An efficient representation on GPU for transition rate matrices for Markov chains

Abstract

The authors present a novel modification of the HYB format - known from the CUSP library. The new format is suitable for sparse Markovian transition rate matrices and enables processing two times bigger matrices on single GPU, also improving computation performance at the same time. Particularly, the SpMV operation - that is the multiplication of a sparse matrix by a vector - is analyzed for this format on one GPU and two GPUs. Numerical experiments for transition rate matrices of Markov chains from [18] show that the proposed format allows to process matrices of sizes about 3.6 × 107 rows with the use of single GPU (3 GB RAM). When the plain HYB format is used the matrices of these sizes do not fit in one GPUs memory. Moreover, the use of the modified HYB format can give the speedup even up to 13 times in comparison to multi-threaded CPU (12 cores). © 2014 Springer-Verlag.