SRC/dlaneg.f(3)

NAME
SRC/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 (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,  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

Definition at line 117 of file dlaneg.f.

Author

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