1 research outputs found
Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions
Mathematical operators whose transformation rules constitute the building
blocks of a multi-linear algebra are widely used in physics and engineering
applications where they are very often represented as tensors. In the last
century, thanks to the advances in tensor calculus, it was possible to uncover
new research fields and make remarkable progress in the existing ones, from
electromagnetism to the dynamics of fluids and from the mechanics of rigid
bodies to quantum mechanics of many atoms. By now, the formal mathematical and
geometrical properties of tensors are well defined and understood; conversely,
in the context of scientific and high-performance computing, many tensor-
related problems are still open. In this paper, we address the problem of
efficiently computing contractions among two tensors of arbitrary dimension by
using kernels from the highly optimized BLAS library. In particular, we
establish precise conditions to determine if and when GEMM, the kernel for
matrix products, can be used. Such conditions take into consideration both the
nature of the operation and the storage scheme of the tensors, and induce a
classification of the contractions into three groups. For each group, we
provide a recipe to guide the users towards the most effective use of BLAS.Comment: 27 Pages, 7 figures and additional tikz generated diagrams. Submitted
to Applied Mathematics and Computatio