spbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
SUBROUTINE SPBRFS( UPLO, N, NDIAG, NRHS, A, LDA, AF, LDAF, B, LDB, * X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER * 1 UPLO INTEGER N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER WORK2(*) REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE SPBRFS_64( UPLO, N, NDIAG, NRHS, A, LDA, AF, LDAF, B, * LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER * 1 UPLO INTEGER*8 N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 WORK2(*) REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE PBRFS( UPLO, [N], NDIAG, [NRHS], A, [LDA], AF, [LDAF], B, * [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL, DIMENSION(:) :: FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X
SUBROUTINE PBRFS_64( UPLO, [N], NDIAG, [NRHS], A, [LDA], AF, [LDAF], * B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL, DIMENSION(:) :: FERR, BERR, WORK REAL, DIMENSION(:,:) :: A, AF, B, X
#include <sunperf.h>
void spbrfs(char uplo, int n, int ndiag, int nrhs, float *a, int lda, float *af, int ldaf, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);
void spbrfs_64(char uplo, long n, long ndiag, long nrhs, float *a, long lda, float *af, long ldaf, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);
spbrfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
A(kd+1+i-j,j)
= A(i,j)
for max(1,j-kd)
< =i < =j;
if UPLO = 'L', A(1+i-j,j)
= A(i,j)
for j < =i < =min(n,j+kd).
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