zgesv(3)

NAME

ZGESV - compute the solution to a complex system of linear

equations A * X = B,

SYNOPSIS

SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
    INTEGER       INFO, LDA, LDB, N, NRHS
    INTEGER       IPIV( * )
    COMPLEX*16    A( LDA, * ), B( LDB, * )

PURPOSE

ZGESV computes the solution to a complex system of linear

equations A * X = B, where A is an N-by-N matrix and X and B are

N-by-NRHS matrices.

The LU decomposition with partial pivoting and row inter

changes is used to factor A as

A = P * L * U,

where P is a permutation matrix, L is unit lower triangu

lar, and U is upper triangular. The factored form of A is then

used to solve the system of equations A * X = B.

ARGUMENTS

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 N-by-N coefficient matrix A. On ex

it, the factors L and U from the factorization A = P*L*U; the

unit diagonal elements of L are not stored.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

IPIV (output) INTEGER array, dimension (N)

The pivot indices that define the permutation ma

trix P; row i of the matrix was interchanged with row IPIV(i).

B (input/output) COMPLEX*16 array, dimension

(LDB,NRHS)

On entry, the N-by-NRHS matrix of 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, U(i,i) is exactly zero. The

factorization has been completed, but the factor U is exactly

singular, so the solution could not be computed.

LAPACK version 3.0 15 June 2000

ZGESV(3)