Python Pfaffian for GPUs

This repository contains a differentiable implementation of the Pfaffian operation for PyTorch, with optional GPU acceleration via Triton. 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 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.

Installation

pip install torchpfaff

For GPU-accelerated Triton kernels on CUDA:

pip install torchpfaff[triton]

Alternatively, you can download the source code and install directly.

Using this package

from torchpfaff import pfaffian, log_pfaffian

# Construct an antisymmetric matrix:
M = ...

pf = pfaffian(M)

# For numerical stability with large matrices, use log-space:
sign, log_pf = log_pfaffian(M)

Backends

PyTorch

Full implementation with LTL (Parlett-Reid), direct, and recursive methods. Analytical backward pass via torch.autograd.Function. Supports torch.vmap and batched inputs.

Triton (CUDA)

GPU kernel for the LTL decomposition on CUDA devices. When Triton is installed and the input tensor is on CUDA, log_pfaffian automatically dispatches to the Triton kernel. You can also force a specific backend:

sign, log_pf = log_pfaffian(M, backend="triton")   # force Triton
sign, log_pf = log_pfaffian(M, backend="pytorch")  # force PyTorch