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, 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.

• 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.