DTPRFS(l)		LAPACK routine (version	1.1)		    DTPRFS(l)

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

SYNOPSIS

  SUBROUTINE DTPRFS( UPLO, TRANS, DIAG,	N, NRHS, AP, B,	LDB, X,	LDX, FERR,
		     BERR, WORK, IWORK,	INFO )

      CHARACTER	     DIAG, TRANS, UPLO

      INTEGER	     INFO, LDB,	LDX, N,	NRHS

      INTEGER	     IWORK( * )

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

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

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

  AP	  (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	  The upper or lower triangular	matrix A, packed columnwise in a
	  linear array.	 The j-th column of A is stored	in the array AP	as
	  follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if
	  UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  If DIAG =
	  'U', the diagonal elements of	A are not referenced and are assumed
	  to be	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