---
name: "zgesv"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zgesv/3lapack"
---

# zgesv(3lapack)

computes the solution to a complex system of linear equations A \* X = B,

## NAME

ZGESV - computes 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.