On sparse matrix-vector product optimization

Summary form only given. Sparse matrices are matrices having a large number of zero elements. When such matrices are used, both computing time and memory space may be dramatically reduced by taking into account their sparsity. It is well known that the sparse matrix-vector product (SMVP) where the matrix is sparse and the vector is dense is an important kernel in many scientific applications e.g. iterative methods for linear systems and/or eigen problem. The final aim of this work is to design a kind of user-"expert system" that can be used to improve performances in computing environments, particularly grids involving heterogeneous nodes, on which the SMVP kernel is distributed. In this paper, we study the unrolling as an optimization technique and we apply it to the SMVP when the CRS sparse matrix compression format (CSF) is used. After an analysis of the problem, we detail a series of experiments achieved on three different machines. A set of conclusions could be obtained, particularly, the fact that the compiler optimization does not always lead to the best performances. Indeed, specific manual optimizations through loop unrolling could be better.