CTRRFS(l) ) CTRRFS(l)NAME
CTRRFS - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular coefficient
matrix
SYNOPSIS
SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDA, LDB, LDX, N, NRHS
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )
PURPOSE
CTRRFS 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 CTRTRS or some other
means before entering this routine. CTRRFS does not do iterative
refinement because doing so cannot improve the backward error.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS (input) CHARACTER*1
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) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading N-by-N
upper triangular part of the array A contains the upper trian‐
gular matrix, and the strictly lower triangular part of A is
not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
gular 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 refer‐
enced and are assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input) COMPLEX array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
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 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.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vec‐
tor X(j) (i.e., the smallest relative change in any element of
A or B that makes X(j) an exact solution).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK version 3.0 15 June 2000 CTRRFS(l)
