Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations

• Published in: 2014 IEEE 28th International Parallel and Distributed Processing Symposium pp. 1213 - 1222
• Main Authors: Aktulga, Hasan Metin, Buluc, Aydin, Williams, Samuel, Chao Yang
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.05.2014
• Subjects: Arrays; Bandwidth; Block Eigensolver; Eigenvalues and eigenfunctions; Extended Roofline Model; Instruction sets; Nuclear Configuration Interaction; Sparse matrices; Sparse Matrix Multiplication; Vectors; Wave functions
• ISBN: 1479937991; 9781479937998
• ISSN: 1530-2075
• DOI: 10.1109/IPDPS.2014.125

Obtaining highly accurate predictions on the properties of light atomic nuclei using the configuration interaction (CI) approach requires computing a few extremal Eigen pairs of the many-body nuclear Hamiltonian matrix. In the Many-body Fermion Dynamics for nuclei (MFDn) code, a block Eigen solver is used for this purpose. Due to the large size of the sparse matrices involved, a significant fraction of the time spent on the Eigen value computations is associated with the multiplication of a sparse matrix (and the transpose of that matrix) with multiple vectors (SpMM and SpMM_T). Existing implementations of SpMM and SpMM_T significantly underperform expectations. Thus, in this paper, we present and analyze optimized implementations of SpMM and SpMM_T. We base our implementation on the compressed sparse blocks (CSB) matrix format and target systems with multi-core architectures. We develop a performance model that allows us to understand and estimate the performance characteristics of our SpMM kernel implementations, and demonstrate the efficiency of our implementation on a series of real-world matrices extracted from MFDn. In particular, we obtain 3-4 speedup on the requisite operations over good implementations based on the commonly used compressed sparse row (CSR) matrix format. The improvements in the SpMM kernel suggest we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn.