50$ points will win the game.\n",
      "\n",
      "To code this game, it is useful to introduce another random function, random.randint. `random.randint(a, b)`. This returns a uniformly distributed random number uniformly distributed between `a` and `b` with the end points included. As an example, I print 100 random integers between `1` and `6`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "no = [0, 0, 0, 0, 0, 0]\n",
      "for _ in range(100) :\n",
      "    r = random.randint(1, 6)\n",
      "    no[r - 1] += 1\n",
      "    print r, \",\",\n",
      "print\n",
      "print \"-\"*10, \"Distribution\", \"-\"*10\n",
      "print \"1 : %3d \\t 2 : %3d \\t 3 : % 3d \\n4 : %3d \\t 5 \\\n",
      ": %3d \\t 6 : %3d\\nSum = %d\" % tuple(no + [sum(no)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 , 6 , 2 , 4 , 2 , 4 , 6 , 5 , 4 , 2 , 3 , 6 , 6 , 6 , 6 , 2 , 2 , 5 , 2 , 2 , 2 , 5 , 1 , 2 , 3 , 6 , 3 , 4 , 5 , 6 , 6 , 4 , 5 , 2 , 2 , 6 , 3 , 4 , 5 , 1 , 5 , 1 , 1 , 6 , 1 , 6 , 4 , 4 , 1 , 2 , 1 , 3 , 3 , 5 , 1 , 2 , 3 , 2 , 1 , 2 , 3 , 6 , 3 , 5 , 1 , 2 , 6 , 6 , 3 , 5 , 3 , 6 , 6 , 2 , 6 , 5 , 6 , 2 , 1 , 6 , 4 , 1 , 1 , 2 , 5 , 2 , 5 , 3 , 6 , 6 , 6 , 4 , 1 , 2 , 6 , 1 , 1 , 5 , 6 , 4 ,\n",
        "---------- Distribution ----------\n",
        "1 :  17 \t 2 :  21 \t 3 :  12 \n",
        "4 :  11 \t 5 :  14 \t 6 :  25\n",
        "Sum = 100\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def stupid_game(withplayer=True) :\n",
      "    \"\"\"withplayer : If the user is going to input his value.\n",
      "    Setting this to False will make the computer play with\n",
      "    itself.\n",
      "    \"\"\"\n",
      "    t = 50 # total to reach\n",
      "    c = 0 # Computer's score\n",
      "    p = 0 # player's score\n",
      "    toss = random.randint(1, 2)\n",
      "    if toss == 1 :\n",
      "        print \"Computer wins the toss.\"\n",
      "    else :\n",
      "        print \"Player wins the toss.\"\n",
      "        \n",
      "    # Play if toss = 1\n",
      "    if toss == 1 :\n",
      "        throw = random.randint(1, 6)\n",
      "        c += throw\n",
      "        \n",
      "    while c < t and p < t :\n",
      "        if withplayer :\n",
      "            throw = input(\"Throw : \")\n",
      "            # Penalize cheaters : You can write\n",
      "            # all your AI Stuff here.\n",
      "            if throw > 6 :\n",
      "                throw -= 100\n",
      "        else :\n",
      "            throw = random.randint(1, 6)\n",
      "        p += throw\n",
      "        \n",
      "        throw = random.randint(1, 6)\n",
      "        c += throw\n",
      "        if c > p :\n",
      "            print \"Scores : COMP : %3d;   Player : %3d.\" % (c, p)\n",
      "        elif c < p :\n",
      "            print \"Scores : Comp : %3d;   PLAYER : %3d.\" % (c, p)\n",
      "        else :\n",
      "            print \"Scores : Comp : %3d;   Player : %3d.\" % (c, p)\n",
      "\n",
      "        \n",
      "    if c >= t and p >= t :\n",
      "        print \"There is a tie! :)\"\n",
      "    elif c >= t :\n",
      "        print \"The computer wins.\"\n",
      "    else :\n",
      "        print \"The player wins.\"\n",
      "    return None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stupid_game(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Player wins the toss.\n",
        "Scores : COMP :   3;   Player :   2.\n",
        "Scores : Comp :   4;   PLAYER :   6.\n",
        "Scores : Comp :  10;   Player :  10.\n",
        "Scores : COMP :  15;   Player :  14.\n",
        "Scores : Comp :  16;   PLAYER :  17.\n",
        "Scores : Comp :  17;   PLAYER :  22.\n",
        "Scores : Comp :  23;   PLAYER :  25.\n",
        "Scores : Comp :  25;   PLAYER :  26.\n",
        "Scores : COMP :  30;   Player :  28.\n",
        "Scores : COMP :  35;   Player :  33.\n",
        "Scores : Comp :  36;   Player :  36.\n",
        "Scores : Comp :  38;   PLAYER :  41.\n",
        "Scores : Comp :  44;   PLAYER :  45.\n",
        "Scores : Comp :  46;   PLAYER :  49.\n",
        "Scores : Comp :  49;   PLAYER :  50.\n",
