Extensions to ScaLAPACK.
Next: Monte Carlo Simulation.
Up: No Title
Previous: No Title
We discussed ScaLAPACK in class. It is a library of routines for
numerical linear algebra being constructed here and
at the University of Tennessee. We released version 1.0 at
the end of February; there have been 16,000 accesses to it
on the Web, so it is widely distributed.
There are a number of extensions and additions we would like
to make. One or more of them could constitute an interesting
project.
- ScaLAPACK - Split-C interface. We would like to be able
to call ScaLAPACK from Split-C. First, this requires changing the
internals of the underlying message passing system used by
ScaLAPACK (the BLACS, or Basic Linear Algebra Communication
Subroutines) to use Generic Active Messages, on which Split-C
is based. Second, it required building an interface so that
spread arrays can be passed to ScaLAPACK. Both use quite
similar data layouts, so this should be doable efficiently.
- A guaranteed accurate symmetric eigensolver for ScaLAPACK.
The current routine in ScaLAPACK for finding eigenvalues and
eigenvectors of symmetric matrices makes certain compromises
to guarantee speed, at the expense of occasionally getting
inaccurate vectors (in which case a warning is given!).
We have several plans to provide a routine with guaranteed
accuracy. The easiest (and slowest) one is based on an
algorithm called QR iteration. I expect this to be quite
easy to build of existing routines in LAPACK in ScaLAPACK.
You should also do performance modeling and testing to
see how much slower the QR routine is than the existing
ScaLAPACK routine, and how the accuracy compares.
- Singular Value Decomposition for ScaLAPACK.
This problem is closely related to the symmetric eigenvalue
problem, and with algorithms analogous both to the current
ScaLAPACK eigensolver, and to the QR algorithm just proposed.
The project would produce an SVD analogous to the
current ScaLAPACK routine. I expect many existing ScaLAPACK
routines could be used. Performance modeling would be done as well.
- Other ScaLAPACK routines. I can propose a large number
of other similar projects as well.
Next: Monte Carlo Simulation.
Up: No Title
Previous: No Title
Boris Vaysman
Sun Jan 14 22:42:23 PST 1996