Contents
sgbrfs - improve the computed solution to a system of linear
equations when the coefficient matrix is banded, and pro-
vides error bounds and backward error estimates for the
solution
SUBROUTINE SGBRFS(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
INTEGER N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
SUBROUTINE SGBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
INTEGER*8 N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
F95 INTERFACE
SUBROUTINE GBRFS([TRANSA], [N], KL, KU, [NRHS], A, [LDA], AF,
[LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2],
[INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X
SUBROUTINE GBRFS_64([TRANSA], [N], KL, KU, [NRHS], A, [LDA],
AF, [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X
C INTERFACE
#include <sunperf.h>
void sgbrfs(char transa, int n, int kl, int ku, int nrhs,
float *a, int lda, float *af, int ldaf, int
*ipivot, float *b, int ldb, float *x, int ldx,
float *ferr, float *berr, int *info);
void sgbrfs_64(char transa, long n, long kl, long ku, long
nrhs, float *a, long lda, float *af, long ldaf,
long *ipivot, float *b, long ldb, float *x, long
ldx, float *ferr, float *berr, long *info);
sgbrfs improves the computed solution to a system of linear
equations when the coefficient matrix is banded, and pro-
vides error bounds and backward error estimates 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 = Tran-
spose)
TRANSA is defaulted to 'N' for F95 INTERFACE.
N (input) The order of the matrix A. N >= 0.
KL (input)
The number of subdiagonals within the band of A.
KL >= 0.
KU (input)
The number of superdiagonals within the band of A.
KU >= 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 band matrix A, stored in rows 1 to
KL+KU+1. The j-th column of A is stored in the
j-th column of the array A as follows: A(ku+1+i-
j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDA (input)
The leading dimension of the array A. LDA >=
KL+KU+1.
AF (input)
Details of the LU factorization of the band matrix
A, as computed by SGBTRF. U is stored as an upper
triangular band matrix with KL+KU superdiagonals
in rows 1 to KL+KU+1, and the multipliers used
during the factorization are stored in rows
KL+KU+2 to 2*KL+KU+1.
LDAF (input)
The leading dimension of the array AF. LDAF >=
2*KL*KU+1.
IPIVOT (input)
The pivot indices from SGBTRF; 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
SGBTRS. 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(3*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value