HLinear: Exact Dense Linear Algebra in Haskell

TL;DR

This paper introduces HLinear, a Haskell implementation of exact dense linear algebra algorithms, specifically PLE decomposition, demonstrating competitive performance with C-based tools like Flint.

Contribution

It presents a novel high-performance functional programming approach to exact dense linear algebra in Haskell, including implementation and benchmarking.

Findings

HLinear achieves performance comparable to C-based implementations.

The paper demonstrates the viability of functional programming for high-performance linear algebra.

Provides insights into high-performance functional programming principles.

Abstract

We present an implementation in the functional programming language Haskell of the PLE decomposition of matrices over division rings. Our benchmarks indicate that it is competitive with the C-based implementation provided in Flint. Describing the guiding principles of our work, we introduce the reader to basic ideas from high-performance functional programming.