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

Abstract

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 wemore » may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn.« less

Authors:
 [1];  [1];  [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1407214
DOE Contract Number:  
AC02-05CH11231
Resource Type:
Conference
Resource Relation:
Conference: International Parallel and Distributed Processing Symposium, IPDPS (2014 IEEE), Phoenix, AZ (United States), 19-23 May 2014
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Sparse Matrix Multiplication; Block Eigensolver; Nuclear Configuration Interaction; Extended Roofline Model

Citation Formats

Aktulga, Hasan Metin, Buluc, Aydin, Williams, Samuel, and Yang, Chao. Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations. United States: N. p., 2014. Web. doi:10.1109/IPDPS.2014.125.
Aktulga, Hasan Metin, Buluc, Aydin, Williams, Samuel, & Yang, Chao. Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations. United States. doi:10.1109/IPDPS.2014.125.
Aktulga, Hasan Metin, Buluc, Aydin, Williams, Samuel, and Yang, Chao. Thu . "Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations". United States. doi:10.1109/IPDPS.2014.125. https://www.osti.gov/servlets/purl/1407214.
@article{osti_1407214,
title = {Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations},
author = {Aktulga, Hasan Metin and Buluc, Aydin and Williams, Samuel and Yang, Chao},
abstractNote = {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.},
doi = {10.1109/IPDPS.2014.125},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Aug 14 00:00:00 EDT 2014},
month = {Thu Aug 14 00:00:00 EDT 2014}
}

Conference:
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