        "The player wins.\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another example can be a simple random walk. Instead of doing graphics, let us do it using character drawings. We'll have an array of say 41 characters with a `*` at the 21st place and blanks everywhere else. Then we generate a random number which takes values -1 and 1 with equal probability. If it is -1 we go one character left, otherwise we go one character forward. If we hit an end, we always go away from the end."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def genm1p1() :\n",
      "    \"\"\"Generate -1 and 1 with equal probability.\"\"\"\n",
      "    r = random.randint(0,1)\n",
      "    return 2*r - 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def random_step(path, pm) :\n",
      "    \"\"\"Given a path and position, it gives a new \n",
      "    path with updated position\"\"\"\n",
      "    n = len(path)\n",
      "    # Find the current position, cp\n",
      "    cp = -1\n",
      "    hitl = 0\n",
      "    hitr = 0\n",
      "    for i in range(n) :\n",
      "        if path[i] == '*' :\n",
      "            cp = i\n",
      "    if cp == -1 :\n",
      "        print \"Cannot find current position.\"\n",
      "        retval = None\n",
      "    else :\n",
      "        if cp == n-1 :\n",
      "            np = cp - 1 # np : new position\n",
      "            hitr += 1\n",
      "        elif cp == 0 :\n",
      "            np = cp + 1\n",
      "            hitl += 1\n",
      "        else :\n",
      "            np = cp + pm\n",
      "        path[cp] = ' '\n",
      "        path[np] = '*'\n",
      "        retval = (path, hitl, hitr)\n",
      "    return retval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def displaypath(path) :\n",
      "    pathstr = \"\"\n",
      "    for i in range(len(path)) :\n",
      "        pathstr += path[i]\n",
      "    print '[' + pathstr + ']'\n",
      "    return None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def random_walk(len_path=41, no_steps=100, init_pos = -1) :\n",
      "    hitl = 0\n",
      "    hitr = 0\n",
      "    if init_pos < 0 :\n",
      "        init_pos = int(len_path/2 + 1)\n",
      "    \n",
      "    path = [' ']*len_path\n",
      "    path[init_pos] = '*'\n",
      "    displaypath(path)\n",
      "    for _ in range(no_steps) :\n",
      "        pm = genm1p1()\n",
      "        (path, hl, hr) = random_step(path, pm)\n",
      "        hitl += hl\n",
      "        hitr += hr\n",
      "        if path == None :\n",
      "            break\n",
      "        else :\n",
      "            displaypath(path)\n",
      "    print \"Left wall hits : %d; Right wall hits : %d.\" % (hitl, hitr)\n",
      "    return None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random_walk()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[                     *                   ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                    *                    ]\n",
        "[                     *                   ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                    *                    ]\n",
        "[                     *                   ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                    *                    ]\n",
        "[                     *                   ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                    *                    ]\n",
        "[                   *                     ]\n",
        "[                  *                      ]\n",
        "[                   *                     ]\n",
        "[                  *                      ]\n",
        "[                 *                       ]\n",
        "[                *                        ]\n",
        "[               *                         ]\n",
        "[              *                          ]\n",
        "[             *                           ]\n",
        "[            *                            ]\n",
        "[             *                           ]\n",
        "[              *                          ]\n",
        "[             *                           ]\n",
        "[            *                            ]\n",
        "[             *                           ]\n",
        "[            *                            ]\n",
        "[             *                           ]\n",
        "[            *                            ]\n",
        "[             *                           ]\n",
        "[              *                          ]\n",
        "[             *                           ]\n",
        "[              *                          ]\n",
