dtbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coeffi- cient matrix
SUBROUTINE DTBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG INTEGER N, KD, NRHS, LDA, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DTBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG INTEGER*8 N, KD, NRHS, LDA, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE TBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG INTEGER :: N, KD, NRHS, LDA, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, B, X SUBROUTINE TBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG INTEGER(8) :: N, KD, NRHS, LDA, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: A, B, X C INTERFACE #include <sunperf.h> void dtbrfs(char uplo, char transa, char diag, int n, int kd, int nrhs, double *a, int lda, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dtbrfs_64(char uplo, char transa, char diag, long n, long kd, long nrhs, double *a, long lda, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library dtbrfs(3P)
NAME
dtbrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band coeffi-
cient matrix
SYNOPSIS
SUBROUTINE DTBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO, TRANSA, DIAG
INTEGER N, KD, NRHS, LDA, LDB, LDX, INFO
INTEGER WORK2(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
SUBROUTINE DTBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO, TRANSA, DIAG
INTEGER*8 N, KD, NRHS, LDA, LDB, LDX, INFO
INTEGER*8 WORK2(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
F95 INTERFACE
SUBROUTINE TBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER :: N, KD, NRHS, LDA, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: A, B, X
SUBROUTINE TBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA,
B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER(8) :: N, KD, NRHS, LDA, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: A, B, X
C INTERFACE
#include <sunperf.h>
void dtbrfs(char uplo, char transa, char diag, int n, int kd, int nrhs,
double *a, int lda, double *b, int ldb, double *x, int ldx,
double *ferr, double *berr, int *info);
void dtbrfs_64(char uplo, char transa, char diag, long n, long kd, long
nrhs, double *a, long lda, double *b, long ldb, double *x,
long ldx, double *ferr, double *berr, long *info);
PURPOSE
dtbrfs provides error bounds and backward error estimates for the solu-
tion to a system of linear equations with a triangular band coefficient
matrix.
The solution matrix X must be computed by DTBTRS or some other means
before entering this routine. DTBRFS does not do iterative refinement
because doing so cannot improve the backward error.
ARGUMENTS
UPLO (input)
= 'U': A is upper triangular;
= 'L': A is lower triangular.
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 = Transpose)
DIAG (input)
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) The order of the matrix A. N >= 0.
KD (input)
The number of superdiagonals or subdiagonals of the triangu-
lar band matrix A. 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 triangular 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). If DIAG = 'U',
the diagonal elements of A are not referenced and are assumed
to be 1.
LDA (input)
The leading dimension of the array A. LDA >= 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) The 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
7 Nov 2015 dtbrfs(3P)