GPU accelerated sparse matrix-vector multiplication and sparse matrix-transpose vector multiplication

Many high performance computing applications require computing both sparse matrix-vector product (SMVP) and sparse matrix-transpose vector product (SMTVP) for better overall performance. Under such a circumstance, it is critical to maintain a similarly high throughput for these two computing patterns with the underlying sparse matrix encoded in a single storage format. The compressed sparse block (CSB) format proposed by Buluc et al. allows computing both problems on multi-core CPUs with nearly identical throughputs. On the other hand, a direct porting of CSB to graphics processing units (GPUs), which have been recently recognized as a powerful general purpose computing platform, turns out to be inefficient. In this work, we propose a new data structure, designated as expanded CSB (eCSB), to minimize the throughput gap between SMVP and SMTVP computations on GPUs, while at the same time enable a high computing throughput. We also use a hybrid storage format to store elements in each block, which can be selected dynamically at runtime. Experimental results show that the proposed techniques implemented on a Kepler GPU delivers similar throughput on both SMVP and SMTVP and the throughput is up to 13 times faster than that of the CPU-based CSB implementation. In addition, our eCSB procedure outperforms the previous GPU results by up to 188% and 914% in computing SMVP and SMTVP, and we validate the effectiveness of eCSB by means of wall-clock time of bi-conjugate gradient algorithm; our eCSB is 25% faster than Compressed Sparse Rows (CSR) and 6% faster than HYB, respectively. Copyright (C) 2014 John Wiley & Sons, Ltd.