NAME

       dlaneg.f -

SYNOPSIS

   Functions/Subroutines
       integer function dlaneg (N, D, LLD, SIGMA, PIVMIN, R)
           DLANEG computes the Sturm count.

Function/Subroutine Documentation

   integer function dlaneg (integerN, double precision, dimension( * )D, double precision,
       dimension( * )LLD, double precisionSIGMA, double precisionPIVMIN, integerR)
       DLANEG computes the Sturm count.

       Purpose:

            DLANEG 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 DLARRB.

            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 DOUBLE PRECISION array, dimension (N)
                     The N diagonal elements of the diagonal matrix D.

           LLD

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

           SIGMA

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

           PIVMIN

                     PIVMIN is DOUBLE PRECISION
                     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 dlaneg.f.

Author

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