Estimating pi with simulation

Estimating pi with simulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# On how to engage learning through programming and simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "In this post, I want to present how we can engage student and long life learners to learn complicated concepts with some programing and simulation.\n",
    "\n",
    "We all hear from primary school about $\\pi$ but mostly nobody told us what that value represent and how we can calculate it!\n",
    "\n",
    "Look at at below picture and guess how we can appriximately do calculate $\\pi$ ? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Counting number of blue points and red points and then\n",
    "\n",
    "$\\pi \\approx$ 4 $\\times$ $\\frac{number  of  blue  points}{number of red points + number of blue points}$\n",
    "\n",
    "Could you explain why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Plot of algorithm to be used](Pi_statistisch.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We write Python code to generate random points in square of length 1 to estimate $\\pi$. We plot how accuracy of calculation improve when number of points $n$ increase.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "imports required librairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from random import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "generating 1000 random numbers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Fixing random state for reproducibility\n",
    "np.random.seed(19680801)\n",
    "\n",
    "N = 1000\n",
    "r0 = 1\n",
    "x = 1 * np.random.rand(N)\n",
    "y = 1 * np.random.rand(N)\n",
    "#area = (20 * np.random.rand(N))**2  # 0 to 10 point radii\n",
    "#c = np.sqrt(area)\n",
    "r = np.sqrt(x ** 2 + y ** 2)\n",
    "#c1 = np.ma.masked_where(r < r0, area)\n",
    "#c2= np.ma.masked_where(r >= r0, area)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "plotting points, circle and square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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l5zHiHoKKl3XwCHdQfjLFJE9EjWGecK2I/NJOtrzHjhwcoQMPH6C1V9k7bTa/ajMd/+5x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\nYDAYahAj7gaDwVCD/H8wSoJsV0y4TwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "theta = np.arange(0, np.pi / 2, 0.01)\n",
    "plt.plot(r0 * np.cos(theta), r0 * np.sin(theta), c = 'm')\n",
    "#plt.grid()\n",
    "plt.hlines([0,1],0,1,alpha = 0.1)\n",
    "plt.vlines([0,1],0,1,alpha = 0.1)\n",
    "#plt.axis('off')\n",
    "#plt.show()\n",
    "for i in range(len(r)):\n",
    "    if r[i]>r0:\n",
    "        plt.scatter(x[i], y[i], c= 'r',s=1)\n",
    "        #time.sleep(0.01)\n",
    "    else:\n",
    "        plt.scatter(x[i], y[i], c= 'b',s=1)\n",
    "        #time.sleep(0.01)\n",
    "    #plt.show()\n",
    "# Show the boundary between the regions:\n",
    "\n",
    "#plt.Circle((0, 0), 1, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to count number of blue points, points where $x^2 + y^2 \\leqslant 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = [i for _ in r if _<= 1.0000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "781"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.124"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4* len(t)/len(r) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is in it intresting?\n",
    "\n",
    "What we can do more?\n",
    "\n",
    "Lets try to see result for 30 number of $n$ starting 4 and ending 10,000,000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hits : 1, trials: 4, estimate pi = 2.0000\n",
      "hits : 270569, trials: 344831, estimate pi = 3.1405\n",
      "hits : 541384, trials: 689658, estimate pi = 3.1406\n",
      "hits : 813118, trials: 1034486, estimate pi = 3.1401\n",
      "hits : 1082250, trials: 1379313, estimate pi = 3.1409\n",
      "hits : 1353879, trials: 1724141, estimate pi = 3.1426\n",
      "hits : 1624575, trials: 2068968, estimate pi = 3.1425\n",
      "hits : 1896013, trials: 2413796, estimate pi = 3.1417\n",
      "hits : 2167855, trials: 2758623, estimate pi = 3.1402\n",
      "hits : 2437830, trials: 3103451, estimate pi = 3.1410\n",
      "hits : 2709926, trials: 3448278, estimate pi = 3.1412\n",
      "hits : 2979078, trials: 3793105, estimate pi = 3.1412\n",
      "hits : 3251268, trials: 4137933, estimate pi = 3.1423\n",
      "hits : 3521662, trials: 4482760, estimate pi = 3.1410\n",
      "hits : 3791750, trials: 4827588, estimate pi = 3.1417\n",
      "hits : 4062262, trials: 5172415, estimate pi = 3.1426\n",
      "hits : 4332207, trials: 5517243, estimate pi = 3.1417\n",
      "hits : 4604405, trials: 5862070, estimate pi = 3.1422\n",
      "hits : 4875946, trials: 6206898, estimate pi = 3.1416\n",
      "hits : 5146525, trials: 6551725, estimate pi = 3.1424\n",
      "hits : 5416219, trials: 6896552, estimate pi = 3.1412\n",
      "hits : 5688434, trials: 7241380, estimate pi = 3.1416\n",
      "hits : 5956796, trials: 7586207, estimate pi = 3.1423\n",
      "hits : 6227996, trials: 7931035, estimate pi = 3.1425\n",
      "hits : 6499109, trials: 8275862, estimate pi = 3.1422\n",
      "hits : 6771243, trials: 8620690, estimate pi = 3.1423\n",
