Contents
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, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER N, KD, 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, KD, NRHS, A, LDA, AF, LDAF, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 WORK2(*)
REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
F95 INTERFACE
SUBROUTINE PBRFS(UPLO, [N], KD, [NRHS], A, [LDA], AF, [LDAF], B,
[LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, 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], KD, [NRHS], A, [LDA], AF, [LDAF],
B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X
C INTERFACE
#include <sunperf.h>
void spbrfs(char uplo, int n, int kd, 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 kd, 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.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
KD (input)
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KD >= 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 upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the
array. The j-th column of A is stored in the j-th
column of the array A as follows: if UPLO = 'U',
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).
LDA (input)
The leading dimension of the array A. LDA >=
KD+1.
AF (input)
The triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T of the band
matrix A as computed by SPBTRF, in the same
storage format as A (see A).
LDAF (input)
The leading dimension of the array AF. LDAF >=
KD+1.
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
SPBTRS. 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