# RedHat 9 (Linux i386) - man page for zposv (redhat section l)

```ZPOSV(l)								 )								  ZPOSV(l)

NAME
ZPOSV - compute the solution to a complex system of linear equations A * X = B,

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

CHARACTER	 UPLO

INTEGER	 INFO, LDA, LDB, N, NRHS

COMPLEX*16	 A( LDA, * ), B( LDB, * )

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

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

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

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

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

INFO    (output) 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 version 3.0						   15 June 2000 							  ZPOSV(l)```