LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
 All Classes Files Functions Variables Typedefs Macros
slaneg.f File Reference

Go to the source code of this file.

Functions/Subroutines

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

Function/Subroutine Documentation

INTEGER function slaneg ( integer  N,
real, dimension( * )  D,
real, dimension( * )  LLD,
real  SIGMA,
real  PIVMIN,
integer  R 
)

SLANEG computes the Sturm count.

Download SLANEG + dependencies [TGZ] [ZIP] [TXT]
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
[in]N
          N is INTEGER
          The order of the matrix.
[in]D
          D is REAL array, dimension (N)
          The N diagonal elements of the diagonal matrix D.
[in]LLD
          LLD is REAL array, dimension (N-1)
          The (N-1) elements L(i)*L(i)*D(i).
[in]SIGMA
          SIGMA is REAL
          Shift amount in T - sigma I = L D L^T.
[in]PIVMIN
          PIVMIN is REAL
          The minimum pivot in the Sturm sequence.  May be used
          when zero pivots are encountered on non-IEEE-754
          architectures.
[in]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.

Here is the call graph for this function:

Here is the caller graph for this function: