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README.md

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# Differentiable and accelerated spherical transforms
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`S2FFT` is a Python package for computing Fourier transforms on the sphere
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and rotation group [(Price & McEwen 2023)](https://arxiv.org/abs/2311.14670) using
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and rotation group [(Price & McEwen 2024)](https://arxiv.org/abs/2311.14670) using
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JAX or PyTorch. It leverages autodiff to provide differentiable transforms, which are
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also deployable on hardware accelerators (e.g. GPUs and TPUs).
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of hardware accelerators (i.e. GPUs and TPUs). In particular, these
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algorithms are based on new Wigner-d recursions that are stable to high
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angular resolution $L$. The diagram below illustrates the recursions
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(for further details see Price & McEwen, in prep.).
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(for further details see [Price & McEwen 2024]((https://arxiv.org/abs/2311.14670))).
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![image](./docs/assets/figures/Wigner_recursion_legend_darkmode.png)
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With this recursion to hand, the spherical harmonic coefficients of an
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computing only a portion of the projection at a time, hence incurring
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negligible memory overhead at the cost of slightly slower execution. The
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diagram below illustrates the separable spherical harmonic transform
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(for further details see Price & McEwen, in prep.).
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(for further details see [Price & McEwen 2024]((https://arxiv.org/abs/2311.14670))).
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![image](./docs/assets/figures/sax_schematic_legend_darkmode.png)
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A brief summary is shown in the table below for the recursion (left) and
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precompute (right) algorithms, with `S2FFT` running on GPUs (for further
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details see Price & McEwen, in prep.). Note that our compute time is
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agnostic to spin number (which is not the case for many other methods
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that scale linearly with spin).
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details see [Price & McEwen 2024]((https://arxiv.org/abs/2311.14670))).
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Note that our compute time is agnostic to spin number (which is not the
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case for many other methods that scale linearly with spin).
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| L | Wall-Time | Speed-up | Error | Wall-Time | Speed-up | Error | Memory |
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|------|-----------|----------|----------|-----------|----------|----------|---------|

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