dgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
SUBROUTINE DGBRFS( TRANSA, N, NSUB, NSUPER, NRHS, A, LDA, AF, LDAF, * IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER * 1 TRANSA INTEGER N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*), WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE DGBRFS_64( TRANSA, N, NSUB, NSUPER, NRHS, A, LDA, AF, * LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER * 1 TRANSA INTEGER*8 N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*), WORK2(*) DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE GBRFS( [TRANSA], [N], NSUB, NSUPER, [NRHS], A, [LDA], AF, * [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], * [INFO]) CHARACTER(LEN=1) :: TRANSA INTEGER :: N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT, WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X
SUBROUTINE GBRFS_64( [TRANSA], [N], NSUB, NSUPER, [NRHS], A, [LDA], * AF, [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], * [WORK2], [INFO]) CHARACTER(LEN=1) :: TRANSA INTEGER(8) :: N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, AF, B, X
#include <sunperf.h>
void dgbrfs(char transa, int n, int nsub, int nsuper, 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 dgbrfs_64(char transa, long n, long nsub, long nsuper, 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);
dgbrfs improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
A(ku+1+i-j,j)
= A(i,j)
for max(1,j-ku)
< =i < =min(n,j+kl).
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
element 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.
X(j)
(i.e., the smallest relative change in
any element of A or B that makes X(j)
an exact solution).
dimension(3*N)
dimension(N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value