# 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 »

- Authors:

- 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}

}