cgerfs(3P) Sun Performance Library cgerfs(3P)NAMEcgerfs - improve the computed solution to a system of linear equations
and provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
REAL 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, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL, 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, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void cgerfs(char transa, int n, int nrhs, complex *a, int lda, complex
*af, int ldaf, int *ipivot, complex *b, int ldb, complex *x,
int ldx, float *ferr, float *berr, int *info);
void cgerfs_64(char transa, long n, long nrhs, complex *a, long lda,
complex *af, long ldaf, long *ipivot, complex *b, long ldb,
complex *x, long ldx, float *ferr, float *berr, long *info);
PURPOSEcgerfs 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 CGETRF.
LDAF (input)
The leading dimension of the array AF. LDAF >= max(1,N).
IPIVOT (input)
The pivot indices from CGETRF; 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 CGETRS. 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 cgerfs(3P)
