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slaneg.f(3)				      LAPACK				      slaneg.f(3)

NAME
       slaneg.f -

SYNOPSIS
   Functions/Subroutines
       INTEGER function slaneg (N, D, LLD, SIGMA, PIVMIN, R)
	   SLANEG computes the Sturm count.

Function/Subroutine Documentation
   INTEGER function slaneg (integerN, real, dimension( * )D, real, dimension( * )LLD, realSIGMA,
       realPIVMIN, integerR)
       SLANEG computes the Sturm count.

       Purpose:

	    SLANEG computes the Sturm count, the number of negative pivots
	    encountered while factoring tridiagonal T - sigma I = L D L^T.
	    This implementation works directly on the factors without forming
	    the tridiagonal matrix T.  The Sturm count is also the number of
	    eigenvalues of T less than sigma.

	    This routine is called from SLARRB.

	    The current routine does not use the PIVMIN parameter but rather
	    requires IEEE-754 propagation of Infinities and NaNs.  This
	    routine also has no input range restrictions but does require
	    default exception handling such that x/0 produces Inf when x is
	    non-zero, and Inf/Inf produces NaN.  For more information, see:

	      Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in
	      Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
	      Scientific Computing, v28, n5, 2006.  DOI 10.1137/050641624
	      (Tech report version in LAWN 172 with the same title.)

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix.

	   D

		     D is REAL array, dimension (N)
		     The N diagonal elements of the diagonal matrix D.

	   LLD

		     LLD is REAL array, dimension (N-1)
		     The (N-1) elements L(i)*L(i)*D(i).

	   SIGMA

		     SIGMA is REAL
		     Shift amount in T - sigma I = L D L^T.

	   PIVMIN

		     PIVMIN is REAL
		     The minimum pivot in the Sturm sequence.  May be used
		     when zero pivots are encountered on non-IEEE-754
		     architectures.

	   R

		     R is INTEGER
		     The twist index for the twisted factorization that is used
		     for the negcount.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Osni Marques, LBNL/NERSC, USA
	    Christof Voemel, University of California, Berkeley, USA
	    Jason Riedy, University of California, Berkeley, USA

       Definition at line 119 of file slaneg.f.

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

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