CPTRFS(l)		LAPACK routine (version	1.1)		    CPTRFS(l)

NAME
  CPTRFS - improve the computed	solution to a system of	linear equations when
  the coefficient matrix is Hermitian positive definite	and tridiagonal, and
  provides error bounds	and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,	BERR,
		     WORK, RWORK, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, LDB,	LDX, N,	NRHS

      REAL	     BERR( * ),	D( * ),	DF( * ), FERR( * ), RWORK( * )

      COMPLEX	     B(	LDB, * ), E( * ), EF( *	), WORK( * ), X( LDX, *	)

PURPOSE
  CPTRFS improves the computed solution	to a system of linear equations	when
  the coefficient matrix is Hermitian positive definite	and tridiagonal, and
  provides error bounds	and backward error estimates for the solution.

ARGUMENTS

  UPLO	  (input) CHARACTER*1
	  Specifies whether the	superdiagonal or the subdiagonal of the	tri-
	  diagonal matrix A is stored and the form of the factorization:
	  = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
	  = 'L':  E is the subdiagonal of A, and A = L*D*L**H.	(The two
	  forms	are equivalent if A is real.)

  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
	  matrix B.  NRHS >= 0.

  D	  (input) REAL array, dimension	(N)
	  The n	real diagonal elements of the tridiagonal matrix A.

  E	  (input) COMPLEX array, dimension (N-1)
	  The (n-1) off-diagonal elements of the tridiagonal matrix A (see
	  UPLO).

  DF	  (input) REAL array, dimension	(N)
	  The n	diagonal elements of the diagonal matrix D from	the factori-
	  zation computed by CPTTRF.

  EF	  (input) COMPLEX array, dimension (N-1)
	  The (n-1) off-diagonal elements of the unit bidiagonal factor	U or
	  L from the factorization computed by CPTTRF (see UPLO).

  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/output) COMPLEX array,	dimension (LDX,NRHS)
	  On entry, the	solution matrix	X, as computed by CPTTRS.  On exit,
	  the improved 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 (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

PARAMETERS

  ITMAX	is the maximum number of steps of iterative refinement.