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Scalable, Portable, Verifiable Kronecker Products on Multi-scale Computers

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Constraint Programming and Decision Making

Part of the book series: Studies in Computational Intelligence ((SCI,volume 539))

Abstract

Understanding the layout of data and the accessing of that data is paramount to the optimal performance of an algorithm on one or many processors. This paper addresses the need for efficient tools to implement and carry out tensor based computations for scientific and engineering applications. In particular, we focus on certain ubiquitous operations such as outer products of arbitrary multi-dimensional arrays and matrix Kronecker products. We advocate an algebraic methodology based on A Mathematics of Arrays (MoA) and the ψ-Calculus, in which, any array based computer language (such as MATLAB) would be augmented to achieve optimal performance for the computation of multiple outer products. In this approach, an Operational Normal Form (ONF), which specifies the most efficient implementation in terms of starts, stops, and strides is mathematically derived given specific details of the processor/memory hierarchy. The vision of this research is the creation of a system in which the application scientist or engineer can use a functional subset of his/her favorite language and, in so doing, have the ability to generate code with high efficiency and compiler-like optimizations.

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Author information

Authors and Affiliations

  1. College of Computing and Information (CCI), University at Albany, State University of New York, Albany, NY, USA

    Lenore Mullin

  2. Drinker Biddle & Reath, L.L.P., Washington. D.C., USA

    James Raynolds

Authors
  1. Lenore Mullin
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  2. James Raynolds
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Corresponding author

Correspondence to Lenore Mullin .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Martine Ceberio

  2. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

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Mullin, L., Raynolds, J. (2014). Scalable, Portable, Verifiable Kronecker Products on Multi-scale Computers. In: Ceberio, M., Kreinovich, V. (eds) Constraint Programming and Decision Making. Studies in Computational Intelligence, vol 539. Springer, Cham. https://doi.org/10.1007/978-3-319-04280-0_14

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  • DOI: https://doi.org/10.1007/978-3-319-04280-0_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04279-4

  • Online ISBN: 978-3-319-04280-0

  • eBook Packages: EngineeringEngineering (R0)

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