Characterizing dataset dependence for sparse matrix-vector multiplication on GPUs

Sparse matrix-vector multiplication (SpMV) is a widely used kernel in scientific applications as well as data analytics. Many GPU implementations of SpMV have been proposed, proposing different sparse matrix representations. However, no sparse matrix representation is consistently superior, and the best representation varies for sparse matrices with different sparsity patterns. In this paper we study four popular sparse representations implemented in the NVIDIA cuSPARSE library: CSR, ELL, COO and a hybrid ELL-COO scheme. We analyze statistical features of a dataset of 27 matrices, covering a wide spectrum of sparsity features, and attempt to correlate SpMV performance with each representation with simple aggregate metrics of the matrices. We present some insights on the correlation between matrix features and the best choice for sparse matrix representation.