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clatdf.f(3)				      LAPACK				      clatdf.f(3)

NAME
       clatdf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine clatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
	   CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes
	   a contribution to the reciprocal Dif-estimate.

Function/Subroutine Documentation
   subroutine clatdf (integerIJOB, integerN, complex, dimension( ldz, * )Z, integerLDZ, complex,
       dimension( * )RHS, realRDSUM, realRDSCAL, integer, dimension( * )IPIV, integer, dimension(
       * )JPIV)
       CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a
       contribution to the reciprocal Dif-estimate.

       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.

       Parameters:
	   IJOB

		     IJOB is 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

		     N is INTEGER
		     The number of columns of the matrix Z.

	   Z

		     Z is 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

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

	   RHS

		     RHS is 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

		     RDSUM is 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 current sub-system.
		     If TRANS = 'T' RDSUM is not touched.
		     NOTE: RDSUM only makes sense when CTGSY2 is called by CTGSYL.

	   RDSCAL

		     RDSCAL is 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

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

	   JPIV

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

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

       Contributors:
	   Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901
	   87 Umea, Sweden.

       References:
	   [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.

       Definition at line 169 of file clatdf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      clatdf.f(3)
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