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DLATDF(l)			       )			     DLATDF(l)

NAME
       DLATDF  -  use  the LU factorization of the n-by-n matrix Z computed by
       DGETC2 and computes a contribution to the  reciprocal  Dif-estimate  by
       solving Z * x = b for x, and choosing the r.h.s

SYNOPSIS
       SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )

	   INTEGER	  IJOB, LDZ, N

	   DOUBLE	  PRECISION RDSCAL, RDSUM

	   INTEGER	  IPIV( * ), JPIV( * )

	   DOUBLE	  PRECISION RHS( * ), Z( LDZ, * )

PURPOSE
       DLATDF  uses  the  LU  factorization of the n-by-n matrix Z computed by
       DGETC2 and computes a contribution to the  reciprocal  Dif-estimate  by
       solving	Z  * x = b for x, and choosing the r.h.s. b such that the norm
       of x is as large as possible. On entry RHS = b holds  the  contribution
       from earlier solved sub-systems, and on return RHS = x.

       The  factorization  of  Z  returned by DGETC2 has the form Z = P*L*U*Q,
       where P and Q are permutation matrices. L is lower triangular with unit
       diagonal elements and U is upper triangular.

ARGUMENTS
       IJOB    (input) INTEGER
	       IJOB  =	2:  First  compute an approximative null-vector e of Z
	       using DGECON, e is normalized and solve for Zx = +-e -  f  with
	       the  sign  giving the greater value of 2-norm(x). About 5 times
	       as expensive as Default.	 IJOB .ne. 2: Local look ahead	stratā€
	       egy  where  all entries of the r.h.s. b is choosen as either +1
	       or -1 (Default).

       N       (input) INTEGER
	       The number of columns of the matrix Z.

       Z       (input) DOUBLE PRECISION array, dimension (LDZ, N)
	       On entry, the LU part of the factorization of the n-by-n matrix
	       Z computed by DGETC2:  Z = P * L * U * Q

       LDZ     (input) INTEGER
	       The leading dimension of the array Z.  LDA >= max(1, N).

       RHS     (input/output) DOUBLE PRECISION array, dimension N.
	       On entry, RHS contains contributions from other subsystems.  On
	       exit, RHS contains the solution of the subsystem	 with  entries
	       acoording to the value of IJOB (see above).

       RDSUM   (input/output) DOUBLE PRECISION
	       On  entry,  the sum of squares of computed contributions to the
	       Dif-estimate under computation by  DTGSYL,  where  the  scaling
	       factor  RDSCAL (see below) has been factored out.  On exit, the
	       corresponding sum of squares  updated  with  the	 contributions
	       from  the  current  sub-system.	 If  TRANS  = 'T' RDSUM is not
	       touched.	 NOTE: RDSUM only makes sense when DTGSY2 is called by
	       STGSYL.

       RDSCAL  (input/output) DOUBLE PRECISION
	       On entry, scaling factor used to prevent overflow in RDSUM.  On
	       exit, RDSCAL is updated w.r.t.  the  current  contributions  in
	       RDSUM.	If  TRANS  = 'T', RDSCAL is not touched.  NOTE: RDSCAL
	       only makes sense when DTGSY2 is called by DTGSYL.

       IPIV    (input) INTEGER array, dimension (N).
	       The pivot indices; for 1 <= i <= N, row i  of  the  matrix  has
	       been interchanged with row IPIV(i).

       JPIV    (input) INTEGER array, dimension (N).
	       The  pivot indices; for 1 <= j <= N, column j of the matrix has
	       been interchanged with column JPIV(j).

FURTHER DETAILS
       Based on contributions by
	  Bo Kagstrom and Peter Poromaa, Department of Computing Science,
	  Umea University, S-901 87 Umea, Sweden.

       This routine is a further developed implementation of algorithm	BSOLVE
       in [1] using complete pivoting in the LU factorization.

       [1] Bo Kagstrom and Lars Westin,
	   Generalized Schur Methods with Condition Estimators for
	   Solving the Generalized Sylvester Equation, IEEE Transactions
	   on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.

       [2] Peter Poromaa,
	   On Efficient and Robust Estimators for the Separation
	   between two Regular Matrix Pairs with Applications in
	   Condition Estimation. Report IMINF-95.05, Departement of
	   Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

LAPACK version 3.0		 15 June 2000			     DLATDF(l)
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