PLAPACK: high performance through high-level abstraction

Coding parallel algorithms is generally regarded as a formidable task. To make this task manageable in the arena of linear algebra algorithms, we have developed the Parallel Linear Algebra Package (PLAPACK), an infrastructure for coding such algorithms at a high level of abstraction. It is often believed that by raising the level of abstraction in this fashion, performance is sacrificed. Throughout, we have maintained that indeed there is a performance penalty, but that by coding at a higher level of abstraction, more sophisticated algorithms can be implemented, which allows high levels of performance to be regained. In this paper, we show this to be the case for the parallel solver package implemented using PLAPACK, which includes Cholesky, LU, and QR factorization based solvers for symmetric positive definite, general, and overdetermined systems of equations, respectively. Contributions of this paper include new parallel algorithms for these factorizations and performance results on a Cray T3E-600