        "[             *                           ]\n",
        "[              *                          ]\n",
        "[             *                           ]\n",
        "[              *                          ]\n",
        "[               *                         ]\n",
        "[              *                          ]\n",
        "[             *                           ]\n",
        "[            *                            ]\n",
        "[           *                             ]\n",
        "[          *                              ]\n",
        "[         *                               ]\n",
        "[          *                              ]\n",
        "[         *                               ]\n",
        "[          *                              ]\n",
        "[         *                               ]\n",
        "[          *                              ]\n",
        "[           *                             ]\n",
        "[          *                              ]\n",
        "[           *                             ]\n",
        "[          *                              ]\n",
        "[         *                               ]\n",
        "[          *                              ]\n",
        "[         *                               ]\n",
        "[          *                              ]\n",
        "[           *                             ]\n",
        "[          *                              ]\n",
        "[         *                               ]\n",
        "[        *                                ]\n",
        "[       *                                 ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[      *                                  ]\n",
        "[       *                                 ]\n",
        "[        *                                ]\n",
        "[       *                                 ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[      *                                  ]\n",
        "[       *                                 ]\n",
        "[      *                                  ]\n",
        "[       *                                 ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[    *                                    ]\n",
        "[   *                                     ]\n",
        "[    *                                    ]\n",
        "[     *                                   ]\n",
        "[      *                                  ]\n",
        "[     *                                   ]\n",
        "[    *                                    ]\n",
        "[     *                                   ]\n",
        "[    *                                    ]\n",
        "[     *                                   ]\n",
        "Left wall hits : 0; Right wall hits : 0.\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Monte Carlo Integration"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The method relies of the fact that if $x_1, x_2, \\dotsc, x_n$ are $n$ uniformly distributed random numbers between $a$ and $b$, then\n",
      "\n",
      "\\begin{equation}\n",
      "\\int_a^b f(x) dx \\simeq \\frac{(b - a)}{n} \\sum_{i=1}^n f(x_i)\n",
      "\\end{equation}\n",
      "\n",
      "Let us try this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mc_int(f, a, b, n) :\n",
      "    s = 0\n",
      "    for i in range(n) :\n",
      "        x = random.uniform(a, b)\n",
      "        s += f(x)\n",
      "    integral = (float(b-a)/n) * s\n",
      "    return integral"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print mc_int(lambda x : 2*x, 0, 10, 10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "99.719487342\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Vectorized version\n",
      "\n",
      "def mc_int_vec(f, a, b, n) :\n",
      "    x = numpy.random.uniform(a, b, n)\n",
      "    s = numpy.sum(f(x))\n",
      "    i = (float(b-a)/n) * s\n",
      "    return i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "totval = 0\n",
      "for i in range(100) :\n",
      "    intval = mc_int_vec(lambda x : 1 + 2*x, 0, 10, 10000)\n",
      "    totval += intval\n",
      "    #print intval, \":\",\n",
      "#print\n",
      "print \"Avg val = \", (totval/100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Avg val =  110.061918581\n"
       ]
      }
     ],
     "prompt_number": 20
    }
   ],
   "metadata": {}
  }
 ]
}