1313# Differentiable and accelerated spherical transforms
1414
1515` S2FFT ` is a Python package for computing Fourier transforms on the sphere
16- and rotation group [ (Price & McEwen 2023 )] ( https://arxiv.org/abs/2311.14670 ) using
16+ and rotation group [ (Price & McEwen 2024 )] ( https://arxiv.org/abs/2311.14670 ) using
1717JAX or PyTorch. It leverages autodiff to provide differentiable transforms, which are
1818also deployable on hardware accelerators (e.g. GPUs and TPUs).
1919
@@ -44,7 +44,7 @@ parallelised and distributed, and so map very well onto the architecture
4444of hardware accelerators (i.e. GPUs and TPUs). In particular, these
4545algorithms are based on new Wigner-d recursions that are stable to high
4646angular resolution $L$. The diagram below illustrates the recursions
47- (for further details see Price & McEwen, in prep. ).
47+ (for further details see [ Price & McEwen 2024 ] ( (https://arxiv.org/abs/2311.14670) ) ).
4848
4949![ image] ( ./docs/assets/figures/Wigner_recursion_legend_darkmode.png )
5050With this recursion to hand, the spherical harmonic coefficients of an
@@ -57,7 +57,7 @@ Alternatively, the real polar-d functions may calculated recursively,
5757computing only a portion of the projection at a time, hence incurring
5858negligible memory overhead at the cost of slightly slower execution. The
5959diagram below illustrates the separable spherical harmonic transform
60- (for further details see Price & McEwen, in prep. ).
60+ (for further details see [ Price & McEwen 2024 ] ( (https://arxiv.org/abs/2311.14670) ) ).
6161
6262![ image] ( ./docs/assets/figures/sax_schematic_legend_darkmode.png )
6363
@@ -185,9 +185,9 @@ in `S2FFT` against the C implementations in the
185185
186186A brief summary is shown in the table below for the recursion (left) and
187187precompute (right) algorithms, with `S2FFT` running on GPUs (for further
188- details see Price & McEwen, in prep.). Note that our compute time is
189- agnostic to spin number (which is not the case for many other methods
190- that scale linearly with spin).
188+ details see [ Price & McEwen 2024]((https://arxiv.org/abs/2311.14670))).
189+ Note that our compute time is agnostic to spin number (which is not the
190+ case for many other methods that scale linearly with spin).
191191
192192| L | Wall-Time | Speed-up | Error | Wall-Time | Speed-up | Error | Memory |
193193|------|-----------|----------|----------|-----------|----------|----------|---------|
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