man zgesv (Fonctions bibliothèques) - compute the solution to a complex system of linear equations A * X = B,

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 interchanges is used to factor A as

A = P * L * U,

where P is a permutation matrix, L is unit lower triangular, 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 exit, 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 matrix 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 illegal 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.