CXML
        	    
LAPACK version 3.0
zptrfs(3)

PURPOSE
  ZPTRFS - 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

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

      CHARACTER	     UPLO

      INTEGER	     INFO, LDB, LDX, N, NRHS

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

      COMPLEX*16     B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

DESCRIPTION
  ZPTRFS 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
	  tridiagonal 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) DOUBLE PRECISION array, dimension (N)
	  The n real diagonal elements of the tridiagonal matrix A.

  E	  (input) COMPLEX*16 array, dimension (N-1)
	  The (n-1) off-diagonal elements of the tridiagonal matrix A (see
	  UPLO).

  DF	  (input) DOUBLE PRECISION array, dimension (N)
	  The n diagonal elements of the diagonal matrix D from the
	  factorization computed by ZPTTRF.

  EF	  (input) COMPLEX*16 array, dimension (N-1)
	  The (n-1) off-diagonal elements of the unit bidiagonal factor U or
	  L from the factorization computed by ZPTTRF (see UPLO).

  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 ZPTTRS.  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 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).

  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 (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.