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.

    2.0 (changed to concrete class in 3.0)
    See Also:
    MathWorld, Wikipedia