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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 RandomVectorGenerator that generates vectors with with correlated components. 
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.
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 
Multivariate Normal Distribution. 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 normalized values like GaussianRandomGenerator or UniformRandomGenerator.
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 C = UT.U
where C is the covariance matrix and U
is an upper-triangular matrix, we compute C = B.BT
where B is a rectangular matrix having
more rows than columns. The number of columns of 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.
Since:
1.2/**
 * 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 = 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>
 *
 * @since 1.2
 */

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

    
Builds a correlated random vector generator from its mean
vector and covariance matrix.
Params:
mean – Expected mean values for all components.
covariance – Covariance matrix.
small – Diagonal elements threshold under which  column are
considered to be dependent on previous ones and are discarded
generator – underlying generator for uncorrelated normalized
components.
Throws:
NonPositiveDefiniteMatrixException – 
if the covariance matrix is not strictly positive definite.
DimensionMismatchException – if the mean and covariance
arrays dimensions do not match./**
     * 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.
Params:
covariance – Covariance matrix.
small – Diagonal elements threshold under which  column are
considered to be dependent on previous ones and are discarded.
generator – Underlying generator for uncorrelated normalized
components.
Throws:
NonPositiveDefiniteMatrixException – 
if the covariance matrix is not strictly positive definite./**
     * 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.
Returns:
underlying uncorrelated components generator/** 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.
See Also:
getRootMatrix()
Returns:
rank of the square matrix./** 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 B such that
the covariance matrix is equal to B.BT
See Also:
getRank()
Returns:
root of the square matrix/** Get the root of the covariance matrix.
     * The root is the rectangular matrix <code>B</code> such that
     * the covariance matrix is equal to <code>B.B<sup>T</sup></code>
     * @return root of the square matrix
     * @see #getRank()
     */
    public RealMatrix getRootMatrix() {
        return root;
    }

    
Generate a correlated random vector.
Returns:
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./** 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;

    }

}