This repository contains implementations of the Pfaffian operation to be used in machine learning frameworks (Pytorch, JAX). Implementations are based on the algorithms published by M. Wimmer: https://arxiv.org/abs/1102.3440
What's the difference between this package and pfapack? This package is implemented directly in the machine learning frameworks (JAX, Pytorch) to enable GPU computations while pfapack is implemented with C / Fortran bindings for use in numpy on CPUs. This package is also differentiable through the pfaffian operation.
To install this package, simple pip install py-pfaffian. Alternatively, you can download the source code and install directly.
To call the pfaffian function from a framework, you can work like this:
from py_pfaffian.jax import pfaffian
# Construct an antisymmetric matrix:
M = ...
pf = pfaffian(M)Currently, the pfaffian has implementations only in JAX, and only with the Parlett-Reid algorithm via decomposition. The gradient computation is supported via a custom_jvp interface in JAX. The algorithm is compatible with jax.jit, jax.vmap, and differentiation in JAX.
Pytorch has a basic implementation that may not be performant for larger matrices - and isn't vmapped at this time.