Towards scalable pattern-based optimization for dense linear algebra

Dániel Berényi, András Leitereg, Gábor Lehel

Research output: Contribution to journalArticle

1 Citation (Scopus)


Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient machine-level representations is far from trivial: developers should be assisted by automatic optimization tools so that they can focus their attention on high-level problems, rather than low-level details. The tractability of these optimizations is highly dependent on the choice of the primitive constructs in terms of which the computations are to be expressed. In this work, we propose to describe operations on multi-dimensional arrays using a selection of higher-order functions, inspired by functional programming, and we present rewrite rules for these such that they can be automatically optimized for modern hierarchical and heterogeneous architectures. Using this formalism, we systematically construct and analyze different subdivisions and permutations of the dense matrix multiplication problem.

Original languageEnglish
Article numbere4696
JournalConcurrency Computation
Issue number22
Publication statusPublished - Nov 25 2018


  • functional programming
  • higher-order function fusion
  • optimization patterns
  • rewrite rules

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computer Science Applications
  • Computer Networks and Communications
  • Computational Theory and Mathematics

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