.TH ZGESV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH NAME ZGESV - the solution to a complex system of linear equations A * X = B, .SH SYNOPSIS .TP 18 SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) .TP 18 .ti +4 INTEGER INFO, LDA, LDB, N, NRHS .TP 18 .ti +4 INTEGER IPIV( * ) .TP 18 .ti +4 COMPLEX*16 A( LDA, * ), B( LDB, * ) .SH 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 .br A = P * L * U, .br 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. .br .SH ARGUMENTS .TP 8 N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. .TP 8 NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. .TP 8 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 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). .TP 8 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. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 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.