pfapack: Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices

Code and algorithms are taken from arXiv:1102.3440 which is authored by Michael Wimmer.

Install

Recommended way (because it includes faster C/FORTRAN bindings)

conda install -c conda-forge pfapack

Alternatively use

pip install pfapack

Usage

from pfapack import pfaffian as pf
import numpy.matlib

A = numpy.matlib.rand(100, 100)
A = A - A.T
pfa1 = pf.pfaffian(A)
pfa2 = pf.pfaffian(A, method="H")
pfa3 = pf.pfaffian_schur(A)

print(pfa1, pfa2, pfa3)

If installed with conda, C/FORTRAN code is included with Python bindings, use it like:

from pfapack.ctypes import pfaffian as cpf

pfa1 = cpf(A)
pfa2 = cpf(A, method="H")

print(pfa1, pfa2)

Citing

If you have used pfapack in your research, please cite it using the following bib entry:

@article{wimmer2012algorithm,
  title={Efficient numerical computation of the pfaffian for dense and banded skew-symmetric matrices},
  author={Michael Wimmer},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  volume={38},
  number={4},
  pages={1--17},
  year={2012},
  publisher={ACM New York, NY, USA}
}

License

MIT License

Contributions

• Bas Nijholt
• Michael Wimmer (author of the algorithms)