Data Distribution Schemes for Dense Linear Algebra Factorizations on Any Number of Nodes

Abstract

In this paper, we consider the problem of distributing the tiles of a dense matrix onto a set of homogeneous nodes. We consider both the case of non-symmetric (LU) and symmetric (Cholesky) factorizations. The efficiency of the well-known 2D Block-Cyclic (2DBC) distribution degrades significantly if the number of nodes P cannot be written as the product of two close numbers. Similarly, the recently introduced Symmetric Block Cyclic (SBC) distribution is only valid for specific values of P. In both contexts, we propose generalizations of these distributions to adapt them to any number of nodes. We show that this provides improvements to existing schemes (2DBC and SBC) both in theory and in practice, using the flexibility and ease of programming induced by task-based runtime systems like Chameleon and StarPU.