ILIAS, a Sequential Language for Parallel Matrix Computations

The ILIAS system consists of a. sequential language for matrix computations, a compiler translating a. source program into ILIAS pseudo code and a parallel interpreter for this code. The pseudo code is independent of a target architecturej it merely specifies scalar and matrix computations. We present the ILIAS language and discuss its implementation on a square torus network of transputers. Subscription of matrices causes data-alignment problems, which are solved by redistributions. To reduce redistribution overhead we use a new data distribution called the grid-base distribution. Furthermore, we develop several run-time heuristics that, together with the grid.base distribution, efficiently implement matrix subscription. The feasibility and scalability of the ILIAS system is demonstrated by timing results for two example ILIAS programs, an L U decomposition and a Strassen matrix multiplication, on transputer networks up to 400 processors.