An Auto-tuning Method for Run-time Data Transformation for Sparse Matrix-Vector Multiplication

In this paper, we research the run-time sparse matrix data transformation from Compressed Row Storage (CRS) to Coordinate (COO) storage and an ELL (ELLPACK/ITPACK) format with OpenMP parallelization for sparse matrix-vector multiplication (SpMV). We propose an auto-tuning (AT) method by using the Dmat i Rell graph, which plots the derivation/average for the number of non-zero elements per row (Dmat) and the ratio, SpMV speedups/transformation time from the CRS to ELL (Rell ). The experimental results show the ELL format is very effective in the Earth Simulator 2. The speedup factor of 151 with the ELL-Row inner-parallelized format is obtained. The transformation overhead is also very small, such as 0.01 to 1.0 SpMV time with the CRS format. In addition, the Dmat i Rell graph can be modeled for the effectiveness of transformation according to the Dmat i value. 疎行列-ベクトル積における