dlaneg-f(3)

dlaneg.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

INTEGER function dlaneg (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, double precisionSIGMA, double precisionPIVMIN, integerR)

DLANEG computes the Sturm count.

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.)

Parameters:

 N is INTEGER
 The order of the matrix.

 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 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 dlaneg.f.

Author

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