zgerfs(3P) Sun Performance Library zgerfs(3P)NAMEzgerfs - improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE GERFS([TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF], IPIVOT,
B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE GERFS_64([TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF],
IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zgerfs(char transa, int n, int nrhs, doublecomplex *a, int lda,
doublecomplex *af, int ldaf, int *ipivot, doublecomplex *b,
int ldb, doublecomplex *x, int ldx, double *ferr, double
*berr, int *info);
void zgerfs_64(char transa, long n, long nrhs, doublecomplex *a, long
lda, doublecomplex *af, long ldaf, long *ipivot, doublecom‐
plex *b, long ldb, doublecomplex *x, long ldx, double *ferr,
double *berr, long *info);
PURPOSEzgerfs improves the computed solution to a system of linear equations
and provides error bounds and backward error estimates for the solu‐
tion.
ARGUMENTS
TRANSA (input)
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)
TRANSA is defaulted to 'N' for F95 INTERFACE.
N (input) The order of the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) The original N-by-N matrix A.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
AF (input)
The factors L and U from the factorization A = P*L*U as com‐
puted by ZGETRF.
LDAF (input)
The leading dimension of the array AF. LDAF >= max(1,N).
IPIVOT (input)
The pivot indices from ZGETRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIVOT(i).
B (input) The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input/output)
On entry, the solution matrix X, as computed by ZGETRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X). If XTRUE is
the true solution corresponding to X(j), FERR(j) is an esti‐
mated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest ele‐
ment in X(j). The estimate is as reliable as the estimate
for RCOND, and is almost always a slight overestimate of the
true error.
BERR (output)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any ele‐
ment of A or B that makes X(j) an exact solution).
WORK (workspace)
dimension(2*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zgerfs(3P)
