Towards a functional run-time for dense NLA domain

Abstract

We investigate the use of functional programming to develop a numerical linear algebra run-time; i.e. a framework where the solvers can be adapted easily to different contexts and task parallelism can be attained (semi-) automatically. We follow a bottom up strategy, where the first step is the design and implementation of a framework layer, composed by a functional version of BLAS (Basic Linear Algebra Subprograms) routines. The framework allows the manipulation of arbitrary representations for matrices and vectors and it is also possible to write and combine multiple implementations of BLAS operations based on different algorithms and parallelism strategies. Using this framework, we implement a functional version of Cholesky factorization, which serves as a proof of concept to evaluate the flexibility and performance of our approach.