dlaneg.f (3) - Linux Manuals
NAME
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:
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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
N is INTEGER The order of the matrix.
DD is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D.
LLDLLD is DOUBLE PRECISION array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i).
SIGMASIGMA is DOUBLE PRECISION Shift amount in T - sigma I = L D L^T.
PIVMINPIVMIN is DOUBLE PRECISION The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures.
RR is INTEGER The twist index for the twisted factorization that is used for the negcount.
Author:
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Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- September 2012
Contributors:
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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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