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