https://github.com/ray-chew/tensor-train-decomposition

A short look at tensor-train decomposition with the Xerus library
https://github.com/ray-chew/tensor-train-decomposition

cpp tensor-decomposition tensor-train xerus

Last synced: over 1 year ago
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A short look at tensor-train decomposition with the Xerus library

• Host: GitHub
• URL: https://github.com/ray-chew/tensor-train-decomposition
• Owner: ray-chew
• License: mit
• Created: 2018-06-29T05:03:32.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2018-06-29T05:10:50.000Z (almost 8 years ago)
• Last Synced: 2025-01-11T13:54:35.122Z (over 1 year ago)
• Topics: cpp, tensor-decomposition, tensor-train, xerus
• Language: C++
• Homepage:
• Size: 23.4 KB
• Stars: 0
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
A simple benchmarking of calculations involving a tensor-train decomposition (TTD) against a simple-tensor. This is 

based on the Xerus library[1], and on the nearest-neighbour interaction system (NNIS) example [published 

here](https://libxerus.org/cascade/), and mentioned in-depth in the paper by Gelß et. al.[2].

* *nnis.cxx* is the TTD example. The complete source code is published on the [Xerus 

website](https://libxerus.org/cascade/).

* *nnis_noTT.cxx* is my attempt at using the Xerus library to solve the simple-tensor format of the same system.

* The accuracy are similar. See *plot_noTT_long.pdf* or, for the TT-format vs the simple-tensor,  

    Residual: 0.00134 vs 0.00133,  

    Norm:  0.976103 vs 0.976128.

    

* However, the TTD calculations are about 500 times faster.

    |  | TT-format| simple-tensor|

    | ---- | :----: | :----: |

    | Run 1 | 1.751 | 874.2 | 

    | Run 2 | 1.568 | 887.6 |

    | Run 3 |  1.550 | 911.4 |

    | **Avg. time** |  **1.623s** | **891.1s** |

    

* The advantage of the tensor-train decomposition for large arrays is significant.

*References*:  

[1] Huber, B. & Wolf, S. Xerus - A General Purpose Tensor Library. *https://libxerus.org*, (2014–2018).  

[2] Gelß, P., Klus, S., Matera, S., & Schütte, C. Nearest-Neighbor Interaction Systems in the Tensor-Train Format. *Journal of Computational Physics 341*, (2017), 140-162.  

[3] Oseledets, I. V. Tensor-Train Decomposition. *SIAM Journal on Scientific Computing 33*, 5 (2011), 2295-2317.