Block Algorithms for Sparse Matrix by Dense Matrix Multiplication

Sparse matrix computations appear in many linear algebra kernels of scienti c applications. The study, evaluation and optimization of sparse matrix codes is more complex than the dense case. Moreover, the irregularity of some memory accesses and the a-priory lack of knowledge of the number of iterations to be perfomed in some loops (both depending on the sparsity pettern) limit the succes of programmer and compilaer optimizations. In this report we consider some speci c examples in which we apply the evaluation techniques discussed in previous reports. We determine the perfomance of forms without blocking and show the improvement that can be obtained by using two levels of blocking (at the register and cache levels). Speci cally, we consider matrix multiplication C=C+A*B, where matrix A, of size NxN, is sparse and stored in row-wise ordered format and matrices B and C, of sizes NxP, are dense and stored by colums, as in fortram. Sparse matrix by dense matrix multiplications (SpMxM) appear, for instance, in iterative methods to obtain the eigenvalue vectors of a sparse matrix. 2