ZPBRFS(l)		LAPACK routine (version	1.1)		    ZPBRFS(l)

NAME
  ZPBRFS - improve the computed	solution to a system of	linear equations when
  the coefficient matrix is Hermitian positive definite	and banded, and	pro-
  vides	error bounds and backward error	estimates for the solution

SYNOPSIS

  SUBROUTINE ZPBRFS( UPLO, N, KD, NRHS,	AB, LDAB, AFB, LDAFB, B, LDB, X, LDX,
		     FERR, BERR, WORK, RWORK, INFO )

      CHARACTER	     UPLO

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

      DOUBLE	     PRECISION BERR( * ), FERR(	* ), RWORK( * )

      COMPLEX*16     AB( LDAB, * ), AFB( LDAFB,	* ), B(	LDB, * ), WORK(	* ),
		     X(	LDX, * )

PURPOSE
  ZPBRFS improves the computed solution	to a system of linear equations	when
  the coefficient matrix is Hermitian positive definite	and banded, and	pro-
  vides	error bounds and backward error	estimates for the solution.

ARGUMENTS

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper	triangle of A is stored;
	  = 'L':  Lower	triangle of A is stored.

  N	  (input) INTEGER
	  The order of the matrix A.  N	>= 0.

  KD	  (input) INTEGER
	  The number of	superdiagonals of the matrix A if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'.	 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 triangle of the Hermitian 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).

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

  AFB	  (input) COMPLEX*16 array, dimension (LDAFB,N)
	  The triangular factor	U or L from the	Cholesky factorization A =
	  U**H*U or A =	L*L**H of the band matrix A as computed	by ZPBTRF, in
	  the same storage format as A (see AB).

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

  B	  (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
	  On entry, the	solution matrix	X, as computed by ZPBTRS.  On exit,
	  the improved 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) COMPLEX*16 array,	dimension (2*N)

  RWORK	  (workspace) DOUBLE PRECISION 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.