Complex rational kernel-based interpolation

What is this?

This software package contains some code & data associated with the paper:

Julien Bect (‡), Niklas Georg (§), Ulrich Römer (†), Sebastian Schöps (§),
Rational kernel-based interpolation for complex-valued frequency response functions,
arXiv:2307.13484

‡ Laboratoire des signaux et systèmes, Université Paris-Saclay, CNRS, CentraleSupélec, Gif-sur-Yvette, France.

§ Computational Electromagnetics Group, Technische Universität Darmstadt, Darmstadt, Germany

† Institut für Akustik und Dynamik, Technische Universität Braunschweig, Braunschweig, Germany

How to use it?

This software should run with any reasonably recent version of Matlab.

FIXME: Be more specific. Make it work on Octave too.

Start Matlab from the root of the project: the initialization script (startup.m) will automatically start, download the dependencies and then set the path. (If Matlab is already started, you can run startup.m manually.)

Then have a look at the script directory, which contains all the scripts needed to reproduce the results of the article.

Directory layout

The code is organized as follows:

• BenchmarkFunctions: test cases
• CplxGPR: main functions implementing the proposed method
• dependencies: helper function for dependencies
• scripts: scripts to reproduce the results
• utils: various helper functions, wrapper for other methods, etc.

Dependencies

This software has three dependencies: Chebfun, STK, and VFIT3.

Only STK is actually needed to use the proposed method. The other two (Chebfun, VFIT3) provide the state-of-the-art methods AAA and vector fitting, used in the benchmarking scripts.

The startup script will automatically download, on its first run, a suitable version of each dependency. For Chebfun and STK, this is done by cloning the git repository (therefore git is needed). For VFIT3, the downloaded file is checked for correctness using its SHA1 checksum (on Linux/Mac, sha1sum is needed for that).

If for some reason the startup script does not work for you, you can alternatively download manually the source code for each of the dependencies and unpack inside the dependencies directory with a suitable directory name (cf. startup.m).

• Chebfun: https://github.com/chebfun/chebfun/archive/refs/heads/master.zip
• STK: https://github.com/n-georg/stk/archive/refs/heads/lm-param.zip
• VFIT3: https://www.sintef.no/globalassets/project/vectfit/vfit3.zip

Authors

Most of the code for this research has been written by Niklas Georg, with occasional contributions by Julien Bect.

The file barylag.m has been written by Greg von Winckel.

Acknowledgments

The work of Niklas Georg and Ulrich Römer was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – RO4937/1-1.

The work of Niklas Georg was also supported by the Graduate School CE within the Centre for Computational Engineering at Technische Universität Darmstadt.

We thank Christopher Blech, Harikrishnan Sreekumar and Sabine Langer for suggesting acoutstic benchmarks and for providing the implementation of the finite element solver used to compute the vibroacoustics data set.

Copyright & license

Copyright 2023 TU Braunschweig & CentraleSupélec

Copyright 2004 Greg von Winckel

These computer programs are free software: you can redistribute them and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the license, or (at your option) any later version.

They are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.

You should have received a copy of the license along with the software (see COPYING.md). If not, see http://www.gnu.org/licenses/.