MatRox: A Model-Based Algorithm with an Efficient Storage Format for Parallel HSS-Structured Matrix Approximations

12/18/2018

∙

by   Bangtian Liu, et al.

∙

UNIVERSITY OF TORONTO

∙

Rutgers University

∙

0

∙

share

We present MatRox, a novel model-based algorithm and implementation of Hierarchically Semi-Separable (HSS) matrix computations on parallel architectures. MatRox uses a novel storage format to improve data locality and scalability of HSS matrix-matrix multiplications on shared memory multicore processors. We build a performance model for HSS matrix-matrix multiplications. Based on the performance model, a mixed-rank heuristic is introduced to find an optimal HSS-tree depth for a faster HSS matrix evaluation. Uniform sampling is used to improve the performance of HSS compression. MatRox outperforms state-of-the-art HSS matrix multiplication codes, GOFMM and STRUMPACK, with average speedups of 2.8x and 6.1x respectively on target multicore processors.