Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  the  Sturm  count,  the number of negative pivots encountered while
       factoring tridiagonal T - sigma I = L D L^T

SYNOPSIS

       INTEGER FUNCTION SLANEG( N, D, LLD, SIGMA, PIVMIN, R )

           IMPLICIT     NONE

           INTEGER      N, R

           REAL         PIVMIN, SIGMA

           REAL         D( * ), LLD( * )

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.)

ARGUMENTS

        N       (input) INTEGER
                The order of the matrix.

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

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

        SIGMA   (input) REAL
                Shift amount in T - sigma I = L D L^T.

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

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

FURTHER DETAILS

        Based on contributions by
           Osni Marques, LBNL/NERSC, USA
           Christof Voemel, University of California, Berkeley, USA
           Jason Riedy, University of California, Berkeley, USA

 LAPACK auxiliary routine (version 3.2.2)   April 2011                            SLANEG(3lapack)