slaneg (3)

Functions/Subroutines

integer function slaneg (N, D, LLD, SIGMA, PIVMIN, R)

SLANEG computes the Sturm count.

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.

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