1414# Differentiable and accelerated spherical transforms
1515
1616` S2FFT ` is a Python package for computing Fourier transforms on the sphere
17- and rotation group [ (Price & McEwen 2023 )] ( https://arxiv.org/abs/2311.14670 ) using
17+ and rotation group [ (Price & McEwen 2024 )] ( https://arxiv.org/abs/2311.14670 ) using
1818JAX or PyTorch. It leverages autodiff to provide differentiable transforms, which are
1919also deployable on hardware accelerators (e.g. GPUs and TPUs).
2020
@@ -45,7 +45,7 @@ parallelised and distributed, and so map very well onto the architecture
4545of hardware accelerators (i.e. GPUs and TPUs). In particular, these
4646algorithms are based on new Wigner-d recursions that are stable to high
4747angular resolution $L$. The diagram below illustrates the recursions
48- (for further details see Price & McEwen, in prep. ).
48+ (for further details see [ Price & McEwen 2024 ] ( (https://arxiv.org/abs/2311.14670) ) ).
4949
5050![ image] ( ./docs/assets/figures/Wigner_recursion_legend_darkmode.png )
5151With this recursion to hand, the spherical harmonic coefficients of an
@@ -58,7 +58,7 @@ Alternatively, the real polar-d functions may calculated recursively,
5858computing only a portion of the projection at a time, hence incurring
5959negligible memory overhead at the cost of slightly slower execution. The
6060diagram below illustrates the separable spherical harmonic transform
61- (for further details see Price & McEwen, in prep. ).
61+ (for further details see [ Price & McEwen 2024 ] ( (https://arxiv.org/abs/2311.14670) ) ).
6262
6363![ image] ( ./docs/assets/figures/sax_schematic_legend_darkmode.png )
6464
@@ -186,9 +186,9 @@ in `S2FFT` against the C implementations in the
186186
187187A brief summary is shown in the table below for the recursion (left) and
188188precompute (right) algorithms, with `S2FFT` running on GPUs (for further
189- details see Price & McEwen, in prep.). Note that our compute time is
190- agnostic to spin number (which is not the case for many other methods
191- that scale linearly with spin).
189+ details see [ Price & McEwen 2024]((https://arxiv.org/abs/2311.14670))).
190+ Note that our compute time is agnostic to spin number (which is not the
191+ case for many other methods that scale linearly with spin).
192192
193193| L | Wall-Time | Speed-up | Error | Wall-Time | Speed-up | Error | Memory |
194194|------|-----------|----------|----------|-----------|----------|----------|---------|
@@ -248,9 +248,12 @@ referenced. A BibTeX entry for this reference may look like:
248248@article{price:s2fft,
249249 author = "Matthew A. Price and Jason D. McEwen",
250250 title = "Differentiable and accelerated spherical harmonic and Wigner transforms",
251- journal = "Journal of Computational Physics, submitted",
252- year = "2023",
253- eprint = "arXiv:2311.14670"
251+ journal = "Journal of Computational Physics",
252+ year = "2024",
253+ volume = "510",
254+ pages = "113109",
255+ eprint = "arXiv:2311.14670",
256+ doi = "10.1016/j.jcp.2024.113109"
254257}
255258```
256259
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