| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.rng.examples.quadrature; |
| |
| import org.apache.commons.rng.UniformRandomProvider; |
| import org.apache.commons.rng.simple.RandomSource; |
| |
| /** |
| * Computation of \( \pi \) using Monte-Carlo integration. |
| * |
| * The computation estimates the value by computing the probability that |
| * a point \( p = (x, y) \) will lie in the circle of radius \( r = 1 \) |
| * inscribed in the square of side \( r = 1 \). |
| * The probability could be computed by \[ area_{circle} / area_{square} \], |
| * where \( area_{circle} = \pi * r^2 \) and \( area_{square} = 4 r^2 \). |
| * Hence, the probability is \( \frac{\pi}{4} \). |
| * |
| * The Monte Carlo simulation will produce \( N \) points. |
| * Defining \( N_c \) as the number of point that satisfy \( x^2 + y^2 \le 1 \), |
| * we will have \( \frac{N_c}{N} \approx \frac{\pi}{4} \). |
| */ |
| public class ComputePi extends MonteCarloIntegration { |
| /** Expected number of arguments. */ |
| private static final int EXPECTED_ARGUMENTS = 2; |
| /** Domain dimension. */ |
| private static final int DIMENSION = 2; |
| |
| /** |
| * @param rng RNG. |
| */ |
| public ComputePi(UniformRandomProvider rng) { |
| super(rng, DIMENSION); |
| } |
| |
| /** |
| * Program entry point. |
| * |
| * @param args Arguments. |
| * The order is as follows: |
| * <ol> |
| * <li> |
| * Number of random 2-dimensional points to generate. |
| * </li> |
| * <li> |
| * {@link RandomSource Random source identifier}. |
| * </li> |
| * </ol> |
| */ |
| public static void main(String[] args) { |
| if (args.length != EXPECTED_ARGUMENTS) { |
| throw new IllegalStateException("Require arguments: [points] [RNG name]"); |
| } |
| |
| final long numPoints = Long.parseLong(args[0]); |
| final RandomSource randomSource = RandomSource.valueOf(args[1]); |
| |
| final ComputePi piApp = new ComputePi(randomSource.create()); |
| final double piMC = piApp.compute(numPoints); |
| |
| //CHECKSTYLE: stop all |
| System.out.printf("After generating %d random numbers, the error on |𝛑 - %s| is %s%n", |
| DIMENSION * numPoints, piMC, Math.abs(piMC - Math.PI)); |
| //CHECKSTYLE: resume all |
| } |
| |
| /** |
| * @param numPoints Number of random points to generate. |
| * @return the approximate value of pi. |
| */ |
| public double compute(long numPoints) { |
| return 4 * integrate(numPoints); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected boolean isInside(double... rand) { |
| final double r2 = rand[0] * rand[0] + rand[1] * rand[1]; |
| return r2 <= 1; |
| } |
| } |