This subroutine uses Cholesky factorization.
L is a lower triangular matrix.
U is an upper triangular matrix. If the assumed-shape array has a size of zero, no computation is performed, and the subroutine returns after doing some parameter checking. On Return a is the updated matrix A , containing the results of the factorization. A is positive definite, and the factorization completed normally. A is not positive definite.