      "hits : 7043284, trials: 8965517, estimate pi = 3.1419\n",
      "hits : 7310967, trials: 9310345, estimate pi = 3.1410\n",
      "hits : 7585558, trials: 9655172, estimate pi = 3.1423\n",
      "hits : 7854343, trials: 10000000, estimate pi = 3.1410\n"
     ]
    }
   ],
   "source": [
    "trials = list(np.linspace(4,10**7, 30))  # different number of trials\n",
    "pi = []\n",
    "\n",
    "def mc_multiple_runs(trials, hits = 0):\n",
    "    '''\n",
    "    (float, int) -> (float)\n",
    "    This function returns the number of hits you get for each monte carlo run\n",
    "    '''\n",
    "    for i in range(int(trials)):\n",
    "        x, y = random() , random()  # generate random x,y in (0,1] at each run \n",
    "\n",
    "        if x**2 + y**2 < 1 :  # defines the edge of the quadrant df['r']<1:#\n",
    "           hits = hits + 1\n",
    "    return float(hits)\n",
    "\n",
    "for i in trials:\n",
    "    pi.append(4*(mc_multiple_runs(i)/i)) \n",
    "    print('hits : %d, trials: %d, estimate pi = %1.4F' %(mc_multiple_runs(i), i, 4*(mc_multiple_runs(i)/i) ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot how estimation of $\\pi$ vary over $n$, when n increase?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GPqTG6eo5tNhov2ZmVeVJDo9Juhh4D/D/JI3KufwWp70dtt4ahg9vdiRmZluW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\nBzMz68XJwczMevn/bInXTWz6DbAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1038851704923003 0.20498862986380842\n"
     ]
    },
    {
     "data": {
      "image/png": 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2iUDSx9Ljq8oLx8zMytZpj+AwSRsBp5QVjJmZla/TyeKLyFoP3VLSvWTtDMXYY0RsU0J8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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot graphs\n",
    "plt.plot(trials, pi, 'bo-')\n",
    "plt.title('Estimating the value of $\\pi$ via Monte Carlo')\n",
    "plt.xlabel('# of Trials = number of points')\n",
    "plt.ylabel('Estimated value of $\\pi$')\n",
    "#plt.ylim(3.11,3.17)\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.hist(pi, bins = np.linspace(3.12,3.16,30), histtype= 'stepfilled', color='blue',alpha= 0.3)\n",
    "plt.title('Estimating the value of $\\pi$ via Monte Carlo')\n",
    "plt.xlabel('Estimated value of $\\pi$')\n",
    "plt.ylabel('Trials = number of points')\n",
    "plt.grid()\n",
    "#plt.vlines(np.mean(pi),0,12,colors='b',label= 'Mean value')\n",
    "#plt.hlines(5,np.mean(pi)-np.std(pi),np.mean(pi)+np.std(pi),colors='r',label= 'Mean value')\n",
    "plt.vlines(np.pi,0,12,colors='m',label= 'Exact value')\n",
    "#plt.xlim(3.13,3.15)\n",
    "print(np.mean(pi),np.std(pi))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.139956"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 1000000\n",
    "df = pd.DataFrame(np.random.rand(N, 2), columns = ['x','y']) \n",
    "df['r'] = np.sqrt(df['x']**2 + df['y']**2)\n",
    "df[df.r <=1].shape[0]/N * 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 4.0\n",
      "10 2.8\n",
      "100 3.08\n",
      "1000 3.04\n",
      "10000 3.1204\n",
      "100000 3.14436\n",
      "1000000 3.138816\n",
      "10000000 3.1417424\n",
      "100000000 3.14159432\n"
     ]
    }
   ],
   "source": [
    "temp = pd.DataFrame()\n",
    "my_list = []\n",
    "for n in [10**i for i in range(0,9)]:#list(np.linspace(10,10**8, 30)):\n",
    "    #print(int(np.floor(n)),estimate_pi(int(np.floor(n))))\n",
    "    print(n, estimate_pi(n))\n",
    "    my_list.append(estimate_pi(n))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.145564"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def estimate_pi(n = 1000000):\n",
    "    df = pd.DataFrame(np.random.rand(n, 2), columns = ['x','y']) \n",
    "    df['r'] = np.sqrt(df['x']**2 + df['y']**2)\n",
    "    return df[df.r <=1].shape[0]/n * 4\n",
    "estimate_pi()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MmR1MU/YwAQAAAAxDg4mlZd6YFvJCLVmhhbxQS1ZoIS/UkhX6pMEEAAAAwEyWZgfTvXvJ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\n6QTCqaFejwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot graphs\n",
    "plt.figure(figsize=(20,20))\n",
    "plt.plot([10**i for i in range(0,9)], my_list, 'b-o')\n",
    "plt.title('Estimating the value of $\\pi$ via Monte Carlo')\n",
    "plt.xlabel('# of Trials')\n",
    "plt.xscale('log')\n",
    "plt.ylabel('Estimated value of $\\pi$')\n",
    "#plt.ylim(3.11,3.17)\n",
    "plt.hlines(np.pi,1,10**8,colors='r',label= 'Mean value')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AGGwKT/QtM57oB7JCG/JCU7JCG/JCU7JCG/JCt4z1egGwJ4cckmzf3utVAAAA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\n4PcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot graphs\n",
    "plt.figure(figsize=(20,20))\n",
    "plt.plot([10**i for i in range(0,9)], my_list, 'b-o',label= 'Simulation', alpha = 0.5)\n",
    "plt.title('Estimating the value of $\\pi$ via Monte Carlo\\n Closer view')\n",
    "plt.xlabel('# of Trials')\n",
    "plt.xscale('log')\n",
    "plt.ylabel('Estimated value of $\\pi$')\n",
    "plt.ylim(np.pi-0.2,np.pi+0.2)\n",
    "plt.hlines(np.pi,1,10**8,colors='r',label= 'Exact value')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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