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

# zcgesv(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE ZCGESV(

  N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,

- \+

  SWORK, RWORK, ITER, INFO )

- INTEGER

  INFO, ITER, LDA, LDB, LDX, N, NRHS

- INTEGER

  IPIV( \* )

- DOUBLE

  PRECISION RWORK( \* )

- COMPLEX

  SWORK( \* )

- COMPLEX\*16

  A( LDA, \* ), B( LDB, \* ), WORK( N, \* ),

- \+

  X( LDX, \* )

## PURPOSE

ZCGESV 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. ZCGESV first attempts to factorize the matrix in COMPLEX and use this factorization within an iterative refinement procedure to produce a solution with COMPLEX\*16 normwise backward error quality (see below). If the approach fails the method switches to a COMPLEX\*16 factorization and solve.\
 The iterative refinement is not going to be a winning strategy if the ratio COMPLEX performance over COMPLEX\*16 performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.\
 The iterative refinement process is stopped if\
\
     ITER \> ITERMAX\
 or for all the RHS we have:\
\
     RNRM \< SQRT(N)\*XNRM\*ANRM\*EPS\*BWDMAX\
 where\
\
     o ITER is the number of the current iteration in the iterative\
       refinement process\
\
     o RNRM is the infinity-norm of the residual\
\
     o XNRM is the infinity-norm of the solution\
\
     o ANRM is the infinity-operator-norm of the matrix A\
\
     o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00\
 respectively.\

## 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 or input/ouptut) COMPLEX\*16 array,

  dimension (LDA,N) On entry, the N-by-N coefficient matrix A. On exit, if iterative refinement has been successfully used (INFO.EQ.0 and ITER.GE.0, see description below), then A is unchanged, if double precision factorization has been used (INFO.EQ.0 and ITER.LT.0, see description below), then the array A contains 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). Corresponds either to the single precision factorization (if INFO.EQ.0 and ITER.GE.0) or the double precision factorization (if INFO.EQ.0 and ITER.LT.0).

- B (input) COMPLEX\*16 array, dimension (LDB,NRHS)

  The N-by-NRHS right hand side matrix B.

- LDB (input) INTEGER

  The leading dimension of the array B.  LDB \>= max(1,N).

- X (output) COMPLEX\*16 array, dimension (LDX,NRHS)

  If INFO = 0, the N-by-NRHS solution matrix X.

- LDX (input) INTEGER

  The leading dimension of the array X.  LDX \>= max(1,N).

- WORK (workspace) COMPLEX\*16 array, dimension (N\*NRHS)

  This array is used to hold the residual vectors.

- SWORK (workspace) COMPLEX array, dimension (N\*(N+NRHS))

  This array is used to use the single precision matrix and the right-hand sides or solutions in single precision.

- RWORK (workspace) DOUBLE PRECISION array, dimension (N)

  - ITER (output) INTEGER

  \< 0: iterative refinement has failed, COMPLEX\*16 factorization has been performed -1 : the routine fell back to full precision for implementation- or machine-specific reasons -2 : narrowing the precision induced an overflow, the routine fell back to full precision -3 : failure of CGETRF\
   \-31: stop the iterative refinement after the 30th iterations \> 0: iterative refinement has been sucessfully used. Returns the number of iterations

- 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) computed in COMPLEX\*16 is exactly zero.  The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. =========