CLATDF(l)								 )								 CLATDF(l)

NAME

       CLATDF  -  compute the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x
       is as large as possible

SYNOPSIS

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

	   INTEGER	  IJOB, LDZ, N

	   REAL 	  RDSCAL, RDSUM

	   INTEGER	  IPIV( * ), JPIV( * )

	   COMPLEX	  RHS( * ), Z( LDZ, * )

PURPOSE

       CLATDF computes the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is
       as  large  as  possible. It is assumed that LU decomposition of Z has been computed by CGETC2. On entry RHS = f holds the contribution from
       earlier solved sub-systems, and on return RHS = x.

       The factorization of Z returned by CGETC2 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 CGECON, 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 strategy 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) REAL array, dimension (LDZ, N)
	       On entry, the LU part of the factorization of the n-by-n matrix Z computed by CGETC2:  Z = P * L * U * Q

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

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

       RDSUM   (input/output) REAL
	       On  entry,  the	sum of squares of computed contributions to the Dif-estimate under computation by CTGSYL, where the scaling factor
	       RDSCAL (see below) has been factored out.  On exit, the corresponding sum of squares updated with the contributions from  the  cur-
	       rent sub-system.  If TRANS = 'T' RDSUM is not touched.  NOTE: RDSUM only makes sense when CTGSY2 is called by CTGSYL.

       RDSCAL  (input/output) REAL
	       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 CTGSY2 is called by CTGSYL.

       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 UMINF-95.05, Department of
	      Computing Science, Umea University, S-901 87 Umea, Sweden,
	      1995.

LAPACK version 3.0						   15 June 2000 							 CLATDF(l)