This repository accompanies the article Concepts in Monte Carlo sampling by Gabriele Tartero and Werner Krauth. It contains all the supplementary material discussed in Appendix B.
This article may be downloaded for personal use only. Any other use requires prior permission of the authors and AIP Publishing. This article appeared in American Journal of Physics, Volume 92, Issue 1 (January 2024) and may be found also here.
The Mathematica directory contains a Mathematica notebook, both in .nb and .pdf formats, that can be used to reproduce the mathematical results presented in Appendix A.
The Python
directory contains thirteen simulations of one particle
subject to a one-dimensional anharmonic potential, both
at constant energy (Algorithm 0) and at constant temperature
(Algorithms from 1 to 12), as discussed in the paper.
In every program,
The implementation of Algorithm 0 is self-contained: it samples the position of the particle and compares the experimental histogram with the theoretical result, given by Equation (7) in Section IIA.
Algorithms from 1 to 12 all sample the position of the particle and store the results in a text file. To compare the experimental histograms with the theoretical Boltzmann distribution, it suffices to produce the data with the concerned program and then run the script histograms.py.
All programs can be executed with any Python3 implementation (e.g., standard CPython or PyPy3). The scripts 00_isolated-dynamics.py and histograms.py rely both on NumPy and Matplotlib to produce the histograms, while all other programs do not have any further requirements.
The authors of this project are:
- Gabriele Tartero (gabriele.tartero@phys.ens.fr);
- Werner Krauth (werner.krauth@ens.fr).
For any question about the MCMCNutshell software package, or the related paper, please raise an issue here on GitHub or contact us via e-mail.
This project is licensed under the GNU General Public License, version 3 (see the LICENSE file).