Java Code Examples for org.apache.commons.math3.linear.Array2DRowRealMatrix#multiply()

The following examples show how to use org.apache.commons.math3.linear.Array2DRowRealMatrix#multiply() . You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may check out the related API usage on the sidebar.
Example 1
Source File: DemoMihcComputation.java    From orbit-image-analysis with GNU General Public License v3.0 5 votes vote down vote up 
public DemoMihcComputation() {
    MihcConfigData conf = new MihcConfigData();
    Array2DRowRealMatrix AsnInv = (Array2DRowRealMatrix) MatrixUtils.createRealMatrix(conf.inverse);
    double[] gain = new double[]{1,1,1,1,1,1};
    for (int i=0; i<gain.length; i++) gain[i] = 1d/gain[i];
    RealMatrix GiiInv = MatrixUtils.createRealDiagonalMatrix(gain);
    Array2DRowRealMatrix AsnInvNorm = (Array2DRowRealMatrix) AsnInv.multiply(GiiInv);
    inverseMatrix = AsnInvNorm;
}
Example 2
Source File: MatrixMultiplyEvaluator.java    From lucene-solr with Apache License 2.0 5 votes vote down vote up 
@Override
public Object doWork(Object first, Object second) throws IOException {
  if(null == first){
    throw new IOException(String.format(Locale.ROOT,"Invalid expression %s - null found for the first value",toExpression(constructingFactory)));
  }
  if(null == second){
    throw new IOException(String.format(Locale.ROOT,"Invalid expression %s - null found for the second value",toExpression(constructingFactory)));
  }

  Array2DRowRealMatrix realMatrix1 = getMatrix(first);
  Array2DRowRealMatrix realMatrix2 = getMatrix(second);
  Array2DRowRealMatrix realMatrix3 = realMatrix1.multiply(realMatrix2);
  return new Matrix(realMatrix3.getDataRef());

}
Example 3
Source File: Math_11_MultivariateNormalDistribution_s.java    From coming with MIT License 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 4
Source File: Math_11_MultivariateNormalDistribution_t.java    From coming with MIT License 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 5
Source File: MultivariateNormalDistribution.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 6
Source File: MultivariateNormalDistribution.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 7
Source File: MultivariateNormalDistribution.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 8
Source File: MultivariateNormalDistribution.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 9
Source File: MultivariateNormalDistribution.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}
Example 10
Source File: MultivariateNormalDistribution.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Creates a multivariate normal distribution with the given mean vector and
 * covariance matrix.
 * <br/>
 * The number of dimensions is equal to the length of the mean vector
 * and to the number of rows and columns of the covariance matrix.
 * It is frequently written as "p" in formulae.
 *
 * @param rng Random Number Generator.
 * @param means Vector of means.
 * @param covariances Covariance matrix.
 * @throws DimensionMismatchException if the arrays length are
 * inconsistent.
 * @throws SingularMatrixException if the eigenvalue decomposition cannot
 * be performed on the provided covariance matrix.
 * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
 * negative.
 */
public MultivariateNormalDistribution(RandomGenerator rng,
                                      final double[] means,
                                      final double[][] covariances)
        throws SingularMatrixException,
               DimensionMismatchException,
               NonPositiveDefiniteMatrixException {
    super(rng, means.length);

    final int dim = means.length;

    if (covariances.length != dim) {
        throw new DimensionMismatchException(covariances.length, dim);
    }

    for (int i = 0; i < dim; i++) {
        if (dim != covariances[i].length) {
            throw new DimensionMismatchException(covariances[i].length, dim);
        }
    }

    this.means = MathArrays.copyOf(means);

    covarianceMatrix = new Array2DRowRealMatrix(covariances);

    // Covariance matrix eigen decomposition.
    final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);

    // Compute and store the inverse.
    covarianceMatrixInverse = covMatDec.getSolver().getInverse();
    // Compute and store the determinant.
    covarianceMatrixDeterminant = covMatDec.getDeterminant();

    // Eigenvalues of the covariance matrix.
    final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();

    for (int i = 0; i < covMatEigenvalues.length; i++) {
        if (covMatEigenvalues[i] < 0) {
            throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
        }
    }

    // Matrix where each column is an eigenvector of the covariance matrix.
    final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
    for (int v = 0; v < dim; v++) {
        final double[] evec = covMatDec.getEigenvector(v).toArray();
        covMatEigenvectors.setColumn(v, evec);
    }

    final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

    // Scale each eigenvector by the square root of its eigenvalue.
    for (int row = 0; row < dim; row++) {
        final double factor = FastMath.sqrt(covMatEigenvalues[row]);
        for (int col = 0; col < dim; col++) {
            tmpMatrix.multiplyEntry(row, col, factor);
        }
    }

    samplingMatrix = covMatEigenvectors.multiply(tmpMatrix);
}