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Java example source code file (CorrelatedRandomVectorGenerator.java)

This example Java source code file (CorrelatedRandomVectorGenerator.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

correlatedrandomvectorgenerator, normalizedrandomgenerator, realmatrix, rectangularcholeskydecomposition

The CorrelatedRandomVectorGenerator.java Java example source code

/*
 * 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.math3.random;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.RectangularCholeskyDecomposition;

/**
 * A {@link RandomVectorGenerator} that 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 for 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
 * interesting 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>. The approach using a Cholesky
 * decomposition is quite usual in this case. However, it can be extended
 * to other cases as long as the underlying random generator provides
 * {@link NormalizedRandomGenerator normalized values} like {@link
 * GaussianRandomGenerator} or {@link UniformRandomGenerator}.</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 = UT.U
 * where <code>C is the covariance matrix and U
 * is an upper-triangular matrix, we compute <code>C = B.BT
 * where <code>B is a rectangular matrix having
 * more rows than columns. The number of columns of <code>B 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>
 *
 * @since 1.2
 */

public class CorrelatedRandomVectorGenerator
    implements RandomVectorGenerator {
    /** Mean vector. */
    private final double[] mean;
    /** Underlying generator. */
    private final NormalizedRandomGenerator generator;
    /** Storage for the normalized vector. */
    private final double[] normalized;
    /** Root of the covariance matrix. */
    private final RealMatrix root;

    /**
     * Builds a correlated random vector generator from its mean
     * vector and covariance matrix.
     *
     * @param mean Expected mean values for all components.
     * @param covariance Covariance matrix.
     * @param small Diagonal elements threshold under which  column are
     * considered to be dependent on previous ones and are discarded
     * @param generator underlying generator for uncorrelated normalized
     * components.
     * @throws org.apache.commons.math3.linear.NonPositiveDefiniteMatrixException
     * if the covariance matrix is not strictly positive definite.
     * @throws DimensionMismatchException if the mean and covariance
     * arrays dimensions do not match.
     */
    public CorrelatedRandomVectorGenerator(double[] mean,
                                           RealMatrix covariance, double small,
                                           NormalizedRandomGenerator generator) {
        int order = covariance.getRowDimension();
        if (mean.length != order) {
            throw new DimensionMismatchException(mean.length, order);
        }
        this.mean = mean.clone();

        final RectangularCholeskyDecomposition decomposition =
            new RectangularCholeskyDecomposition(covariance, small);
        root = decomposition.getRootMatrix();

        this.generator = generator;
        normalized = new double[decomposition.getRank()];

    }

    /**
     * Builds a null mean random correlated vector generator from its
     * covariance matrix.
     *
     * @param covariance Covariance matrix.
     * @param small Diagonal elements threshold under which  column are
     * considered to be dependent on previous ones and are discarded.
     * @param generator Underlying generator for uncorrelated normalized
     * components.
     * @throws org.apache.commons.math3.linear.NonPositiveDefiniteMatrixException
     * if the covariance matrix is not strictly positive definite.
     */
    public CorrelatedRandomVectorGenerator(RealMatrix covariance, double small,
                                           NormalizedRandomGenerator generator) {
        int order = covariance.getRowDimension();
        mean = new double[order];
        for (int i = 0; i < order; ++i) {
            mean[i] = 0;
        }

        final RectangularCholeskyDecomposition decomposition =
            new RectangularCholeskyDecomposition(covariance, small);
        root = decomposition.getRootMatrix();

        this.generator = generator;
        normalized = new double[decomposition.getRank()];

    }

    /** Get the underlying normalized components generator.
     * @return underlying uncorrelated components generator
     */
    public NormalizedRandomGenerator getGenerator() {
        return generator;
    }

    /** Get the rank of the covariance matrix.
     * The rank is the number of independent rows in the covariance
     * matrix, it is also the number of columns of the root matrix.
     * @return rank of the square matrix.
     * @see #getRootMatrix()
     */
    public int getRank() {
        return normalized.length;
    }

    /** Get the root of the covariance matrix.
     * The root is the rectangular matrix <code>B such that
     * the covariance matrix is equal to <code>B.BT
     * @return root of the square matrix
     * @see #getRank()
     */
    public RealMatrix getRootMatrix() {
        return root;
    }

    /** Generate a correlated random vector.
     * @return a random vector as an array of double. The returned array
     * is created at each call, the caller can do what it wants with it.
     */
    public double[] nextVector() {

        // generate uncorrelated vector
        for (int i = 0; i < normalized.length; ++i) {
            normalized[i] = generator.nextNormalizedDouble();
        }

        // compute correlated vector
        double[] correlated = new double[mean.length];
        for (int i = 0; i < correlated.length; ++i) {
            correlated[i] = mean[i];
            for (int j = 0; j < root.getColumnDimension(); ++j) {
                correlated[i] += root.getEntry(i, j) * normalized[j];
            }
        }

        return correlated;

    }

}

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