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# dtrrfs

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NAME
DTRRFS - provide error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular coefficient matrix

SYNOPSIS
SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B,
LDB, X, LDX, FERR, BERR, WORK, IWORK,
INFO )

CHARACTER      DIAG, TRANS, UPLO

INTEGER        INFO, LDA, LDB, LDX, N, NRHS

INTEGER        IWORK( * )

DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), BERR(
* ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE
DTRRFS provides error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular coefficient matrix.

The solution matrix X must be computed by DTRTRS or some
other means before entering this routine.  DTRRFS 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 = Tran-
spose)

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

B       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
The solution matrix X.

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

FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution
vector X(j) (the j-th column of the solution matrix
X).  If XTRUE is the true solution, FERR(j) bounds
the magnitude of the largest entry in (X(j) - XTRUE)
divided by the magnitude of the largest entry in
X(j).  The quality of the error bound depends on the
quality of the estimate of norm(inv(A)) computed in
the code; if the estimate of norm(inv(A)) is accu-
rate, the error bound is guaranteed.

BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each
solution vector X(j) (i.e., the smallest relative
change in any entry of A or B that makes X(j) an
exact solution).

WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

IWORK   (workspace) INTEGER array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit

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