Lecture06.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monte Carlo Techniques"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: coin flip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Heads\n",
      "Tails\n",
      "Heads\n",
      "Heads\n",
      "Heads\n",
      "Heads\n",
      "Heads\n",
      "Tails\n",
      "Tails\n",
      "Heads\n"
     ]
    }
   ],
   "source": [
    "# standard preamble\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "outcomes = ('Heads','Tails')\n",
    "\n",
    "def flip():\n",
    "    if np.random.random() > 0.5:\n",
    "        return outcomes[1]\n",
    "    \n",
    "    return outcomes[0]\n",
    "\n",
    "for i in range(10):\n",
    "    print flip()\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Example: dice roll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "2\n",
      "6\n",
      "3\n",
      "1\n",
      "4\n",
      "5\n",
      "5\n",
      "1\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "def dice():\n",
    "    return int(np.random.random()*6)+1\n",
    "\n",
    "for i in range(10):\n",
    "    print dice()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: deck of cards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['4d', 'Ts', '7d', 'Jh', '3h']\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import itertools\n",
    "SUITS = 'cdhs'\n",
    "RANKS = '23456789TJQKA'\n",
    "DECK = tuple(''.join(card) for card in itertools.product(RANKS, SUITS))\n",
    "hand = random.sample(DECK, 5)\n",
    "print hand"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Linear Congruent Generator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33031656 198186408 957896856 65108986 127826865 \n",
      "0 3 2 5 4 7 6 1 0 3 2 5 4 7 6 1 0 3 2 5 \n"
     ]
    }
   ],
   "source": [
    "myRandomSeed = 504\n",
    "def myRandom(a=65539, b=0, c=int(2**31-1)):\n",
    "    global myRandomSeed\n",
    "    x = (a*myRandomSeed+b) % c\n",
    "    myRandomSeed = x\n",
    "    return x\n",
    "\n",
    "out = \"\"\n",
    "for i in range(5):\n",
    "    out += str(myRandom())\n",
    "    out += \" \"\n",
    "    \n",
    "print out\n",
    "    \n",
    "out = \"\"\n",
    "myRandomSeed = 1\n",
    "for i in range(20):\n",
    "    out += str(myRandom(a=5, b=3, c=8))\n",
    "    out += \" \"\n",
    "\n",
    "print out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Python random numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "# integer random number between [a..b]\n",
    "print np.random.randint(0,2**32-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.438199656262\n"
     ]
    }
   ],
   "source": [
    "# float random number between [0..1)\n",
    "print np.random.random()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.87384900137\n"
     ]
    }
   ],
   "source": [
    "# float random number between [a..b)\n",
    "print np.random.uniform(5,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g\n"
     ]
    }
   ],
   "source": [
    "# Choose a random element\n",
    "print np.random.choice(['a','b','c','d','e','f','g','h','i','j'])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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c33cxPXoF8HCSW7rbGjuT/FzfRS0DvwX8bd9F9KWqHgX+DPgvBl93fqyqvtRvVb35FvDO\n7pbGauBazvyqeIteWlUnAKrqv4GXjhqwHEL/yu7X+GuBDya5qu+CerISeCvwF935+BGDX92alWQV\n8KvA5/qupS/d7YuPAOuBXwAuSvK+fqvqR1UdAP4EuBO4A7gPONVrUcvPyG/m9B76VXW8+/kQg/u2\nrd7XPwocqaqvdft/z+BFoGXvAb7eXRutejuwt6oe6W5p/APwiz3X1JuquqWq3l5Vm4DHgIM9l9S3\nE93/c0aSS4H/GTWg19BPsjrJRd3jC4FrGPwK15zuV7QjSV7THboa+I8eS1oOttHwrZ3Od4CNSV6Q\nJAyuiyY/4AdIckn3cx3wa8Bn+61o5sKZf5p7O/B73ePfBb4wcoI+v6ef5BUM3t0Xg9sbt1bVH/dW\nUM+SvAn4G2AV8H3guqp6vN+q+tHdsz0MvLKq/rfvevqU5A8Z/MM+xeCWxge6/7W2OUm+DLwEOAl8\npKru6rei2UnyWWAT8PPACeAm4B8Z3P58GYN/L79ZVY8tOo9/nCVJ7ej9nr4kaXYMfUlqiKEvSQ0x\n9CWpIYa+JDXE0Jekhhj6ktQQQ1+SGvL/86+7qww/EvIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b0aa7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot distribution\n",
    "plt.hist(np.random.uniform(5,10,size=10000000),50,normed=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Python random number generators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V1b6qunlw/8f0C+vULjPBfW/2FwF/3XUWgMEI7xeq6v0AVXVvVf2o41g/An4CbExyPPBg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b64e110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.random.exponential(scale=2,size=10000),50,normed=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115fb6e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.random.standard_cauchy(size=100),20,normed=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b64e790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.random.triangular(5,10,15,size=1000000),50,normed=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}