# CAST: Contraction Algorithm for Symmetric Tensors

## Abstract

Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1178516

- Report Number(s):
- PNNL-SA-103757

KJ0402000

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Conference

- Resource Relation:
- Conference: 43rd International Conference on Parallel Processing (ICPP 2014), September 9-12, 2014, Minneapolis, Minnesota, 261-272

- Country of Publication:
- United States

- Language:
- English

- Subject:
- tensor contractions; symmetry; distributed memory

### Citation Formats

```
Rajbhandari, Samyam, NIkam, Akshay, Lai, Pai-Wei, Stock, Kevin, Krishnamoorthy, Sriram, and Sadayappan, Ponnuswamy.
```*CAST: Contraction Algorithm for Symmetric Tensors*. United States: N. p., 2014.
Web. doi:10.1109/ICPP.2014.35.

```
Rajbhandari, Samyam, NIkam, Akshay, Lai, Pai-Wei, Stock, Kevin, Krishnamoorthy, Sriram, & Sadayappan, Ponnuswamy.
```*CAST: Contraction Algorithm for Symmetric Tensors*. United States. doi:10.1109/ICPP.2014.35.

```
Rajbhandari, Samyam, NIkam, Akshay, Lai, Pai-Wei, Stock, Kevin, Krishnamoorthy, Sriram, and Sadayappan, Ponnuswamy. Mon .
"CAST: Contraction Algorithm for Symmetric Tensors". United States. doi:10.1109/ICPP.2014.35.
```

```
@article{osti_1178516,
```

title = {CAST: Contraction Algorithm for Symmetric Tensors},

author = {Rajbhandari, Samyam and NIkam, Akshay and Lai, Pai-Wei and Stock, Kevin and Krishnamoorthy, Sriram and Sadayappan, Ponnuswamy},

abstractNote = {Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.},

doi = {10.1109/ICPP.2014.35},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2014},

month = {9}

}