RectangularCholeskyDecomposition.java

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 *
 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math.linear;


/**
 * An interface to classes that implement an algorithm to calculate a
 * rectangular variation of Cholesky decomposition of a real symmetric
 * positive semidefinite matrix.
 * <p>The rectangular Cholesky decomposition of a real symmetric positive
 * semidefinite matrix A consists of a rectangular matrix B with the same
 * number of rows such that: A is almost equal to BB<sup>T</sup>, depending
 * on a user-defined tolerance. In a sense, this is the square root of A.</p>
 * <p>The difference with respect to the regular {@link CholeskyDecomposition}
 * is that rows/columns may be permuted (hence the rectangular shape instead
 * of the traditional triangular shape) and there is a threshold to ignore
 * small diagonal elements. This is used for example to generate {@link
 * org.apache.commons.math.random.CorrelatedRandomVectorGenerator correlated
 * random n-dimensions vectors} in a p-dimension subspace (p < n).
 * In other words, it allows generating random vectors from a covariance
 * matrix that is only positive semidefinite, and not positive definite.</p>
 * <p>Rectangular Cholesky decomposition is <em>not</em> suited for solving
 * linear systems, so it does not provide any {@link DecompositionSolver
 * decomposition solver}.</p>
 *
 * @see CholeskyDecomposition
 * @see org.apache.commons.math.random.CorrelatedRandomVectorGenerator
 * @version $Id: RectangularCholeskyDecomposition.java 1131229 2011-06-03 20:49:25Z luc $
 * @since 3.0
 */
public interface RectangularCholeskyDecomposition {

    /** 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()
     */
    RealMatrix getRootMatrix();

    /** Get the rank of the symmetric positive semidefinite matrix.
     * The r is the number of independent rows in the symmetric positive semidefinite
     * matrix, it is also the number of columns of the rectangular
     * matrix of the decomposition.
     * @return r of the square matrix.
     * @see #getRootMatrix()
     */
    int getRank();

}