Experiments with Sparse Cholesky Using a Parametrized Task Graph Implementation

Abstract

We describe the design of a sparse direct solver for symmetric positive-definite systems using the PaRSEC runtime system. In this approach the application is represented as a DAG of tasks and the runtime system runs the DAG on the target architecture. Portability of the code across different architectures is enabled by delegating to the runtime system the task scheduling and data management. Although runtime systems have been exploited widely in the context of dense linear algebra, the DAGs arising in sparse linear algebra algorithms remain a challenge for such tools because of their irregularity. In addition to overheads induced by the runtime system, the programming model used to describe the DAG impacts the performance and the scalability of the code. In this study we investigate the use of a Parametrized Task Graph (PTG) model for implementing a task-based supernodal method. We discuss the benefits and limitations of this model compared to the popular Sequential Task Flow model (STF) and conduct numerical experiments on a multicore system to assess our approach. We also validate the performance of our solver SpLLT by comparing it to the state-of-the-art solver MA87 from the HSL library.