Analysis of non-strict functional implementations of the Dongarra-Sorensen eigensolver

Abstract

We study the producer-consumer parallelism of Eigensolvers composed of a tridiagonalization function, a tridiagonal solver, and a matrix multiplication, written in the non-strict functional programming language Id. We v erify the claim that non-strict functional languages allow the natural exploitation of this type of parallelism, in the framework of realistic numerical codes. We compare the standard top-down Dongarra-Sorensen solver with a new, bottom-up version. We show that this bottom-up implementation is much more space e cient than the top-down version. Also, we compare both versions of the Dongarra-Sorensen solver with the more traditional QL algorithm, and verify that the Dongarra-Sorensen solver is much more e cient, even when run in a serial mode. We show that in a non-strict functional execution model, the Dongarra-Sorensen algorithm can run completely in parallel with the Householder function. Moreover, this can be achieved without any c hange in the code components. We also indicate how the critical path of the complete Eigensolver can be improved.

A Comparison of Implicitly Parallel Multithreaded and Data-Parallel Implementations of an Ocean Model

“…Hammes et al [21] have performed a comparison of Id and Haskell for a Monte Carlo photon transport code. Sur and Bohm [46] study different Id implementations of FFT in the context of solving partial differential equations and implementations of the Dongarra-Sorensen eigensolver [45]. Arvind and Ekanadham [8] have compared the implementation of the hydrodynamics modeling application SIMPLE in Id and in Fortran; Arvind et al [7] have also explored the benefits of fine-grained parallelism in scientific applications.…”