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slaneg.f(3) LAPACK slaneg.f(3)

NAME

slaneg.f -

SYNOPSIS

Functions/Subroutines


INTEGER function slaneg (N, D, LLD, SIGMA, PIVMIN, R)
SLANEG computes the Sturm count.

Function/Subroutine Documentation

INTEGER function slaneg (integerN, real, dimension( * )D, real, dimension( * )LLD, realSIGMA, realPIVMIN, integerR)

SLANEG computes the Sturm count.

Purpose:


SLANEG 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 SLARRB.
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.)

Parameters:

N


N is INTEGER
The order of the matrix.

D


D is REAL array, dimension (N)
The N diagonal elements of the diagonal matrix D.

LLD


LLD is REAL array, dimension (N-1)
The (N-1) elements L(i)*L(i)*D(i).

SIGMA


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

PIVMIN


PIVMIN is REAL
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.

Date:

September 2012

Contributors:

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

Definition at line 119 of file slaneg.f.

Author

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Tue Sep 25 2012 Version 3.4.2