LAPACK

NAME¶

laneg - laneg: Sturm count

SYNOPSIS¶

Functions¶

integer function dlaneg (n, d, lld, sigma, pivmin, r)
DLANEG computes the Sturm count. integer function slaneg (n, d, lld, sigma, pivmin, r)
SLANEG computes the Sturm count.

Detailed Description¶

Function 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 is INTEGER


          The order of the matrix.



          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 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.

Contributors:

Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Jason Riedy, University of California, Berkeley, USA

integer function slaneg (integer n, real, dimension( * ) d, real, dimension( * ) lld, real sigma, real pivmin, integer r)¶

SLANEG computes the Sturm count.