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International Conference on Computational Science

ICCS 2022: Computational Science – ICCS 2022 pp 60–74Cite as

Batch QR Factorization on GPUs: Design, Optimization, and Tuning

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13350)

Abstract

QR factorization of dense matrices is a ubiquitous tool in high performance computing (HPC). From solving linear systems and least squares problems to eigenvalue problems, and singular value decompositions, the impact of a high performance QR factorization is fundamental to computer simulations and many applications. More importantly, the QR factorization on a batch of relatively small matrices has acquired a lot of attention in sparse direct solvers and low-rank approximations for Hierarchical matrices. To address this interest and demand, we developed and present a high performance batch QR factorization for Graphics Processing Units (GPUs). We present a multi-level blocking strategy that adjusts various algorithmic designs to the size of the input matrices. We also show that following the LAPACK QR design convention, while still useful, is significantly outperformed by unconventional code structures that increase data reuse. The performance results show multi-fold speedups against the state of the art libraries on the latest GPU architectures from both NVIDIA and AMD.

Keywords

  • Batch linear algebra
  • QR factorization
  • GPU computing

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Author information

Authors and Affiliations

  1. University of Tennessee, Knoxville, USA

    Ahmad Abdelfattah, Stan Tomov & Jack Dongarra

  2. Oak Ridge National Laboratory, Oak Ridge, USA

    Jack Dongarra

  3. University of Manchester, Manchester, UK

    Jack Dongarra

Authors
  1. Ahmad Abdelfattah
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  2. Stan Tomov
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  3. Jack Dongarra
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Corresponding author

Correspondence to Ahmad Abdelfattah .

Editor information

Editors and Affiliations

  1. Brunel University London, London, UK

    Derek Groen

  2. University of Amsterdam, Amsterdam, The Netherlands

    Clélia de Mulatier

  3. AGH University of Science and Technology, Krakow, Poland

    Prof. Maciej Paszynski

  4. University of Amsterdam, Amsterdam, The Netherlands

    Dr. Valeria V. Krzhizhanovskaya

  5. University of Tennessee at Knoxville, Knoxville, TN, USA

    Prof. Jack J. Dongarra

  6. University of Amsterdam, Amsterdam, The Netherlands

    Prof. Dr. Peter M. A. Sloot

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Abdelfattah, A., Tomov, S., Dongarra, J. (2022). Batch QR Factorization on GPUs: Design, Optimization, and Tuning. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13350. Springer, Cham. https://doi.org/10.1007/978-3-031-08751-6_5

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  • DOI: https://doi.org/10.1007/978-3-031-08751-6_5

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