# An Attempt to Generate Code for Symmetric Tensor Computations

@article{Shi2021AnAT, title={An Attempt to Generate Code for Symmetric Tensor Computations}, author={Jessica Shi and Stephen Chou and Fredrik Kjolstad and Saman P. Amarasinghe}, journal={ArXiv}, year={2021}, volume={abs/2110.00186} }

Symmetric matrices, a frequently studied topic in linear algebra, can be extended to higher dimensions through symmetric tensors, which arise in domains such as computational physics and chemistry [5, 11]. The fundamental mathematical appeal of the study of symmetry also renders these tensors useful in contexts ranging from a rather beautiful equivalence with homogenous polynomials [3] to more concrete applications, including decompositions [9] and finding eigenvalues [8]. Knowing about a…

## One Citation

### Looplets: A Language For Structured Coiteration

- Computer ScienceArXiv
- 2022

This work shows how to abstract over array structures so that the compiler can generate code to coiterate over any combination of them, which enables new array formats, new iteration strategies, and new operations over structured data.

## References

SHOWING 1-10 OF 10 REFERENCES

### Efficiently Computing Tensor Eigenvalues on a GPU

- Computer Science2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum
- 2011

This work describes how a GPU can be used to accelerate the computations of an application involving repeatedly solving the tensor eigenproblem for many small tensors, and presents an efficient implementation of Kolda and Mayo's algorithm.

### Exploiting Symmetry in Tensors for High Performance: Multiplication with Symmetric Tensors

- Computer ScienceSIAM J. Sci. Comput.
- 2014

This paper proposes a blocked data structure (blocked compact symmetric storage) wherein the tensor by blocks is considered and store only the unique blocks of a symmetric tensor.

### The tensor algebra compiler

- Computer ScienceProc. ACM Program. Lang.
- 2017

The first compiler technique to automatically generate kernels for any compound tensor algebra operation on dense and sparse tensors is introduced, which is competitive with best-in-class hand-optimized kernels in popular libraries, while supporting far more tensor operations.

### Effective Utilization of Tensor Symmetry in Operation Optimization of Tensor Contraction Expressions

- Computer Science
- 2012

### Format abstraction for sparse tensor algebra compilers

- Computer ScienceProc. ACM Program. Lang.
- 2018

An interface that describes formats in terms of their capabilities and properties is developed, and a modular code generator design makes it simple to add support for new tensor formats, and the performance of the generated code is competitive with hand-optimized implementations.

### A preliminary analysis of Cyclops Tensor Framework

- Computer Science
- 2012

This work details the automatic topology-aware mapping framework deployed by CTF, which maps tensors of any dimension and structure onto torus networks of any Dimension, and employs virtualization to provide completely general mapping support while maintaining perfect load balance.

### Symmetric Tensors and Symmetric Tensor Rank

- Mathematics, Computer ScienceSIAM J. Matrix Anal. Appl.
- 2008

The notion of the generic symmetric rank is discussed, which, due to the work of Alexander and Hirschowitz, is now known for any values of dimension and order.

### Performance Optimizations and Bounds for Sparse Symmetric Matrix-Multiple Vector Multiply

- Computer Science
- 1985

A performance model, which extends the authors' prior bounds for SpMV in the non-symmetric case, bounds performance by considering only the cost of memory operations, and using lower bounds on cache misses.

### New implementation of highlevel correlated methods using a general block tensor library for high-performance electronic structure calculations

- 2013