CXML
        	    
LAPACK version 3.0
zpbrfs(3)

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

SYNTAX
  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, * )

DESCRIPTION
  ZPBRFS improves the computed solution to a system of linear equations when
  the coefficient matrix is Hermitian positive definite and banded, and
  provides 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 bound for each solution vector X(j)
	  (the j-th column of the solution matrix X).  If XTRUE is the true
	  solution corresponding to X(j), FERR(j) is an estimated upper bound
	  for the magnitude of the largest element in (X(j) - XTRUE) divided
	  by the magnitude of the largest element in X(j).  The estimate is
	  as reliable as the estimate for RCOND, and is almost always a
	  slight overestimate of the true error.

  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 element 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.