slaneg.f man page

slaneg.f —



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.  


 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.)


          N is INTEGER
          The order of the matrix.


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


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


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


          PIVMIN is REAL
          The minimum pivot in the Sturm sequence.  May be used
          when zero pivots are encountered on non-IEEE-754


          R is INTEGER
          The twist index for the twisted factorization that is used
          for the negcount.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


September 2012


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.


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Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK