BLAS-like Interface for Binary Tensor Contractions

TL;DR

This paper proposes and tests a BLAS-like interface for binary tensor contractions, demonstrating its sufficiency for standardization in multilinear algebra computations.

Contribution

It introduces a novel C interface for binary tensor contraction, showing its potential as a standard similar to BLAS for tensor operations.

Findings

The interface is sufficient for binary tensor contractions.

Implementation and tests confirm usability for standardization.

Supports portability and efficiency in tensor computations.

Abstract

In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits include portability with efficiency and mitigation of suboptimal re-implementations of linear algebra operations. Multilinear algebra is an extension of linear algebra in which the central objects are tensors, which are generalizations of vectors and matrices. Though tensor operations are becoming more common, they do not have a standard like BLAS. Such standardization would be beneficial and decrease the now-visible replication of work, as many libraries nowadays use their own implementations. This master thesis aims to work towards such a standard by discovering whether or not a BLAS-like interface is possible for the operation binary tensor contraction. To answer this, an interface has been developed in the programming language C together with an implementation and tested to see if it would be sufficient. The interface developed is: xGETT(RANKA, EXTA, INCA, A, RANKB, EXTB, INCB, B, CONTS, CONTA, CONTB, PERM, INCC, C) with the implementation and tests, it has been deemed sufficient as a BLAS-like interface for binary tensor contractions and possible to use in a BLAS-like standardization for tensor operations.