Heterogeneous computation of matrix products

Abstract

The work presented here is an experimental study of performance in execution time and energy consumption of matrix multiplications on a heterogeneous server. The server features three different devices: a multicore CPU, an NVIDIA Tesla GPU, and an Intel Xeon Phi coprocessor. Matrix multiplication is one of the most used linear algebra kernels and, consequently, applications that make an intensive use of this operation can greatly benefit from efficient implementations. This is the case of the evaluation of matrix polynomials, a core operation used to calculate many matrix functions, which involve a very large number of products of square matrices. Although there exist many proposals for efficient implementations of matrix multiplications in heterogeneous environments, it is still difficult to find packages providing a matrix multiplication routine that is so easy to use, efficient, and versatile as its homogeneous counterparts. Our approach here is based on a simple implementation using OpenMP sections. We have also devised a functional model for the execution time that has been successfully applied to the evaluation of matrix polynomials of large degree so that it allows to balance the workload and minimizes the runtime cost.