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Sparse Matrix-Vector Product

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Numerical Computations with GPUs

Abstract

The sparse matrix-vector (SpMV) multiplication is one of the key kernels in scientific computing. We present the foundations of its implementation on CUDA- and OpenCL-enabled devices. After introducing the subject, we briefly present three most popular formats: COO, CRS and ELL. They serve as exemplary data structures on which we discuss hardware-related issues associated with efficient SpMV kernel design, such as matrix size, ordering of data, memory boundedness, storage overhead, thread divergence, and coalescence of memory transfers. Next, we present three widely available libraries with stable and validated SpMV kernels: cuSPARSE, CUSP and Paralution. We present and discuss complete codes of several SpMV kernels for both basic SpMV formats and some of its derivatives, including CMRS, and briefly discuss the principles beyond other popular format extensions.

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Authors and Affiliations

  1. Faculty of Physics & Astronomy, University of Wrocław, Wrocław, Poland

    Zbigniew Koza & Maciej Matyka

  2. Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

    Łukasz Mirosław

  3. Institute of Physics, University of Silesia, Katowice, Poland

    Jakub Poła

Authors
  1. Zbigniew Koza
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  2. Maciej Matyka
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  3. Łukasz Mirosław
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  4. Jakub Poła
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Corresponding author

Correspondence to Zbigniew Koza .

Editor information

Editors and Affiliations

  1. National Center for Supercomputing Applications, University of Illinois, Urbana, Illinois, USA

    Volodymyr Kindratenko

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© 2014 Springer International Publishing Switzerland

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Koza, Z., Matyka, M., Mirosław, Ł., Poła, J. (2014). Sparse Matrix-Vector Product. In: Kindratenko, V. (eds) Numerical Computations with GPUs. Springer, Cham. https://doi.org/10.1007/978-3-319-06548-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-06548-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06547-2

  • Online ISBN: 978-3-319-06548-9

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