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 2.0  —  08 October 1994