DTBRFS(l)		LAPACK routine (version	1.1)		    DTBRFS(l)

NAME
  DTBRFS - provide error bounds	and backward error estimates for the solution
  to a system of linear	equations with a triangular band coefficient matrix

SYNOPSIS

  SUBROUTINE DTBRFS( UPLO, TRANS, DIAG,	N, KD, NRHS, AB, LDAB, B, LDB, X,
		     LDX, FERR,	BERR, WORK, IWORK, INFO	)

      CHARACTER	     DIAG, TRANS, UPLO

      INTEGER	     INFO, KD, LDAB, LDB, LDX, N, NRHS

      INTEGER	     IWORK( * )

      DOUBLE	     PRECISION AB( LDAB, * ), B( LDB, *	), BERR( * ), FERR( *
		     ),	WORK( *	), X( LDX, * )

PURPOSE
  DTBRFS provides error	bounds and backward error estimates for	the solution
  to a system of linear	equations with a triangular band coefficient matrix.

  The solution matrix X	must be	computed by DTBTRS or some other means before
  entering this	routine.  DTBRFS 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.

  KD	  (input) INTEGER
	  The number of	superdiagonals or subdiagonals of the triangular band
	  matrix A.  KD	>= 0.

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

  AB	  (input) DOUBLE PRECISION array, dimension (LDAB,N)
	  The upper or lower triangular	band matrix A, stored in the first
	  kd+1 rows of the array. The j-th column of A is stored in the	j-th
	  column of the	array AB as follows: if	UPLO = 'U', AB(kd+1+i-j,j) =
	  A(i,j) for max(1,j-kd)<=i<=j;	if UPLO	= 'L', AB(1+i-j,j)    =
	  A(i,j) for j<=i<=min(n,j+kd).	 If DIAG = 'U',	the diagonal elements
	  of A are not referenced and are assumed to be	1.

  LDAB	  (input) INTEGER
	  The leading dimension	of the array AB.  LDAB >= KD+1.

  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 accurate, 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