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.
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
PySOFFT has the following non-python dependencies
fftw,openmp, meson and gcc.
The only python dependency is numpy.
Pixi
The advantage of pixi is that all non-python dependencies are installed automatically. You can use the following pixi.toml for installation.
pixi.toml
[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"
after placing the above pixi.toml in an empty directory you can install the environment using
pixi update
pixi shell
PyPi
PySOFFT can be installed via
pip install pysofft
Git Clone + pip
You can also git clone and pip install.
git clone https://github.com/TimBerberich/pysofft
cd pysofft
pip install .
Editable installs are possible by substituting the last line with
pip install --no-build-isolation -e .
CPU specific optimization
This can significally speed up computations.
You can use them by adding -march=native to the lines in
pysofft/pysofft/meson.build starting with c_args and fortran_args, before calling pip install ..
The relevant lines should then be
fortran_args: ['-fopenmp','-lfftw3', '-O3', '-fno-math-errno', '-fno-trapping-math', '-march=native'],
and
c_args: ['-fopenmp','-lfftw3', '-O3', '-fno-math-errno', '-fno-trapping-math', '-march=native'],
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)
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