
 
 Purpose
 =======
 
    LA_POSV computes the solution to a linear system of equations 
 A*X=B, where A is real symmetric or complex Hermitian and, in either
 case, positive definite, and where X and B are rectangular matrices 
 or vectors. The Cholesky decomposition is used to factor A as
 A = U^H*U if UPLO = 'U', or A = L*L^H if UPLO = 'L'
 where U is an upper triangular matrix and L is a lower triangular 
 matrix (L = U^H ). The factored form of A is then used to solve the
 above system.
 
 =========
 
         SUBROUTINE LA_POSV( A, B, UPLO=uplo, INFO=info )
            <type>(<wp>), INTENT(INOUT) :: A(:,:), <rhs>
            CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
            INTEGER, INTENT(OUT), OPTIONAL :: INFO
         where
            <type> ::= REAL | COMPLEX
            <wp>   ::= KIND(1.0) | KIND(1.0D0)
            <rhs>  ::= B(:,:) | B(:)
 
 Arguments
 =========
 
 A     (input/output) REAL or COMPLEX square array, shape (:,:).
       On entry, the matrix A.
       If UPLO = 'U', the upper triangular part of A contains the upper 
       triangular part of the matrix A, and the strictly lower triangular
       part of A is not referenced. If UPLO = 'L', the lower triangular 
       part of A contains the lower triangular part of the matrix A, and
       the strictly upper triangular part of A is not referenced.
       On exit, the factor U or L from the Cholesky factorization 
       A = U^H*U = L*L^H.
 B     (input/output) REAL or COMPLEX array, shape (:,:) with 
       size(B,1) = size(A,1) or shape (:) with size(B) = size(A,1).
       On entry, the matrix B.
       On exit, the solution matrix X.
 UPLO  Optional (input) CHARACTER(LEN=1)
        = 'U': Upper triangle of A is stored;
        = 'L': Lower triangle of A is stored.
       Default value: 'U'.
 INFO  Optional (output) INTEGER
       = 0: sauccessful exit.
       < 0: if INFO = -i, the i-th argument had an illegal value.
       > 0: if INFO = i, the leading minor of order i of A is not
            positive definite, so the factorization could not be 
 	   completed and the solution could not be computed.
       If INFO is not present and an error occurs, then the program is
       terminated with an error message.

