{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Método de Monte Carlo para o cálculo de Pi\n", "\n", "Considere um quadrante (setor circular) inscrito em um quadrado unitário. Dado que a relação de suas áreas é $\\pi / 4$, o valor de $\\pi$ pode ser aproximado pelo método de Monte Carlo, isto é, sorteando-se $N$ pontos uniformemente no primeiro quadrante e verificando a porcentagem de pontos que caem no círculo em relação ao primeiro quadrante. Isto é, se $N$ é o número de pontos sorteados e $C$ é o número de pontos que caem dentro do círculo nesse quadrante, então:\n", "\n", "$\\pi = 4C/N$\n", "\n", "Um dos problemas do método de Monte Carlo é a sua velocidade de convergência.\n", "\n", "Crie um programa Python que simule o método de Monte-Carlo para o cálculo do $\\pi$. O programa deve plotar a simulação e o erro na medida em função do número de pontos amostrados." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math\n", "\n", "def calculaErro(mcPi):\n", " return(math.sqrt((mcPi - math.pi)**2))\n", " \n", "def monteCarloPi(n):\n", " x = np.random.uniform(0,1,n)\n", " y = np.random.uniform(0,1,n)\n", " circleMask = np.sqrt(np.square(x) + np.square(y)) <= 1\n", " circleIndex = np.nonzero(circleMask)\n", " areaSquare = n\n", " areaCircle = np.sum(circleMask)\n", " mcPi = 4.0 * areaCircle / areaSquare\n", " return(mcPi)\n", "\n", "nmin = 10\n", "nmax = 10000\n", "step = 100\n", "PiMCM = []\n", "erroPiMCM = []\n", "for n in range(nmin,nmax,step):\n", " pitmp = monteCarloPi(n)\n", " PiMCM.append(pitmp)\n", " erroPiMCM.append(calculaErro(pitmp))\n", " \n", "plt.plot(PiMCM) \n", "plt.show()\n", "\n", "plt.plot(erroPiMCM)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }