pentapy: A toolbox for pentadiagonal matrizes.

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Development Status
- 5 - Production/Stable
Intended Audience
License
- OSI Approved :: MIT License
Natural Language
- English
Operating System
- Unix
Programming Language
Topic
- Scientific/Engineering
- Utilities

Project description

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

Performance

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 info@geostat-framework.org.

License

Project details

These details have not been verified by PyPI

Project links

Homepage

Development Status
- 5 - Production/Stable
Intended Audience
License
- OSI Approved :: MIT License
Natural Language
- English
Operating System
- Unix
Programming Language
Topic
- Scientific/Engineering
- Utilities

Release history Release notifications | RSS feed

1.3.0

Apr 10, 2024

1.2.0

Apr 15, 2023

1.1.2

Jul 6, 2021

1.1.1

Feb 18, 2021

1.1.1rc1 pre-release

Feb 18, 2021

1.1.0

Mar 22, 2020

1.1.0rc3 pre-release

Mar 22, 2020

1.1.0rc2 pre-release

Mar 22, 2020

1.1.0rc1 pre-release

Mar 21, 2020

1.0.3

Nov 10, 2019

1.0.2

Oct 2, 2019

1.0.1

Oct 2, 2019

This version

1.0.0

Sep 18, 2019

1.0.0rc1 pre-release

Sep 17, 2019

0.1.1

Mar 7, 2019

0.1.0

Mar 7, 2019

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