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

In this work we consider the efficient computation of inner and outer products of arbitrary multi-dimensional arrays (tensors). Our algorithm was presented in a previous work and was derived and expressed using the formalism known as A Mathematics of Arrays (MoA) [1]. The routine maximizes data locality and computes both operations (inner and outer product) in a single piece of code. In this work we emphasize computational experiments and refer the reader to Ref [1] for details of the formalism and the derivation. We now give a brief schematic discussion of the algorithm. Using traditional notation (as opposed to MoA), an outer product of two multi-dimensional arrays (tensors) A and B, is given in terms of components of the result: