NAME

       laneg - laneg: Sturm count

SYNOPSIS

   Functions
       integer function dlaneg (n, d, lld, sigma, pivmin, r)
           DLANEG computes the Sturm count.
       integer function slaneg (n, d, lld, sigma, pivmin, r)
           SLANEG computes the Sturm count.

Detailed Description

Function Documentation

   integer function dlaneg (integer n, double precision, dimension( * ) d, double precision,
       dimension( * ) lld, double precision sigma, double precision pivmin, integer r)
       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.

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

   integer function slaneg (integer n, real, dimension( * ) d, real, dimension( * ) lld, real
       sigma, real pivmin, integer r)
       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.

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

Author

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