| /* |
| * 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.sampling.distribution; |
| |
| import org.apache.commons.rng.UniformRandomProvider; |
| |
| /** |
| * Sampling from the <a href="http://mathworld.wolfram.com/GammaDistribution.html">Gamma distribution</a>. |
| * <ul> |
| * <li> |
| * For {@code 0 < shape < 1}: |
| * <blockquote> |
| * Ahrens, J. H. and Dieter, U., |
| * <i>Computer methods for sampling from gamma, beta, Poisson and binomial distributions,</i> |
| * Computing, 12, 223-246, 1974. |
| * </blockquote> |
| * </li> |
| * <li> |
| * For {@code shape >= 1}: |
| * <blockquote> |
| * Marsaglia and Tsang, <i>A Simple Method for Generating |
| * Gamma Variables.</i> ACM Transactions on Mathematical Software, |
| * Volume 26 Issue 3, September, 2000. |
| * </blockquote> |
| * </li> |
| * </ul> |
| */ |
| public class AhrensDieterMarsagliaTsangGammaSampler |
| extends SamplerBase |
| implements ContinuousSampler { |
| /** The shape parameter. */ |
| private final double theta; |
| /** The alpha parameter. */ |
| private final double alpha; |
| /** Gaussian sampling. */ |
| private final BoxMullerGaussianSampler gaussian; |
| |
| /** |
| * @param rng Generator of uniformly distributed random numbers. |
| * @param alpha Alpha parameter of the distribution. |
| * @param theta Theta parameter of the distribution. |
| */ |
| public AhrensDieterMarsagliaTsangGammaSampler(UniformRandomProvider rng, |
| double alpha, |
| double theta) { |
| super(rng); |
| this.alpha = alpha; |
| this.theta = theta; |
| gaussian = new BoxMullerGaussianSampler(rng, 0, 1); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double sample() { |
| if (theta < 1) { |
| // [1]: p. 228, Algorithm GS. |
| |
| while (true) { |
| // Step 1: |
| final double u = nextDouble(); |
| final double bGS = 1 + theta / Math.E; |
| final double p = bGS * u; |
| |
| if (p <= 1) { |
| // Step 2: |
| |
| final double x = Math.pow(p, 1 / theta); |
| final double u2 = nextDouble(); |
| |
| if (u2 > Math.exp(-x)) { |
| // Reject. |
| continue; |
| } else { |
| return alpha * x; |
| } |
| } else { |
| // Step 3: |
| |
| final double x = -1 * Math.log((bGS - p) / theta); |
| final double u2 = nextDouble(); |
| |
| if (u2 > Math.pow(x, theta - 1)) { |
| // Reject. |
| continue; |
| } else { |
| return alpha * x; |
| } |
| } |
| } |
| } |
| |
| // Now theta >= 1. |
| |
| final double d = theta - 0.333333333333333333; |
| final double c = 1 / (3 * Math.sqrt(d)); |
| |
| while (true) { |
| final double x = gaussian.sample(); |
| final double v = (1 + c * x) * (1 + c * x) * (1 + c * x); |
| |
| if (v <= 0) { |
| continue; |
| } |
| |
| final double x2 = x * x; |
| final double u = nextDouble(); |
| |
| // Squeeze. |
| if (u < 1 - 0.0331 * x2 * x2) { |
| return alpha * d * v; |
| } |
| |
| if (Math.log(u) < 0.5 * x2 + d * (1 - v + Math.log(v))) { |
| return alpha * d * v; |
| } |
| } |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public String toString() { |
| return "Ahrens-Dieter-Marsaglia-Tsang Gamma deviate [" + super.toString() + "]"; |
| } |
| } |