QPmR Python Package

This Python package consists of:

1. enhanced implementation of quasi-polynomial based rootfinder, algorithm for finding roots of given quasi polynomial in given rectangular region in complex plane [1], [2] enhanced with root-multiplicity heuristic and (in some cases) automatic region selection
2. Spectral distribution properties of quasi-polynomials: (i) delay distribution diagram, (ii) exponential asymptotes of root chains, (iii) safe upper bound of neutral spectrum and (iv) spectrum envelope
3. quasi-polynomial (and transfer function) algebra
4. various functions for quickly visualizing results

For original MATLAB® implementation of old QPmR algorithm from 2012, we refer to this page.

[1] Vyhlidal, T., and Zítek, P. (2009). Mapping based algorithm for large-scale computation of quasi-polynomial zeros. IEEE Transactions on Automatic Control, 54(1), 171-177.

[2] Vyhlidal, T. and Zitek, P. (2014). QPmR-Quasi-polynomial root-finder: Algorithm update and examples Editors: Vyhídal T., Lafay J.F., Sipahi R., Sringer 2014.

Please, keep in mind that thisproject is still under development.

Installation

Installing with pip

Using pipy (check the version as software is being developed)

pip install qpmr

From github

pip install qpmr@git+https://github.com/LockeErasmus/qpmr

Local install

pip install <path-to-qpmr>

Installing from source

Clone repository

git clone https://github.com/LockeErasmus/qpmr.git

install from source with -e

pip install -e qpmr

Citing this work

For now, please cite the following article

@article{vyhlidal2009mapping,
  title={Mapping based algorithm for large-scale computation of quasi-polynomial zeros},
  author={Vyhlidal, Tomas and Z{\'\i}tek, Pavel},
  journal={IEEE Transactions on Automatic Control},
  volume={54},
  number={1},
  pages={171--177},
  year={2009},
  publisher={IEEE}
}

Or alternatively, this chapter of book

@incollection{vyhlidal2014qpmr,
  title={QPmR-Quasi-polynomial root-finder: Algorithm update and examples},
  author={Vyhl{\'\i}dal, Tom{\'a}{\v{s}} and Z{\'\i}tek, Pavel},
  booktitle={Delay Systems: From Theory to Numerics and Applications},
  pages={299--312},
  year={2014},
  publisher={Springer}
}

Metadata

Title: QPmR Python Package
ID: QPmRpythonPackage
Version: 1.0
Project: Robotics and Advanced Industrial Production
Project No.: CZ.02.01.01/00/22_008/0004590
Project RO: 1.1-Optimal control of interconnected time-delay systems
Date: 20.9.2025
Authors: Adam Peichl; Tomas Vyhlidal
Keywords: rootfinding algorithm, exponential polynomial, quasi-polynomial, time delay system, spectrum

Acknowledgments

This work was supported by the European Union under the project Robotics and Advanced Industrial Production, reg. no. CZ.02.01.01/00/22_008/0004590; by the project 24-10301S of the Czech Science Foundation; and by by the Grant Agency of the Czech Technical University in Prague, grant No. SGS24/125/0HK2/3T/12.

License

This package is available under GNU GPLv3 license.