Simulacao.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulação Estocástica: Introdução"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Francisco Aparecido Rodrigues, francisco@icmc.usp.br.<br>\n",
    "Universidade de São Paulo, São Carlos, Brasil.<br>\n",
    "https://sites.icmc.usp.br/francisco <br>\n",
    "Copyright: Creative Commons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para executar os códigos abaixo, você deve ter instalado um programa para executar códigos em Python. Você pode usar o Jupyter Notebook, que está presente no pacote Anacoda (https://www.anaconda.com/distribution/), ou o Spyder (https://docs.spyder-ide.org/installation.html), que também está no Anaconda. Para executar os comandos, basta copiar e colar os códigos abaixo em um desses editores de código. Installe a versão do Python maior do que 3.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nesta aula vamos aprender sobre simulação de experimentos probabilísticos. Vamos mostrar vários exemplos em que podemos calcular as probabilidades exatamente e comparar com simulações."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Geração de números aleatórios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O primeiro passo na simulação de processos estocásticos é a geração de números aleatórios, ou seja, gerar números no intervalo [0,1] onde todos os valores tem a mesma chance de ocorrerem. Maiores detalhes sobre o método que vamos  discutir podem ser vistos na Wikipedia: https://en.wikipedia.org/wiki/Linear_congruential_generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No método chamada Linear Congruential Generator, nós geramos uma sequência de números pseudo-aleatórios através da relação de recorrência:\n",
    "$$X_{n+1} = (aX_n + c) \\mod m$$\n",
    "onde $X_0$ é a semente, m, a e c são inteiros maiores do que zero. A sequência obtida satisfaz  $0 \\leq X_i \\leq m$. Para gerar o número no intervalo [0,1], usamos $$U_n = X_n/m.$$\n",
    "Vamos considerar uma exemplo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 11, 9, 3, 1, 11, 9, 3, 1, 11, 9, 3, 1, 11, 9, 3, 1, 11, 9, 3, 1]\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def random(Xi, a, c, m):\n",
    "    Xii = (a*Xi + c)%m\n",
    "    return Xii\n",
    "\n",
    "a = 11\n",
    "c = 0\n",
    "m = 16\n",
    "X0 = 1\n",
    "n = 20 # number of numbers to be generated\n",
    "Xi = X0\n",
    "X = [X0]\n",
    "for i in range(n):\n",
    "    Xi= random(Xi,a,c,m)\n",
    "    X.append(Xi)\n",
    "print(X)\n",
    "plt.hist(X, bins='auto')  \n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notamos que a sequência é periódica, sendo que $[1, 11, 9, 3]$ se repete. Ou seja, não temos um bom gerador de números aleatórios, pois podemos prever o próximo número se descobrir a sequência. Uma possível solução para resolver esse problema é adotar valores maiores para as constantes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 7**5\n",
    "c = 0\n",
    "m = 2**31 - 1\n",
    "X0 = 1\n",
    "n = 500 # number of numbers to be generated\n",
    "Xi = X0\n",
    "X = [X0]\n",
    "for i in range(n):\n",
    "    Xi= random(Xi,a,c,m)\n",
    "    X.append(Xi/m)\n",
    "#print(X)\n",
    "plt.hist(X, bins='auto')  \n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que agora a frequência em que os números ocorrem é praticamente a mesma."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Retirando uma bola em uma urna"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para começarmos a enteder a simulação de processos estocásticos, vamos simular a retirada de uma bola de uma urna com reposição, ou seja, a bola retirada é sempre recolocada na urna antes da próxima retirada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos supor que temos uma urna com 6 bolas brancas e 4 pretas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Urna: ['B', 'B', 'B', 'B', 'B', 'B', 'P', 'P', 'P', 'P']\n"
     ]
    }
   ],
   "source": [
    "urna = ['B','B','B','B','B','B','P','P','P','P']\n",
    "print('Urna:',urna)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para selecinarmos uma bola, basta selecionarmos uma posição no vetor e verificar a respectiva bola. Vamos fazer essa retirada 100 vezes e verificar quantas vezes retiramos uma bola branca."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fração de vezes que saiu uma bola branca: 0.64\n"
     ]
    }
   ],
   "source": [
    "import random # biblioteca para gerar números aleatórios\n",
    "n = 0 # numero de retiradas de bolas brancas\n",
    "nsim = 100 # numero de experimentos\n",
    "for i in range(0,nsim):\n",
    "    posicao = random.randint(0,len(urna)-1)\n",
    "    if(urna[posicao] == 'B'):\n",
    "        n = n + 1        \n",
    "print('Fração de vezes que saiu uma bola branca:', n/nsim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valor teórico da probabilidade: 0.6\n"
     ]
    }
   ],
   "source": [
    "# vamos calcular o valor teórica da probabilidade contanto o número de bolas brancas na urna\n",
