- FUNCTION SLANEG(
- N, D, LLD, SIGMA, PIVMIN, R )
- IMPLICIT NONE
- INTEGER SLANEG
- INTEGER N, R
- REAL PIVMIN, SIGMA
- REAL D( * ), LLD( * )
PURPOSESLANEG 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 (input) INTEGER
- The order of the matrix.
- D (input) REAL array, dimension (N)
- The N diagonal elements of the diagonal matrix D.
- LLD (input) REAL array, dimension (N-1)
- The (N-1) elements L(i)*L(i)*D(i).
- SIGMA (input) REAL
- Shift amount in T - sigma I = L D L^T.
- PIVMIN (input) REAL
- The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures.
- R (input) INTEGER
- The twist index for the twisted factorization that is used for the negcount.
FURTHER DETAILSBased on contributions by
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Jason Riedy, University of California, Berkeley, USA