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

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