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## dlaneg()

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.

Download DLANEG + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix.
      !>

  [in]

  D

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

  [in]

  LLD

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

  [in]

  SIGMA

      !>          SIGMA is DOUBLE PRECISION
      !>          Shift amount in T - sigma I = L D L^T.
      !>

  [in]

  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.
      !>

  [in]

  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