GPU Algorithms for Structured Sparse Matrix Multiplication with Diagonal Storage Schemes

Abstract

Matrix–matrix multiplication is of singular importance in linear algebra operations with a multitude of applications in scientific and engineering computing. Data structures for storing matrix elements are designed to minimize overhead information as well as to optimize the operation count. In this study, we utilize the notion of the compact diagonal storage method (CDM), which builds upon the previously developed diagonal storage—an orientation-independent uniform scheme to store the nonzero elements of a range of matrices. This study exploits both these storage schemes and presents efficient GPU-accelerated parallel implementations of matrix multiplication when the input matrices are banded and/or structured sparse. We exploit the data layouts in the diagonal storage schemes to expose a substantial amount of fine-grained parallelism and effectively utilize the GPU shared memory to improve the locality of data access for numerical calculations. Results from an extensive set of numerical experiments with the aforementioned types of matrices demonstrate orders-of-magnitude speedups compared with the sequential performance.