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

Conference · Thu Aug 14 04:00:00 EDT 2014

DOI:https://doi.org/10.1109/IPDPS.2014.125· OSTI ID:1407214

Aktulga, Hasan Metin ^[1]; Buluc, Aydin ^[1]; Williams, Samuel ^[1]; Yang, Chao ^[1]

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1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 1407214
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Block Eigensolver
Extended Roofline Model
Nuclear Configuration Interaction
Sparse Matrix Multiplication