LAW: A Tool for Improved Productivity with High-Performance Linear Algebra Codes. Design and Applications

TL;DR

The paper introduces LAW, a high-level Fortran 95 library that simplifies developing and modifying high-performance linear algebra codes across diverse architectures, enhancing productivity and code portability.

Contribution

LAW provides a high-level wrapper library for linear algebra kernels, abstracting low-level details and enabling single-source code development for various execution models.

Findings

LAW simplifies code development for diverse architectures.

Application of LAW in Chebyshev matrix exponentiation demonstrates its effectiveness.

LAW reduces code complexity and enhances portability in high-performance computing.

Abstract

LAPACK and ScaLAPACK are arguably the defacto standard libraries among the scientific community for solving linear algebra problems on sequential, shared-memory and distributed-memory architectures. While ease of use was a major design goal for the ScaLAPACK project; with respect to its predecessor LAPACK; it is still a non-trivial exercise to develop a new code or modify an existing LAPACK code to exploit processor grids, distributed-array descriptors and the associated distributed-memory ScaLAPACK/PBLAS routines. In this paper, we introduce what we believe will be an invaluable development tool for the scientific code developer, which exploits ad-hoc polymorphism, derived-types, optional arguments, overloaded operators and conditional compilation in Fortran 95, to provide wrappers to a subset of common linear algebra kernels. These wrappers are introduced to facilitate the abstraction of low-level details which are irrelevant to the science being performed, such as target platform and execution model. By exploiting this high-level library interface, only a single code source is required with mapping onto a diverse range of execution models performed at link-time with no user modification. We conclude with a case study whereby we describe application of the LAW library in the implementation of the well-known Chebyshev Matrix Exponentiation algorithm for Hermitian matrices.