Block size selection of parallel LU and QR on PVP-based and RISC-based supercomputers

  • Authors:

  • Yunquan Zhang;Ying Chen;Yuan Tang

  • Affiliations:

  • CAS, Beijing, P. R. China;CAS, Beijing, P. R. China;Fudan University, Shanghai, P. R. China

  • Venue:
  • CHINA HPC '07 Proceedings of the 2007 Asian technology information program's (ATIP's) 3rd workshop on High performance computing in China: solution approaches to impediments for high performance computing
  • Year:
  • 2007

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Abstract

In this paper, we proposed a unified framework and tried to address the optimal block size selection problem for parallel blocked LU and QR factorization algorithm used in ScaLAPACK package, since they use two dimensional block cyclic data distribution fashion [12], block size plays important role in determining the final performance. Through the analysis with our proposed framework and experiments on small scale system configuration, we found that among all factors that affect performance, load balance and local block size selection play key roles in determining the optimal block size on two different type parallel computing platforms: SR2201 (PVP(Pseudo-Vector Processing) based MPP machine) and DAWNING 3000(RISC-based SMP cluster). In fact, the optimal parallel block size is determined by the processor grid shape and problem size. Based on this observation, optimal block size prediction formula for double precision real parallel blocked LU and QR on SR2201 and DAWNING3000 with processor grid shape and problem size as parameters were given, whose prediction results can match well with the large scale system configuration and large problem size experimental results. The application of our framework on other parallel machines and on other applications program wound be the future work.