Exercise29.10.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# probability density\n",
    "\n",
    "def Prob(x):\n",
    "    if x < 0:\n",
    "        return 0\n",
    "    elif x < 1:\n",
    "        return 10\n",
    "    elif x <11 :\n",
    "        return 1\n",
    "    else :\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEACAYAAACj0I2EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104e63390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# probability density plot \n",
    "\n",
    "x = np.arange(-2.0, 13.0, 0.1)\n",
    "P=[Prob(t) for t in x]\n",
    "y = np.array(P)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# initially start between 0 and 1 (peak)\n",
    "x0 = random.random()\n",
    "\n",
    "# decide the size of the step. Not too small, not too big. \n",
    "w = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = random.random()\n",
    "u = Prob(x0)*random.random()\n",
    "\n",
    "xl = x0 - r * w\n",
    "\n",
    "while Prob(xl) > u:\n",
    "    xl = xl - w\n",
    "\n",
    "    \n",
    "xr = x0 + (1-r)*w\n",
    "\n",
    "while Prob(xr) > u:\n",
    "    xr = xr + w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.28670603780003123, 1.2132939621999688)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xl, xr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# next x between xl and xr\n",
    "x1= random.uniform(xl,xr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Prob(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.333025369265403"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# initially start between 0 and 1 (peak)\n",
    "\n",
    "x0 = random.random()\n",
    "\n",
    "# decide the size of the step. Not too small, not too big. \n",
    "w = 0.5\n",
    "\n",
    "u = Prob(x0)*random.random()\n",
    "\n",
    "cond = True\n",
    "r = random.random()\n",
    "xl = x0-r*w\n",
    "xr = x0 + (1-r)*w\n",
    "\n",
    "while cond: \n",
    "    while Prob(xl) > u:\n",
    "        xl = xl - w\n",
    "        \n",
    "    while Prob(xr) > u:\n",
    "        xr = xr + w\n",
    "        \n",
    "    x1= random.uniform(xl,xr)\n",
    "        \n",
    "    if Prob(x1) > u :\n",
    "        cond = False\n",
    "    else :\n",
    "        if x1>x0:\n",
    "            xr = x1\n",
    "        else:\n",
    "            xl=x1\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def process(x0, w):\n",
    "\n",
    "\n",
    "    # decide the size of the step. Not too small, not too big. \n",
    "    w = 0.5\n",
    "\n",
    "    u = Prob(x0)*random.random()\n",
    "\n",
    "    cond = True\n",
    "    r = random.random()\n",
    "    xl = x0-r*w\n",
    "    xr = x0 + (1-r)*w\n",
    "\n",
    "    while cond: \n",
    "        while Prob(xl) > u:\n",
    "            xl = xl - w\n",
    "        \n",
    "        while Prob(xr) > u:\n",
    "            xr = xr + w\n",
    "        \n",
    "        x1= random.uniform(xl,xr)\n",
    "        \n",
    "        if Prob(x1) > u :\n",
    "            cond = False\n",
    "        else :\n",
    "            if x1>x0:\n",
    "                xr = x1\n",
    "            else:\n",
    "                xl=x1\n",
    "    return x1\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02932225628335429"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "process(0.5, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 6.72393443112\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "# initially start between 0 and 1 (peak)\n",
    "\n",
    "x0 = 0.5\n",
    "\n",
    "turn = 0 \n",
    "while x0 < 1:\n",
    "    turn = turn + 1\n",
    "    x0 = process(x0, 0.5)\n",
    "    \n",
    "print turn, x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def numofturns(x0, w):\n",
    "    turn = 0 \n",
    "    while x0 < 1:\n",
    "        turn = turn + 1\n",
    "        x0 = process(x0, 0.5)\n",
    "    \n",
    "    return turn\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "list =[]\n",
    "for i in range(10000):\n",
    "    list = list+ [numofturns(random.random(),0.5)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEACAYAAABRQBpkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMkqb1AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1057df3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.932499999999999"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.average(list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def numofturns2(x0, w):\n",
    "    turn = 0 \n",
    "    while x0 > 1:\n",
    "        turn = turn + 1\n",
    "        x0 = process(x0, 0.5)\n",
    "    \n",
    "    return turn\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "list2 =[]\n",
    "for i in range(10000):\n",
    "    list2 = list2 + [numofturns2(random.uniform(1,11),0.5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEACAYAAABRQBpkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1057d5b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list2) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.1015"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.average(list2)"
   ]
  },
  {
   "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}