Variable-Size Batched Condition Number Calculation on GPUs

Hartwig Anzt; Jack Dongarra; Goran Flegar; Thomas Grutzmacher

doi:10.1109/CAHPC.2018.8645907

Variable-Size Batched Condition Number Calculation on GPUs

Hartwig Anzt, Jack Dongarra, Goran Flegar, Thomas Grutzmacher

Computer Science and Mathematics Div

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We present a kernel that is designed to quickly compute the condition number of a large collection of tiny matrices on a graphics processing unit (GPU). The matrices can differ in size and the process integrates the use of pivoting to ensure a numerically-stable matrix inversion. The performance assessment reveals that, in double precision arithmetic, the new GPU kernel achieves up to 550 GFLOPs (billions of floating-point operations per second) and 800 GFLOPs on NVIDIA's P100 and V100 GPUs, respectively. The results also demonstrate a considerable speed-up with respect to a workflow that computes the condition number via launching a set of four batched kernels. In addition, we present a variable-size batched kernel for the computation of the matrix infinity norm. We show that this memory-bound kernel achieves up to 90% of the sustainable peak bandwidth.

Original language	English
Title of host publication	Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	132-139
Number of pages	8
ISBN (Electronic)	9781538677698
DOIs	https://doi.org/10.1109/CAHPC.2018.8645907
State	Published - Jul 2 2018
Event	30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018 - Lyon, France Duration: Sep 24 2018 → Sep 27 2018

Publication series

Name	Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018

Conference

Conference	30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018
Country/Territory	France
City	Lyon
Period	09/24/18 → 09/27/18

Funding

ACKNOWLEDGMENTS This work was partly funded by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0010042. H. Anzt was supported by the “Impuls und Vernetzungsfond” of the Helmholtz Association under grant VH-NG-1241. G. Flegar was supported by projects TIN2014-53495-R of the Spanish Ministerio de Economía y Competitividad and the EU H2020 project 732631 OPRECOMP.

Funders	Funder number
EU H2020	732631
U.S. Department of Energy Office of Science
Advanced Scientific Computing Research	DE-SC-0010042
Ministerio de Economía y Competitividad
Helmholtz Association	TIN2014-53495-R, VH-NG-1241

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10.1109/CAHPC.2018.8645907

Cite this

Anzt, H., Dongarra, J., Flegar, G., & Grutzmacher, T. (2018). Variable-Size Batched Condition Number Calculation on GPUs. In Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018 (pp. 132-139). Article 8645907 (Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CAHPC.2018.8645907

Anzt, Hartwig ; Dongarra, Jack ; Flegar, Goran et al. / Variable-Size Batched Condition Number Calculation on GPUs. Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 132-139 (Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018).

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abstract = "We present a kernel that is designed to quickly compute the condition number of a large collection of tiny matrices on a graphics processing unit (GPU). The matrices can differ in size and the process integrates the use of pivoting to ensure a numerically-stable matrix inversion. The performance assessment reveals that, in double precision arithmetic, the new GPU kernel achieves up to 550 GFLOPs (billions of floating-point operations per second) and 800 GFLOPs on NVIDIA's P100 and V100 GPUs, respectively. The results also demonstrate a considerable speed-up with respect to a workflow that computes the condition number via launching a set of four batched kernels. In addition, we present a variable-size batched kernel for the computation of the matrix infinity norm. We show that this memory-bound kernel achieves up to 90% of the sustainable peak bandwidth.",

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Anzt, H, Dongarra, J, Flegar, G & Grutzmacher, T 2018, Variable-Size Batched Condition Number Calculation on GPUs. in Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018., 8645907, Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018, Institute of Electrical and Electronics Engineers Inc., pp. 132-139, 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018, Lyon, France, 09/24/18. https://doi.org/10.1109/CAHPC.2018.8645907

Variable-Size Batched Condition Number Calculation on GPUs. / Anzt, Hartwig; Dongarra, Jack; Flegar, Goran et al.
Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 132-139 8645907 (Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We present a kernel that is designed to quickly compute the condition number of a large collection of tiny matrices on a graphics processing unit (GPU). The matrices can differ in size and the process integrates the use of pivoting to ensure a numerically-stable matrix inversion. The performance assessment reveals that, in double precision arithmetic, the new GPU kernel achieves up to 550 GFLOPs (billions of floating-point operations per second) and 800 GFLOPs on NVIDIA's P100 and V100 GPUs, respectively. The results also demonstrate a considerable speed-up with respect to a workflow that computes the condition number via launching a set of four batched kernels. In addition, we present a variable-size batched kernel for the computation of the matrix infinity norm. We show that this memory-bound kernel achieves up to 90% of the sustainable peak bandwidth.

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Anzt H, Dongarra J, Flegar G, Grutzmacher T. Variable-Size Batched Condition Number Calculation on GPUs. In Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 132-139. 8645907. (Proceedings - 2018 30th International Symposium on Computer Architecture and High Performance Computing, SBAC-PAD 2018). doi: 10.1109/CAHPC.2018.8645907

Variable-Size Batched Condition Number Calculation on GPUs

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