Block size selection of parallel LU factorization

We propose a unified framework and address the optimal block size selection problem for parallel blocked LU factorization based on the ScaLAPACK package. Since it uses block cyclic data distribution, block size plays an important role in determining the final performance. Through the analysis with our proposed framework and experiments on a small-scale system configuration, we found that among all these factors, load balance and local block size selection play key roles in determining the optimal block size on SR2201 (pseudo-vector based MPP machine). The optimal block size is determined by the processer grid shape and problem size. Based on this observation, an optimal block size prediction formula, with processor grid shape and problem size as parameters, is given that can match experimental results well. The application of our framework to scalar based parallel machines and other applications programs is future work.