Contents
dtprfs - provide error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular packed coefficient matrix
SUBROUTINE DTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER WORK2(*)
DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
SUBROUTINE DTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 WORK2(*)
DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
F95 INTERFACE
SUBROUTINE TPRFS(UPLO, [TRANSA], DIAG, [N], NRHS, A, B, [LDB], X, [LDX],
FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
SUBROUTINE TPRFS_64(UPLO, [TRANSA], DIAG, [N], NRHS, A, B, [LDB], X,
[LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void dtprfs(char uplo, char transa, char diag, int n, int
nrhs, double *a, double *b, int ldb, double *x,
int ldx, double *ferr, double *berr, int *info);
void dtprfs_64(char uplo, char transa, char diag, long n,
long nrhs, double *a, double *b, long ldb, double
*x, long ldx, double *ferr, double *berr, long
*info);
dtprfs provides error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular packed coefficient matrix.
The solution matrix X must be computed by DTPTRS or some
other means before entering this routine. DTPRFS 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed
columnwise in a linear array. The j-th column of
A is stored in the array A as follows: if UPLO =
'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if
UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for
j<=i<=n. If DIAG = 'U', the diagonal elements of
A are not referenced and are assumed to be 1.
B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,N).
X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >=
max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
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) DOUBLE PRECISION array, dimension (NRHS)
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)
DOUBLE PRECISION array, dimension(3*N)
WORK2 (workspace)
INTEGER array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value