stprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
SUBROUTINE STPRFS( 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(*) REAL A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE STPRFS_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(*) REAL A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
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, DIMENSION(:) :: A, FERR, BERR, WORK REAL, 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, DIMENSION(:) :: A, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X
#include <sunperf.h>
void stprfs(char uplo, char transa, char diag, int n, int nrhs, float *a, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);
void stprfs_64(char uplo, char transa, char diag, long n, long nrhs, float *a, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);
stprfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix.
The solution matrix X must be computed by STPTRS or some other means before entering this routine. STPRFS does not do iterative refinement because doing so cannot improve the backward error.
= 'U': A is upper triangular;
= 'L': A is lower triangular.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
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.
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
element 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.
X(j)
(i.e., the smallest relative change in
any element of A or B that makes X(j)
an exact solution).
dimension(3*N)
dimension(N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value