Name
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 we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/IPDPS.2014.125 | Phoenix, AZ |
Keywords | Field | DocType |
configuration interactions,distributed memory systems,eigenvalues and eigenfunctions,many-body problems,matrix multiplication,nuclear structure theory,parallel processing,physics computing,sparse matrices,vectors,CI approach,CSB matrix format,CSR matrix format,MFDn code,SpMM kernel,SpMM_T,block eigen solver,compressed sparse block matrix format,compressed sparse row matrix format,distributed memory parallel approaches,eigen value computations,extremal eigen pairs,light atomic nuclei,many-body Fermion dynamics for nuclei code,many-body nuclear Hamiltonian matrix,nuclear configuration interaction calculation,performance model,sparse matrix-multiple vector multiplication optimization,Block Eigensolver,Extended Roofline Model,Nuclear Configuration Interaction,Sparse Matrix Multiplication | Transpose,Matrix (mathematics),Computer science,Parallel computing,Single-entry matrix,Multiplication,Hamiltonian matrix,Eigenvalues and eigenvectors,Sparse matrix,Speedup | Conference |
ISSN | Citations | PageRank |
1530-2075 | 19 | 0.76 |
References | Authors | |
8 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hasan Metin Aktulga | 1 | 87 | 14.15 |
| Aydin Buluc | 2 | 1057 | 67.49 |
| Samuel Williams | 3 | 70 | 7.37 |
| Chao Yang | 4 | 180 | 18.36 |