dgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution
SUBROUTINE DGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*), WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*), WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) 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 INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT, WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X SUBROUTINE GERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X C INTERFACE #include <sunperf.h> void dgerfs(char transa, int n, int nrhs, double *a, int lda, double *af, int ldaf, int *ipivot, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dgerfs_64(char transa, long n, long nrhs, double *a, long lda, double *af, long ldaf, long *ipivot, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library dgerfs(3P)
NAME
dgerfs - improve the computed solution to a system of linear equations
and provide error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE DGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 TRANSA
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
SUBROUTINE DGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 TRANSA
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
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
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: A, AF, B, X
SUBROUTINE GERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: A, AF, B, X
C INTERFACE
#include <sunperf.h>
void dgerfs(char transa, int n, int nrhs, double *a, int lda, double
*af, int ldaf, int *ipivot, double *b, int ldb, double *x,
int ldx, double *ferr, double *berr, int *info);
void dgerfs_64(char transa, long n, long nrhs, double *a, long lda,
double *af, long ldaf, long *ipivot, double *b, long ldb,
double *x, long ldx, double *ferr, double *berr, long *info);
PURPOSE
dgerfs 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 = Transpose)
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 DGETRF.
LDAF (input)
The leading dimension of the array AF. LDAF >= max(1,N).
IPIVOT (input)
The pivot indices from DGETRF; 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 DGETRS. 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(3*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
7 Nov 2015 dgerfs(3P)