dlaneg.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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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 (integer N, double precision, dimension( * ) D, double precision, dimension( * ) LLD, double precision SIGMA, double precision PIVMIN, integer R)

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

          N is INTEGER
          The order of the matrix.


D

          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

          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:

December 2016

Contributors:

Osni Marques, LBNL/NERSC, USA

 Christof Voemel, University of California, Berkeley, USA 

 Jason Riedy, University of California, Berkeley, USA 

Definition at line 120 of file dlaneg.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
integer function dlaneg (integer N, double precision, dimension( * ) D, double precision, dimension( * ) LLD, double precision SIGMA, double precision PIVMIN, integer R)
Author
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