Extensions to ScaLAPACK.

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.