| /* |
| * 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.math4.legacy.random; |
| |
| import java.util.function.Supplier; |
| |
| import org.apache.commons.rng.UniformRandomProvider; |
| import org.apache.commons.rng.sampling.distribution.ContinuousSampler; |
| import org.apache.commons.rng.sampling.distribution.ContinuousUniformSampler; |
| import org.apache.commons.rng.sampling.distribution.ZigguratNormalizedGaussianSampler; |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| import org.apache.commons.math4.legacy.linear.RealMatrix; |
| import org.apache.commons.math4.legacy.linear.RectangularCholeskyDecomposition; |
| |
| /** |
| * Generates vectors with with correlated components. |
| * |
| * <p>Random vectors with correlated components are built by combining |
| * the uncorrelated components of another random vector in such a way |
| * that the resulting correlations are the ones specified by a positive |
| * definite covariance matrix.</p> |
| * |
| * <p>The main use of correlated random vector generation is for Monte-Carlo |
| * simulation of physical problems with several variables (for example to |
| * generate error vectors to be added to a nominal vector). A particularly |
| * common case is when the generated vector should be drawn from a |
| * <a href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution"> |
| * Multivariate Normal Distribution</a>, usually using Cholesky decomposition. |
| * Other distributions are possible as long as the underlying sampler provides |
| * normalized values (unit standard deviation).</p> |
| * |
| * <p>Sometimes, the covariance matrix for a given simulation is not |
| * strictly positive definite. This means that the correlations are |
| * not all independent from each other. In this case, however, the non |
| * strictly positive elements found during the Cholesky decomposition |
| * of the covariance matrix should not be negative either, they |
| * should be null. Another non-conventional extension handling this case |
| * is used here. Rather than computing <code>C = U<sup>T</sup> U</code> |
| * where <code>C</code> is the covariance matrix and <code>U</code> |
| * is an upper-triangular matrix, we compute <code>C = B B<sup>T</sup></code> |
| * where <code>B</code> is a rectangular matrix having more rows than |
| * columns. The number of columns of <code>B</code> is the rank of the |
| * covariance matrix, and it is the dimension of the uncorrelated |
| * random vector that is needed to compute the component of the |
| * correlated vector. This class handles this situation automatically.</p> |
| */ |
| public class CorrelatedVectorFactory { |
| /** Square root of three. */ |
| private static final double SQRT3 = AccurateMath.sqrt(3); |
| /** Mean vector. */ |
| private final double[] mean; |
| /** Root of the covariance matrix. */ |
| private final RealMatrix root; |
| /** Size of uncorrelated vector. */ |
| private final int lengthUncorrelated; |
| /** Size of correlated vector. */ |
| private final int lengthCorrelated; |
| |
| /** |
| * Correlated vector factory. |
| * |
| * @param mean Expected mean values of the components. |
| * @param covariance Covariance matrix. |
| * @param small Diagonal elements threshold under which columns are |
| * considered to be dependent on previous ones and are discarded. |
| * @throws org.apache.commons.math4.legacy.linear.NonPositiveDefiniteMatrixException |
| * if the covariance matrix is not strictly positive definite. |
| * @throws DimensionMismatchException if the mean and covariance |
| * arrays dimensions do not match. |
| */ |
| public CorrelatedVectorFactory(double[] mean, |
| RealMatrix covariance, |
| double small) { |
| lengthCorrelated = covariance.getRowDimension(); |
| if (mean.length != lengthCorrelated) { |
| throw new DimensionMismatchException(mean.length, lengthCorrelated); |
| } |
| this.mean = mean.clone(); |
| |
| final RectangularCholeskyDecomposition decomposition |
| = new RectangularCholeskyDecomposition(covariance, small); |
| root = decomposition.getRootMatrix(); |
| |
| lengthUncorrelated = decomposition.getRank(); |
| } |
| |
| /** |
| * Null mean correlated vector factory. |
| * |
| * @param covariance Covariance matrix. |
| * @param small Diagonal elements threshold under which columns are |
| * considered to be dependent on previous ones and are discarded. |
| * @throws org.apache.commons.math4.legacy.linear.NonPositiveDefiniteMatrixException |
| * if the covariance matrix is not strictly positive definite. |
| */ |
| public CorrelatedVectorFactory(RealMatrix covariance, |
| double small) { |
| this(new double[covariance.getRowDimension()], |
| covariance, |
| small); |
| } |
| |
| /** |
| * @param rng RNG. |
| * @return a generator of vectors with correlated components sampled |
| * from a uniform distribution. |
| */ |
| public Supplier<double[]> uniform(UniformRandomProvider rng) { |
| return with(new ContinuousUniformSampler(rng, -SQRT3, SQRT3)); |
| } |
| |
| /** |
| * @param rng RNG. |
| * @return a generator of vectors with correlated components sampled |
| * from a normal distribution. |
| */ |
| public Supplier<double[]> gaussian(UniformRandomProvider rng) { |
| return with(new ZigguratNormalizedGaussianSampler(rng)); |
| } |
| |
| /** |
| * @param sampler Generator of samples from a normalized distribution. |
| * @return a generator of vectors with correlated components. |
| */ |
| private Supplier<double[]> with(final ContinuousSampler sampler) { |
| return new Supplier<double[]>() { |
| @Override |
| public double[] get() { |
| // Uncorrelated vector. |
| final double[] uncorrelated = new double[lengthUncorrelated]; |
| for (int i = 0; i < lengthUncorrelated; i++) { |
| uncorrelated[i] = sampler.sample(); |
| } |
| |
| // Correlated vector. |
| final double[] correlated = mean.clone(); |
| for (int i = 0; i < correlated.length; i++) { |
| for (int j = 0; j < lengthUncorrelated; j++) { |
| correlated[i] += root.getEntry(i, j) * uncorrelated[j]; |
| } |
| } |
| |
| return correlated; |
| } |
| }; |
| } |
| } |