Development of the application for determination of the optimal partitioning form of large-dimensional matrix’s elements for multiplication on three heterogeneous processors

Abstract

The article presents the results of the development of a web application for finding the optimal form of splitting matrix elements between three abstract heterogeneous processors when performing the operation of their multiplication. The paper considers five classes of parallel matrix multiplication algorithms: serial communication with a barrier, parallel communication with a barrier, serial communication with overlapping, parallel communication with overlapping, parallel overlapping with alternation. The Hockney model is used to estimate the communication complexity of the algorithms. The work uses six non-rectangular candidate partitioning shapes identified by Ashley DeFlumere in her work [1] as a result of applying the «push» technology of redistribution of matrix elements between the processors: Square Corner, Rectangle Corner, Square Rectangle, Block Rectangle, L-Rectangle, Traditional 1D Rectangular. Determination of the optimality of the form is made on the basis of mathematical models presented in the works [2,3]. The programming languages Python and JavaScript, the Django framework, the pip package manager, and Ajax technology were used to develop a web application. Solving the problem of determining the optimal matrix shape will allow for efficient planning of computing power resources for various scientific fields using parallel matrix multiplication.