A generalized inner and outer product of arbitrary multi-dimensional arrays using A Mathematics of Arrays (MoA)

TL;DR

This paper introduces a unified algorithm for computing inner and outer products of multi-dimensional arrays using A Mathematics of Arrays (MoA), applicable in sequential and parallel processing modes.

Contribution

It presents a novel algorithm derived from MoA and $$-calculus that efficiently computes array products in a single implementation.

Findings

Algorithm performs well in sequential mode

Algorithm scales effectively with multiple processors

Extensive testing validates correctness and efficiency

Abstract

An algorithm has been devised to compute the inner and outer product between two arbitrary multi-dimensional arrays A and B in a single piece of code. It was derived using A Mathematics of Arrays (MoA) and the $\psi$-calculus. Extensive tests of the new algorithm are presented for running in sequential as well as OpenMP multiple processor modes.