CTRRFS(l)		LAPACK routine (version	1.1)		    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 solution
  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 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) 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 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 accurate, the	error bound is guaranteed.

  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 entry	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