SYNOPSIS

FUNCTION DLANEG(

N, D, LLD, SIGMA, PIVMIN, R )

    

IMPLICIT NONE

    

INTEGER DLANEG

    

INTEGER N, R

    

DOUBLE PRECISION PIVMIN, SIGMA

    

DOUBLE PRECISION D( * ), LLD( * )

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.)

ARGUMENTS

N (input) INTEGER

The order of the matrix.

D (input) DOUBLE PRECISION array, dimension (N)

The N diagonal elements of the diagonal matrix D.

LLD (input) DOUBLE PRECISION array, dimension (N-1)

The (N-1) elements L(i)*L(i)*D(i).

SIGMA (input) DOUBLE PRECISION

Shift amount in T - sigma I = L D L^T.

PIVMIN (input) DOUBLE PRECISION

The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures.

R (input) INTEGER

The twist index for the twisted factorization that is used for the negcount.

FURTHER DETAILS

Based on contributions by

   Osni Marques, LBNL/NERSC, USA

   Christof Voemel, University of California, Berkeley, USA
   Jason Riedy, University of California, Berkeley, USA