    "valor_teorico = 0\n",
    "for bola in urna:\n",
    "    if (bola == 'B'):\n",
    "        valor_teorico = valor_teorico + 1\n",
    "valor_teorico = valor_teorico/len(urna)\n",
    "print('Valor teórico da probabilidade:', valor_teorico)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou seja, vemos que é próximo do valor teórico: 6/10. Se aumentarmos o número de experimentos, vamos mostrar os resultados em um gráfico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random # biblioteca para gerar números aleatórios\n",
    "import numpy as np # biblioteca numérica numpy\n",
    "import matplotlib.pyplot as plt # biblioteca necessária para mostrar os gráficos\n",
    "\n",
    "\n",
    "vp = [] # lista que armazena a fração de ocorrências em função do número de simulações nsim\n",
    "vsim = [] # armazena o número de simulações\n",
    "Nmax = 1000 # numero maximo de simulacoes\n",
    "for nsim in np.arange(1,Nmax,10):\n",
    "    n = 0 # numero de retiradas de bolas brancas\n",
    "    for i in range(0,nsim):\n",
    "        posicao = random.randint(0,len(urna)-1)\n",
    "        if(urna[posicao] == 'B'):\n",
    "            n = n + 1        \n",
    "    vp.append(n/nsim)\n",
    "    vsim.append(nsim)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.plot(vsim, vp, linestyle='-', color=\"blue\", linewidth=2,label = 'Valor simulado')\n",
    "plt.axhline(y=valor_teorico, color='r', linestyle='--', label = 'Valor teorico')\n",
    "plt.ylabel(\"Fração de bolas brancas\", fontsize=20)\n",
    "plt.xlabel(\"Numero de experimentos\", fontsize=20)\n",
    "plt.xlim([0.0, Nmax])\n",
    "plt.ylim([0.0, 1.0])\n",
    "plt.legend()\n",
    "plt.show(True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou seja, vemos que o valor converge para a probabilide esperada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Exercício**: Considere agora uma urna com 14 bolas brancas e 6 pretas. Repita o procedimento acima e verifique se a estimação é correta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lançando uma moeda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos simular o lançamento de uma moeda. Para isso, precisamos definir uma regra para escolher se saiu cara ou coroa. Para entendermos melhor como definir essa regra, notem que no exemplo anterior, ordenamos as bolas em um vetor. Essa ordenação não faz a menor diferença no exemplo anterior, pois a não consideramos. Se consideramos a ordenação, a regra poderia ser: se a posição no vetor é menor ou igual a 6, então a bola é branca. Caso contrário, é preta. Ou seja, podemos usar essa regra para definir qual dos valores vamos selecionar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No caso de uma moeda, vamos supor que $p$ é a chance de sair cara. Então, a regra pode ser: se o número sorteado em [0,1] for menor do que $p$, então saiu cara. Caso contrário, saiu coroa. Vamos realizar um exmperimento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 0.6 # probabilidade de sair cara"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/franciscoaparecidorodrigues/Anaconda3/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:9: RuntimeWarning: invalid value encountered in long_scalars\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vp = [] # lista que armazena a fração de ocorrências em função do número de simulações nsim\n",
    "vsim = [] # armazena o número de simulações\n",
    "Nmax = 1000 # numero maximo de simulacoes\n",
    "for nsim in np.arange(0,Nmax,10):\n",
    "    nhead = 0 # numero de caras\n",
    "    for i in range(1,nsim):\n",
    "        if(np.random.uniform() < p):\n",
    "            nhead = nhead + 1        \n",
    "    vp.append(nhead/nsim)\n",
    "    vsim.append(nsim)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.plot(vsim, vp, linestyle='-', color=\"blue\", linewidth=2,label = 'Valor simulado')\n",
    "plt.axhline(y=p, color='r', linestyle='--', label = 'Valor teorico')\n",
    "plt.ylabel(\"Fração de caras\", fontsize=20)\n",
    "plt.xlabel(\"Numero de experimentos\", fontsize=20)\n",
    "plt.xlim([0.0, Nmax])\n",
    "plt.ylim([0.0, 1.0])\n",
    "plt.legend()\n",
    "plt.show(True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Exercício**: Varie a probabilidade de sair cara e verifique como muda o gráfico acima."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Calculando o valor de $\\pi$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Para calcular o valor e $\\pi$, vamos considerar um quadrado de raio 2R que contém um círculo de raio R, conforme a figura abaixo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"estimating-pi-monte-carlo-method.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Selecionando posições aleatórias nessa região e incluindo pontos, conforme exemplificado na figura, temos que alguns pontos caem dentro do círculo (pontos vermelhos), enquanto que outros ficam fora (pontos em azul). Inserindo um grande número de pontos de forma aleatória, temos que:<br>\n",
