Application of analytical modeling of matrix-vector multiplication on multicore processors

E. N. Akimova ; R. A. Gareev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 9 (2020) no. 1, pp. 69-82

Résumé

Many areas of study and their applications such as machine learning, data mining, quantum chemistry, mathematical physics, and high-performance computing require effective implementation of matrix-vector multiplication. In this work, we present an overview of the algorithm for automatic optimization of matrix-vector multiplication. The algorithm models computations on the hypothetical multicore processor, which is introduced by the authors, and applies polyhedral modeling. In comparison with methods, which rely on manual tuning and auto-tuning, the algorithm can be utilized when the execution time is a critical factor and the target platform is not accessible. We apply the approach to optimize an implementation of the solution of the inverse gravimetry problem of finding an interface between the layers, which uses the iterative Levenberg-Marquardt method. The performance of the obtained implementation is compared with the performances produced by implementations, which are based on MKL, BLIS, and OpenBLAS. Results of the experimental evaluation show that the considered approach is comparable with the approaches, which are created on target architectures using manual tuning.

Détail

Keywords: compilers, linear algebra, matrix-vector operations, analytical modeling, inverse gravimetry problem.