ctrrfs(3)

NAME

CTRRFS - provide error bounds and backward error estimates

for the solution to a system of linear equations with a triangu

lar 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 solution to a system of linear equations with a triangu

lar coefficient matrix. The solution matrix X must be computed

by CTRTRS or some other means before entering this routine. CTR

RFS does not do iterative refinement because doing so cannot im

prove 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 lead

ing N-by-N upper triangular part of the array A contains the up

per triangular 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 ma

trix, and the strictly upper triangular part of A is not refer

enced. If DIAG = 'U', the diagonal elements of A are also not

referenced 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 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 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 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) 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 ille

gal value

LAPACK version 3.0 15 June 2000

CTRRFS(3)