DLANEG(3)      LAPACK routine of NEC Numeric Library Collection      DLANEG(3)



NAME
       DLANEG

SYNOPSIS
       INTEGER FUNCTION DLANEG (N, D, LLD, SIGMA, PIVMIN, R)



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:





ARGUMENTS
           N         (input)
                     N is INTEGER
                     The order of the matrix.

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

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

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

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



LAPACK routine                  31 October 2017                      DLANEG(3)