Class RectangularCholeskyDecomposition


  • public class RectangularCholeskyDecomposition
    extends Object
    Calculates the rectangular Cholesky decomposition of a matrix.

    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 BBT, depending on a user-defined tolerance. In a sense, this is the square root of A.

    The difference with respect to the regular 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 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.

    Rectangular Cholesky decomposition is not suited for solving linear systems, so it does not provide any decomposition solver.

    See Also:
    MathWorld, Wikipedia
    • Constructor Detail

      • RectangularCholeskyDecomposition

        public RectangularCholeskyDecomposition​(RealMatrix matrix,
                                                double small)
                                         throws MathIllegalArgumentException
        Decompose a symmetric positive semidefinite matrix.
        Parameters:
        matrix - Symmetric positive semidefinite matrix.
        small - Diagonal elements threshold under which columns are considered to be dependent on previous ones and are discarded.
        Throws:
        MathIllegalArgumentException - if the matrix is not positive semidefinite.
    • Method Detail

      • getRootMatrix

        public RealMatrix getRootMatrix()
        Get the root of the covariance matrix. The root is the rectangular matrix B such that the covariance matrix is equal to B.BT
        Returns:
        root of the square matrix
        See Also:
        getRank()
      • getRank

        public int getRank()
        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.
        Returns:
        r of the square matrix.
        See Also:
        getRootMatrix()