    "**o número de pontos dentro do círculo/número de pontos gerados = área do círculo/área do quadrado.**<br>\n",
    "Ou seja, o valor de $\\pi$:<br>\n",
    "o número de pontos dentro do círculo/número de pontos gerados = $\\pi R^2$/$4R^2$<br>\n",
    "Logo:<br>\n",
    "$\\pi$ = 4* o número de pontos dentro do círculo/ número de pontos gerados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of pi: 3.196\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "count_inside = 0\n",
    "for i in np.arange(0,n):\n",
    "    x = np.random.uniform(0,1)\n",
    "    y = np.random.uniform(0,1)\n",
    "    if( x**2 + y**2 < 1):\n",
    "        count_inside = count_inside + 1\n",
    "pi = 4*count_inside/n\n",
    "print(\"Value of pi:\", pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Podemos analisar como essa aproximação muda com o número de pontos gerados."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 500\n",
    "vpi = []\n",
    "vpi_std = []\n",
    "vn = []\n",
    "for n in np.arange(1,N, 10):\n",
    "    aux = []\n",
    "    for s in np.arange(0,10):\n",
    "        count_inside = 0\n",
    "        for i in np.arange(0,n):\n",
    "            x = np.random.uniform(0,1)\n",
    "            y = np.random.uniform(0,1)\n",
    "            if( x**2 + y**2 < 1):\n",
    "                count_inside = count_inside + 1\n",
    "        pi = 4*count_inside/n\n",
    "        aux.append(pi)\n",
    "    vpi.append(np.mean(aux))\n",
    "    vpi_std.append(np.std(aux))\n",
    "    vn.append(n)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "#plt.plot(vn, vpi, linestyle='-', color=\"blue\", linewidth=2.5)\n",
    "plt.errorbar(vn, vpi, yerr=vpi_std, fmt='.-b')\n",
    "plt.axhline(y=np.pi, color='r', linestyle='-')\n",
    "plt.xlabel(\"Number of simulations\", fontsize=20)\n",
    "plt.ylabel(\"Estimated pi\", fontsize=20)\n",
    "plt.show(True)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Exercício:** Verifique quantas simulações são necessárias para você obter um valor que seja 99% próximo de $\\pi$. Dica: use o valor conhecido de $\\pi$ e faça um gráfico da diferença entre o valor obtido e o real em função do número de pontos sorteados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Semente do gerados de número aleatórios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notem que a semente gera uma sequência de número aleatórios e a sequência se repete quando reiniciamos a semente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Primeira sequencia:\n",
      "0.5163986277024462\n",
      "0.5706675868681398\n",
      "0.028474226478096942\n",
      "0.17152165622510307\n",
      "0.6852769816973125\n",
      "0.8338968626360765\n",
      "0.3069662196722378\n",
      "0.8936130796833973\n",
      "0.7215438617683047\n",
      "0.18993895420479678\n",
      "\n",
      "\n",
      "Segunda sequencia:\n",
      "0.5163986277024462\n",
      "0.5706675868681398\n",
      "0.028474226478096942\n",
      "0.17152165622510307\n",
      "0.6852769816973125\n",
      "0.8338968626360765\n",
      "0.3069662196722378\n",
      "0.8936130796833973\n",
      "0.7215438617683047\n",
      "0.18993895420479678\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "print(\"Primeira sequencia:\")\n",
    "np.random.seed(101)\n",
    "for i in np.arange(0,10):\n",
    "    n = np.random.uniform()\n",
    "    print(n)\n",
    "print('\\n')\n",
    "\n",
    "print(\"Segunda sequencia:\")\n",
    "np.random.seed(101)\n",
    "for i in np.arange(0,10):\n",
    "    n = np.random.uniform()\n",
    "    print(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se não reinicarmos a semente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Primeira sequencia:\n",
      "0.5163986277024462\n",
      "0.5706675868681398\n",
      "0.028474226478096942\n",
      "0.17152165622510307\n",
      "0.6852769816973125\n",
      "0.8338968626360765\n",
      "0.3069662196722378\n",
      "0.8936130796833973\n",
      "0.7215438617683047\n",
      "0.18993895420479678\n",
      "\n",
      "\n",
      "Segunda sequencia:\n",
      "0.5542275911247871\n",
      "0.3521319540266141\n",
      "0.18189240266007867\n",
      "0.7856017618643588\n",
      "0.9654832224119693\n",
      "0.2323536618147607\n",
      "0.08356143366334368\n",
      "0.6035484222912185\n",
      "0.7289927572876178\n",
      "0.2762388284972628\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "print(\"Primeira sequencia:\")\n",
    "np.random.seed(101)\n",
    "for i in np.arange(0,10):\n",
    "    n = np.random.uniform()\n",
    "    print(n)\n",
    "print('\\n')\n",
    "\n",
    "print(\"Segunda sequencia:\")\n",
    "for i in np.arange(0,10):\n",
    "    n = np.random.uniform()\n",
    "    print(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Para pensar:** Como você verificaria se esse números gerados são realmente aleatórios?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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