ZPOSV(3)       LAPACK routine of NEC Numeric Library Collection       ZPOSV(3)



NAME
       ZPOSV

SYNOPSIS
       SUBROUTINE ZPOSV (UPLO, N, NRHS, A, LDA, B, LDB, INFO)



PURPOSE
            ZPOSV computes the solution to a complex system of linear equations
               A * X = B,
            where A is an N-by-N Hermitian positive definite matrix and X and B
            are N-by-NRHS matrices.

            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.  The factored form of A is then used to solve the system of
            equations A * X = B.




ARGUMENTS
           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The number of linear equations, i.e., the order of the
                     matrix A.  N >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           A         (input/output)
                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
                     N-by-N 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
                     leading N-by-N 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, if INFO = 0, the factor U or L from the Cholesky
                     factorization A = U**H *U or A = L*L**H.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           B         (input/output)
                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful 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 has not been computed.



LAPACK routine                  31 October 2017                       ZPOSV(3)