DTRRFS(l)								 )								 DTRRFS(l)

NAME

       DTRRFS  -  provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular 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  triangular  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 = 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) 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 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) DOUBLE PRECISION 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) 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

LAPACK version 3.0						   15 June 2000 							 DTRRFS(l)