dlaneg.f3

!>
!> 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.)
!> 

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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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