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

pip install pfapack

Or using conda:

conda install -c conda-forge pfapack

Usage

from pfapack import pfaffian as pf
import numpy.random

A = numpy.random.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)

The package includes optimized C/FORTRAN implementations that can be used for better performance:

from pfapack.ctypes import pfaffian as cpf
pfa1 = cpf(A)
pfa2 = cpf(A, method="H")
print(pfa1, pfa2)

Warning

On Windows, the C bindings require MSYS2 to be installed with the MinGW64 toolchain. The current Windows build system has some limitations and requires external dependencies. We welcome contributions to improve the Windows build system, such as using Microsoft's toolchain (MSVC) directly or finding better ways to handle the OpenBLAS dependency.

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)