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 equationsA * X = B, where A is an NbyN matrix and X and B are NbyNRHS 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 righthand 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 infinitynorm of the residual
o XNRM is the infinitynorm of the solution
o ANRM is the infinityoperatornorm 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 NbyN 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 NbyNRHS 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 NbyNRHS 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 righthand 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 machinespecific 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 ith 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. =========