ztrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
SUBROUTINE ZTRRFS(UPLO, TRANSA, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDA, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZTRRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) 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 COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B, X INTEGER :: N, NRHS, LDA, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 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 COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B, X INTEGER(8) :: N, NRHS, LDA, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void ztrrfs(char uplo, char transa, char diag, int n, int nrhs, double- complex *a, int lda, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void ztrrfs_64(char uplo, char transa, char diag, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, dou- blecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library ztrrfs(3P)
NAME
ztrrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular coefficient
matrix
SYNOPSIS
SUBROUTINE ZTRRFS(UPLO, TRANSA, DIAG, N, NRHS, A, LDA, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDA, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZTRRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, LDA, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
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
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, X
INTEGER :: N, NRHS, LDA, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
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
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, X
INTEGER(8) :: N, NRHS, LDA, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void ztrrfs(char uplo, char transa, char diag, int n, int nrhs, double-
complex *a, int lda, doublecomplex *b, int ldb, doublecomplex
*x, int ldx, double *ferr, double *berr, int *info);
void ztrrfs_64(char uplo, char transa, char diag, long n, long nrhs,
doublecomplex *a, long lda, doublecomplex *b, long ldb, dou-
blecomplex *x, long ldx, double *ferr, double *berr, long
*info);
PURPOSE
ztrrfs provides error bounds and backward error estimates for the solu-
tion to a system of linear equations with a triangular coefficient
matrix.
The solution matrix X must be computed by ZTRTRS or some other means
before entering this routine. ZTRRFS 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)
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 leading N-by-N
upper triangular part of the array A contains the upper tri-
angular matrix, and the strictly lower triangular part of A
is not referenced. If UPLO = 'L', the leading N-by-N lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular 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 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)
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)
dimension(2*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal value.
7 Nov 2015 ztrrfs(3P)