SLATDF(l)								 )								 SLATDF(l)

NAME

       SLATDF  -  use the LU factorization of the n-by-n matrix Z computed by SGETC2 and computes a contribution to the reciprocal Dif-estimate by
       solving Z * x = b for x, and choosing the r.h.s

SYNOPSIS

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

	   INTEGER	  IJOB, LDZ, N

	   REAL 	  RDSCAL, RDSUM

	   INTEGER	  IPIV( * ), JPIV( * )

	   REAL 	  RHS( * ), Z( LDZ, * )

PURPOSE

       SLATDF uses the LU factorization of the n-by-n matrix Z computed by SGETC2 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 SGETC2 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 SGECON, 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 SGETC2:  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 aco-
	       ording 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 STGSYL, 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 STGSY2 is called by STGSYL.

       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 STGSY2 is called by STGSYL.

       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 							 SLATDF(l)