dpbrfs(3P) Sun Performance Library dpbrfs(3P)NAMEdpbrfs - 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
SYNOPSIS
SUBROUTINE DPBRFS(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(*)
DOUBLE PRECISION A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
SUBROUTINE DPBRFS_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(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), 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(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: A, AF, B, X
C INTERFACE
#include <sunperf.h>
void dpbrfs(char uplo, int n, int kd, int nrhs, double *a, int lda,
double *af, int ldaf, double *b, int ldb, double *x, int ldx,
double *ferr, double *berr, int *info);
void dpbrfs_64(char uplo, long n, long kd, long nrhs, double *a, long
lda, double *af, long ldaf, double *b, long ldb, double *x,
long ldx, double *ferr, double *berr, long *info);
PURPOSEdpbrfs 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 solu‐
tion.
ARGUMENTS
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
DPBTRF, 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 DPBTRS. 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
6 Mar 2009 dpbrfs(3P)
