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strrfs.f(3) LAPACK strrfs.f(3)

NAME

strrfs.f

SYNOPSIS

Functions/Subroutines


subroutine strrfs (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
STRRFS

Function/Subroutine Documentation

subroutine strrfs (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldx, * ) X, integer LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

STRRFS

Purpose:


STRRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix.
The solution matrix X must be computed by STRTRS or some other
means before entering this routine. STRRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.

TRANS


TRANS is 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 = Transpose)

DIAG


DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.

N


N is INTEGER
The order of the matrix A. N >= 0.

NRHS


NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

A


A is REAL 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
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
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


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

B


B is REAL array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB


LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X


X is REAL array, dimension (LDX,NRHS)
The solution matrix X.

LDX


LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

FERR


FERR is 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


BERR is 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


WORK is REAL array, dimension (3*N)

IWORK


IWORK is INTEGER array, dimension (N)

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 184 of file strrfs.f.

Author

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Tue Nov 14 2017 Version 3.8.0