LAPACK Working Note 95 ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance

This paper outlines the content and performance of ScaLAPACK, a collection of mathematical software for linear algebra computations on distributed memory computers. The importance of developing standards for computational and message passing interfaces is discussed. We present the di erent components and building blocks of ScaLAPACK. This paper outlines the di culties inherent in producing correct codes for networks of heterogeneous processors. We de ne a theoretical model of parallel computers dedicated to linear algebra applications: the Distributed Linear Algebra Machine (DLAM). This model provides a convenient framework for developing parallel algorithms and investigating their scalability, performance and programmability. Extensive performance results on various platforms are presented and analyzed with the help of the DLAM. Finally, this paper brie y describes future directions for the ScaLAPACK library and concludes by suggesting alternative approaches to mathematical libraries, explaining how ScaLAPACK could be integrated into e cient and user-friendly distributed systems. This work was supported in part by the National Science Foundation Grant No. ASC-9005933; by the Defense Advanced Research Projects Agency under contract DAAL03-91-C-0047, administered by the Army Research O ce; by the O ce of Scienti c Computing, U.S. Department of Energy, under Contract DE-AC05-84OR21400; and by the National Science Foundation Science and Technology Center Cooperative Agreement No. CCR-8809615. Department of Computer Science, University of Tennessee, Knoxville, TN 37996-1301 Computer Science Division, University of California, Berkeley, Berkeley, CA 94720 Department of Computer Science, University of Tennessee, Knoxville, TN 37996-1301, and Mathematical Sciences Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831 Mathematical Sciences Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831