Code to reproduce the numerical experiments in "Approximation in the extended functional tensor train format" by C. Strössner, B. Sun and D. Kressner. (Adv. Comput. Math 50:54 2024 https://doi.org/10.1007/s10444-024-10140-9, Arxiv: https://arxiv.org/abs/2211.11338.)

The novel algorithm for approximating in the extended tensor train format is implemented in MATLAB. The comparison with the algorithm in c3py is implemented in Python.

MATLAB dependencies:

Chebfun (download from https://github.com/chebfun/chebfun)

TT-Toolbox (download from https://github.com/oseledets/TT-Toolbox)

MATLAB Statistics and Machine Learning Toolbox

MATLAB Partial Differential Equation Toolbox

Python dependencies and setup are described in the notebooks (we use https://github.com/goroda/Compressed-Continuous-Computation and https://fenicsproject.org/).

After running MATLAB setup.m, you need to copy the file testPoints.mat from the test folder into the notebook1 and notebook2 folders.

MATLAB file descriptions:

The class @EFTT contains our novel algorithm to approximate functions in the extended functional tensor train format.

The class @FTT contains an approximation algorithm leading to an approximation in the (classical) functional tensor train format.

setup.m: Initalization and correct setting of paths (needs to be run first).

generateData.m: Runs all numerical experiments not involving the solution of PDEs.

displayTables.m: Displays all results not involving PDEs as tables.

plotFigureX.m: Generates the plot for Figure X in the paper.

generatePDEData.: Runs and displays the results for all numerical experiments involving the solution of PDEs.

Python file descriptions:

Notebook1: Generates and displays the data for the table in the appendix and for Figure 3.

Notebook2: Generates and displays the data for Table 1 which involves the solution of PDEs.

How to obtain and use EFTT approximations in MATLAB:

You can approximate a function f:[-1,1]^d to R using eftt = EFTT(f,d).

To evaluate the approximation at point x you can use eftt.fevaluate(x).

To compute the integral over [-1,1]^d of the approximation you can use eftt.fintegrate.

The polynomial degree, the TT and the multilinear rank can be obtained using eftt.degree, eftt.ttrank and eftt.tuckerrank.