FFTL — generalised FFTLog for Python

The FFTL package for Python contains a routine to calculate integral transforms of the type ã(k) = ∫ a(r) T(kr) dr for arbitrary kernels T. It uses a modified FFTLog [2] method of Hamilton [1] to efficiently compute the transform on logarithmic input and output grids.

The package supports any array implementation such as Numpy, JAX, Torch, dask, etc. as long as it provides a reasonable set of standard Array API functions (e.g. log(), exp(), linspace(), etc.) and Fast Fourier Transforms (fft.rfft() and fft.irfft()).

Besides the generalised FFTLog algorithm, the package also provides a number of standard integral transforms.

Installation

Install with pip:

pip install fftl

The package only requires numpy and scipy.

For development, it is recommended to clone the GitHub repository, and perform an editable pip installation.

Usage

The core functionality of the package is provided by the fftl module. The fftl.transform() routine computes the generalised FFTLog integral transform for a given kernel. For convenience, the module provides a number of standard integral transforms.

User manual

• Generalised FFTLog
• Standard Integral Transforms

References

1. Hamilton A. J. S., 2000, MNRAS, 312, 257 (astro-ph/9905191)
2. Talman J. D., 1978, J. Comp. Phys., 29, 35