Inverse of a symmetric positive definite matrix

Cholesky decomposition could be used to invert a symmetric positive definite matrix. This algorithm is able to invert only positive definite matrices. Arbitrary symmetric matrices could be inverted by more general algorithm on the basis of LDLT-decomposition.

Subroutine SPDMatrixCholeskyInverse inverts a symmetric positive definite matrix A whose Cholesky decomposition has already been generated. The subroutine gets an output of subroutine SPDMatrixCholesky - Cholesky decomposition of matrix A (A = U^TU or A = LL^T) as an input, and returns the upper or lower triangle of symmetric matrix A^-1 (depending on which variant of decomposition was returned by SPDMatrixCholesky).

Subroutine SPDMatrixInverse calls subroutine SPDMatrixCholesky to factorize matrix A which is given by its lower or upper triangle, and returns the upper or lower triangle of symmetric matrix A^-1 (depending on which part of the matrix was input).

This algorithm is transferred from the LAPACK library.