Welcome to pentapy
pentapy is a toolbox to deal with pentadiagonal matrices in Python.
Pentadiagonal linear equation systems arise in many areas of science and engineering: e.g. when solving differential equations, in interpolation problems, or in numerical schemes like finite difference.
pip install pentapy
There are pre-built wheels for Linux, MacOS and Windows for most Python versions (2.7, 3.4-3.7).
If your system is not supported and you want to have the Cython routines of pentapy installed, you have to provide a c-compiler and run:
pip install numpy cython pip install pentapy
To get the scipy solvers running, you have to install scipy or you can use the following extra argument:
pip install pentapy[all]
Instead of "all" you can also typ "scipy" or "umfpack" to get one of these specific packages.
If you use
pentapy in your publication, please cite it:
Müller, (2019). pentapy: A Python toolbox for pentadiagonal linear systems. Journal of Open Source Software, 4(42), 1759, https://doi.org/10.21105/joss.01759
To cite a certain release, have a look at the Zenodo site: https://doi.org/10.5281/zenodo.2587158
The solver is based on the algorithms PTRANS-I and PTRANS-II presented by Askar et al. 2015.
Documentation and Examples
You can find the documentation under https://pentapy.readthedocs.org.
Solving a pentadiagonal linear equation system
This is an example of how to solve a LES with a pentadiagonal matrix.
import numpy as np import pentapy as pp size = 1000 # create a flattened pentadiagonal matrix M_flat = (np.random.random((5, size)) - 0.5) * 1e-5 V = np.random.random(size) * 1e5 # solve the LES with M_flat as row-wise flattened matrix X = pp.solve(M_flat, V, is_flat=True) # create the corresponding matrix for checking M = pp.create_full(M_flat, col_wise=False) # calculate the error print(np.max(np.abs(np.dot(M, X) - V)))
This should give something like:
In the following a couple of solvers for pentadiagonal systems are compared:
- Solver 1: Standard linear algebra solver of Numpy
- Solver 2:
- Solver 3: Scipy banded solver
- Solver 4: pentapy.solve with
- Solver 5: pentapy.solve with
The implementations of pentapy are almost one order of magnitude faster than the scipy algorithms for banded or sparse matrices.
You can contact us via firstname.lastname@example.org.
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