Contents
stprfs - provide error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular 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(*)
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, 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
C INTERFACE
#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 tri-
angular 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.
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) REAL 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) REAL 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) REAL array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >=
max(1,N).
FERR (output) REAL 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) REAL 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)
REAL 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