pentapy 1.0.0

pentapy: A toolbox for pentadiagonal matrizes.

Welcome to pentapy

Purpose

pentapy is a toolbox to deal with pentadiagonal matrices in Python.

Installation

The package can be installed via pip. On Windows you can install WinPython to get Python and pip running.

pip install pentapy

References

The solver is based on the algorithms PTRANS-I and PTRANS-II presented by Askar et al. 2015.

Examples

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:

4.257890395820141e-08

Performance

In the following a couple of solvers for pentadiagonal systems is compared:

• Solver 1: Python implementation of pentapy.solve
• Solver 2: Cython implementation of pentapy.solve
• Solver 3: scipy.sparse.linalg.spsolve with use_umfpack=False
• Solver 4: scipy.sparse.linalg.spsolve with use_umfpack=True
• Solver 5: Lapack solver for diagonal matrices scipy.linalg.lapack.dgbsv
• Solver 6: Scipy banded solver scipy.linalg.solve_banded
• Solver 7: Standard solver of Numpy np.linalg.solve

The performance plot was created with perfplot. Have a look at the script: examples/02_perform.py.

Requirements:

• NumPy >= 1.14.5

Contact

You can contact us via [e-mail].

License

MIT © 2019