A C++ implementation and Python binding of the Global complex Root and Pole Finding (GRPF) algorithm GRPF and SA-GRPF (in-progress).
grpfc attempts to find all the zeros and poles of a complex valued function with complex arguments in a fixed region.
These types of problems are frequently encountered in electromagnetics, but the algorithm can also be used for similar problems in e.g. optics, acoustics, etc.
The GRPF algorithm first samples the function on a triangular mesh through Delaunay triangulation. Candidate regions to search for roots and poles are determined and the discretized Cauchy's argument principle is applied without needing the derivative of the function or integration over the contour. To improve the accuracy of the results, a self-adaptive mesh refinement occurs inside the identified candidate regions.
We also provide grpfpy, a Python binding for grpfc, which is a convenient and high-performance solution for your research. A set of pre-compiled wheels could be installed directly via
pip install grpfpyAdditionally, if your platform has not been supported, you can clone the sources and build them yourself using pip or cmake:
pip install .- Pull source codes
git clone --recurse-submodules [email protected]:allegro0132/grpfc.git- Install gcc complier
apt install build-essential- Install clang compiler
brew install cmake llvm- Install MinGW gcc compiler
choco install mingw- Prepare building directory
mkdir build&&cd build- Prepare compile flags using cmake
cmake ..For windows user, you should type it instead:
cmake -G "MinGW Makefiles" ..- Compile the library
make- Run the Roots and Poles solver
./mainPlease consider citing following publications if this code is used in scientific work:
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P. Kowalczyk, “Complex Root Finding Algorithm Based on Delaunay Triangulation”, ACM Transactions on Mathematical Software, vol. 41, no. 3, art. 19, pp. 1-13, June 2015. https://dl.acm.org/citation.cfm?id=2699457
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P. Kowalczyk, "Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems," IEEE Transactions on Antennas and Propagation, vol. 66, no. 12, pp. 7198-7205, Dec. 2018. https://ieeexplore.ieee.org/document/8457320
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S. Dziedziewicz, M. Warecka, R. Lech and P. Kowalczyk, "Self-Adaptive Mesh Generator for Global Complex Roots and Poles Finding Algorithm," in IEEE Transactions on Microwave Theory and Techniques, doi: 10.1109/TMTT.2023.3238014. https://ieeexplore.ieee.org/document/10025853
We also encourage you to cite this package if used in scientific work.
@software{grpfc2025github,
author = {Ziang Wang},
title = {{grpfc}: Global complex Roots and Poles Finding in {C++}},
dol = {10.5281/zenodo.16990552},
url = {https://github.com/allegro0132/grpfc},
year = {2025},
}