Contents
dtrrfs - provide error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular coefficient matrix
SUBROUTINE DTRRFS(UPLO, TRANSA, DIAG, N, NRHS, A, LDA, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER N, NRHS, LDA, LDB, LDX, INFO
INTEGER WORK2(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
SUBROUTINE DTRRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, LDA, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER*8 N, NRHS, LDA, LDB, LDX, INFO
INTEGER*8 WORK2(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)
F95 INTERFACE
SUBROUTINE TRRFS(UPLO, [TRANSA], DIAG, N, NRHS, A, [LDA], B, [LDB],
X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER :: N, NRHS, LDA, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: A, B, X
SUBROUTINE TRRFS_64(UPLO, [TRANSA], DIAG, N, NRHS, A, [LDA], B, [LDB],
X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER(8) :: N, 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 dtrrfs(char uplo, char transa, char diag, int n, int
nrhs, double *a, int lda, double *b, int ldb, dou-
ble *x, int ldx, double *ferr, double *berr, int
*info);
void dtrrfs_64(char uplo, char transa, char diag, long n,
long nrhs, double *a, long lda, double *b, long
ldb, double *x, long ldx, double *ferr, double
*berr, long *info);
dtrrfs provides error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular coefficient matrix.
The solution matrix X must be computed by DTRTRS or some
other means before entering this routine. DTRRFS does not
do iterative refinement because doing so cannot improve the
backward error.
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 = Tran-
spose)
TRANSA is defaulted to 'N' for F95 INTERFACE.
DIAG (input)
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) The order of the matrix A. N >= 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 triangular matrix A. If UPLO = 'U', the lead-
ing N-by-N upper triangular part of the array A
contains the upper triangular matrix, and the
strictly lower triangular part of A is not refer-
enced. If UPLO = 'L', the leading N-by-N lower
triangular part of the array A contains the lower
triangular matrix, and the strictly upper triangu-
lar part of A is not referenced. If DIAG = 'U',
the diagonal elements of A are also not referenced
and are assumed to be 1.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
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 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