SLANEG
June 2010
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.)
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.)
Arguments
| 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 Details
Based on contributions by
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Jason Riedy, University of California, Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Jason Riedy, University of California, Berkeley, USA