slaneg.f man page

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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

slaneg(3) is an alias of slaneg.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK