Determinant of a positive definite matrix

If the symmetric positive definite matrix A is represented by its Cholesky decomposition A = LL^T or A = U^TU, then the determinant of this matrix can be calculated as the product of squares of the diagonal elements of L or U.

As Cholesky decomposition is twice as fast as LU-decomposition which is used to calculate general matrix determinants, it is recommended to use Cholesky decomposition when calculating a determinant of a symmetric positive definite matrix. In order to calculate the determinant of a symmetric matrix which is not positive definite algorithm on the basis of LDLT-decomposition can be used.

Subroutine description

There are two subroutines in this module. The first subroutine, SPDMatrixCholeskyDet, calculates the determinant of a matrix whose Cholesky decomposition has already been generated. The second subroutine, SPDMatrixDet (Symmetric Positive Definite), works with symmetric matrices whose Cholesky decomposition hasn't been generated yet.

If the input matrix is not positive definite, then SPDMatrixDet subroutine cannot calculate the determinant, therefore the subroutine returns to a negative number. This error is easily recognized because the determinant of a positive definite matrix is a strictly positive number.

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