zposv(3)

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 def

inite 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 triangu

lar 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 ille

gal 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(3)