Contents
zgerfs - improve the computed solution to a system of linear
equations and provides error bounds and backward error esti-
mates for the solution
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, doublecomplex *b, long ldb, doublecomplex
*x, long ldx, double *ferr, double *berr, long
*info);
zgerfs improves the computed solution to a system of linear
equations and provides error bounds and backward error esti-
mates for the solution.
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 computed 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 solu-
tion 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 estimated
upper bound for the magnitude of the largest ele-
ment in (X(j) - XTRUE) divided by the magnitude of
the largest element 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 element 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 ille-
gal value