zcgesv(3P) Sun Performance Library zcgesv(3P)NAMEzcgesv - 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, ITER, INFO)
INTEGER N, NRHS, LDA, LDB, LDX, ITER, INFO
INTEGER IPIV(*)
COMPLEX SWORK(*)
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(N,*), X(LDX,*)
SUBROUTINE ZCGESV_64(N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
INTEGER*8 N, NRHS, LDA, LDB, LDX, ITER, INFO
INTEGER*8 IPIV(*)
COMPLEX SWORK(*)
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(N,*), X(LDX,*)
F95 INTERFACE
SUBROUTINE CGESV([N], NRHS, A, [LDA], IPIV, B, [LDB], X, [LDX], [WORK], [SWORK], ITER, [INFO])
INTEGER :: M, N, LDA, INFO
INTEGER, DIMENSION(:) :: IPIV
DOUBLE COMPLEX, DIMENSION(:,:) :: A, B, X, WORK
SUBROUTINE CGESV_64(([N], NRHS, A, [LDA], IPIV, B, [LDB], X, [LDX], [WORK], [SWORK], ITER, [INFO])
INTEGER(8) :: N, NRHS, LDA, LDB, LDX, ITER, INFO
INTEGER(8), DIMENSION(:) :: IPIV
DOUBLE COMPLEX, DIMENSION(:,:) :: A, B, X, WORK
C INTERFACE
#include <sunperf.h>
void zcgesv(int n, int nrhs, doublecomplex *a, int lda, int *ipiv, dou‐
blecomplex *b, int ldb, doublecomplex *x, int ldx, doublecom‐
plex *work, complex *swork, int iter, int *info);
void zcgesv_64(long n, long nrhs, doublecomplex *a, long lda, long
*ipiv, doublecomplex *b, long ldb, doublecomplex *x, long
ldx, doublecomplex *work, complex *swork, long iter, long
*info);
PURPOSEzcgesv 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 SINGLE COMPLEX PRECI‐
SION and use this factorization within an iterative refinement proce‐
dure to produce a solution with DOUBLE COMPLEX PRECISION normwise back‐
ward error quality (see below). If the approach fails the method
switches to a DOUBLE COMPLEX PRECISION factorization and solve.
The iterative refinement is not going to be a winning strategy if the
ratio SINGLE PRECISION performance over DOUBLE PRECISION 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/output) DOUBLE COMPLEX array
On entry, the N-by-N coefficient matrix A. On exit, if iter‐
ative 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) DOUBLE COMPLEX array, dimension (LDB,NRHS)
The N-by-NRHS matrix of right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (output) DOUBLE COMPLEX 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) DOUBLE COMPLEX 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.
ITER (output) INTEGER
< 0: iterative refinement has failed, double precision fac‐
torization has been performed
-1 : taking into account machine parameters, N, NRHS, it is a
priori not worth working in SINGLE PRECISION
-2 : overflow of an entry when moving from double to SINGLE
PRECISION
-3 : failure of SGETRF
-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 DOUBLE PRECISION is
exactly zero. The factorization has been completed, but the
factor U is exactly singular, so the solution could not be
computed.
6 Mar 2009 zcgesv(3P)
