stprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coef- ficient 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);
Oracle Solaris Studio Performance Library stprfs(3P)
NAME
stprfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed coef-
ficient matrix
SYNOPSIS
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);
PURPOSE
stprfs provides error bounds and backward error estimates for the solu-
tion to a system of linear equations with a triangular packed coeffi-
cient 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.
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.
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 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) REAL array, dimension (NRHS)
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)
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 illegal value
7 Nov 2015 stprfs(3P)