Fast Fourier transforms on the 3D rotation group $\mathrm{SO}(3)$

PySOFFT provides high performance routines for harmonic analysis on the 3D rotation group written in Fortran and wrapped in Python.

$$ f:\mathrm{SO}(3) \rightarrow \mathbb{C} \quad \overset{\mathrm{PySOFFT}}{\longleftrightarrow} \quad f^l_{m,n} \text{ with } |m|,|n|\leq l<\infty $$

Some applications:

• Rotational alignment of datasets given by their spherical harmonic coefficients.
• Statistical analysis over SO(3).
• X-ray scattering simulations of randomly oriented particles.

Main features:

• Fast
• OpenMP routines to speed up single transforms or compute many in parallel.
• Dedicated faster transforms for real data.
• Compute rotational cross-correlations.
• Built in Python wrapper.
• On-the-fly computation of Wigner matrices: saving memory.
• Documentation at https://pysofft.readthedocs.io

Origin

PySOFFT started as a partial python port of soft-2.0 released by Peter Kostelec and Daniel Rockmore. Now it is an entire rewrite in Fortran featuring several improvements, e.g higher precission computation of Wigner-D matrices, OpenMP routines and convenient python wrappers.

For details on soft-2.0 see:
FFTs on the Rotation Group
J Fourier Anal Appl (2008) 14: 145–179
DOI 10.1007/s00041-008-9013-5 (pdf)

PySOFT is made available with consent of the original soft-2.0 authors and under the same GPL3 license.

Installation

See the documentation for more details:

You can install PySOFT via

pip install pysofft

The only python dependency is numpy.
Non-python dependencies are: fftw, openmp, meson and gcc/gfortran.
Note: If you don't have some of the non-python dependencies installed the install will fail!

Pixi

If you use pixi you can use the following pixi.toml for installation.
Here you don't have to install the non-python dependencies separately.

[workspace]
channels = ["conda-forge"]
description = "Workspace for pysofft"
name = "temp"
platforms = ["linux-64"]
version = "0.1.0"

[system-requirements]
libc = { family = "glibc", version = "2.34" }

[dependencies]
gfortran = ">=15.2,<15.5.0"
gcc = ">=15.2,<15.5.0"
cpython = ">=3.13.11,<4"
python = ">=3.13.11,<3.14"
pip = ">=26.0.1,<27"
numpy = ">=2.2.6,<2.2.7"
meson = ">=1.8.1,<1.9.0"
meson-python = ">=0.19.0,<0.20"
fftw = ">=3.3.10,<4"
openmp = ">=8.0.1,<9"

[pypi-dependencies]
pysofft = ">=0.9.0, <2.0.0"

Basic Usage Python

Forward and inverse transforms

from pysofft import Soft
bw = 64
s = Soft(bw)

# complex case: inverse then forward 
f_lmn = s.get_coeff(random=True)
f = s.isoft(f_lmn)
f_lmn2 = s.soft(f)

# real case: inverse then forward
g_lmn = s.get_coeff(real=True,random=True)
g = s.irsoft(g_lmn)
g_lmn2 = s.rsoft(g)

Accessing individual harmonic coefficients

from pysofft import Soft
bw = 64
s = Soft(bw)

f_lmn = s.get_coeff(random=True)

l=4
m=-1
n=2

# access single coefficient
print(f_lmn.lmn[l,m,n])

# slicing is also possible
print(f_lmn.lmn[l,m,:])

# as well as value asignment
f_lmn.lmn[l,m,:] = 1 + 1.j