ztrrfs(3P) Sun Performance Library ztrrfs(3P)NAMEztrrfs - 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);
PURPOSEztrrfs 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)
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) 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
6 Mar 2009 ztrrfs(3P)
