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Merge pull request #193 from astro-informatics/feature/gl_sampling
Feature/gl sampling
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‎README.md‎

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@@ -57,8 +57,9 @@ isolattitude sampling scheme. A number of sampling schemes are currently
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supported.
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The equiangular sampling schemes of [McEwen & Wiaux
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(2012)](https://arxiv.org/abs/1110.6298) and [Driscoll & Healy
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(1995)](https://www.sciencedirect.com/science/article/pii/S0196885884710086)
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(2012)](https://arxiv.org/abs/1110.6298), [Driscoll & Healy
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(1995)](https://www.sciencedirect.com/science/article/pii/S0196885884710086)
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and [Gauss-Legendre (1986)](https://link.springer.com/article/10.1007/BF02519350)
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are supported, which exhibit associated sampling theorems and so
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harmonic transforms can be computed to machine precision. Note that the
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McEwen & Wiaux sampling theorem reduces the Nyquist rate on the sphere

‎docs/index.rst‎

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@@ -21,7 +21,8 @@ Algorithms |:zap:|
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``S2FFT`` leverages new algorithmic structures that can he highly parallelised and
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distributed, and so map very well onto the architecture of hardware accelerators (i.e.
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GPUs and TPUs). In particular, these algorithms are based on new Wigner-d recursions
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that are stable to high angular resolution :math:`L`. The diagram below illustrates the recursions (for further details see Price & McEwen 2023).
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that are stable to high angular resolution :math:`L`. The diagram below illustrates the
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recursions (for further details see Price & McEwen 2023).
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.. image:: ./assets/figures/Wigner_recursion_github_docs.png
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@@ -46,7 +47,8 @@ Sampling |:earth_africa:|
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The structure of the algorithms implemented in ``S2FFT`` can support any isolattitude sampling scheme. A number of sampling schemes are currently supported.
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The equiangular sampling schemes of `McEwen & Wiaux (2012) <https://arxiv.org/abs/1110.6298>`_ and `Driscoll & Healy (1995) <https://www.sciencedirect.com/science/article/pii/S0196885884710086>`_ are supported, which exhibit associated sampling theorems and so harmonic transforms can be computed to machine precision. Note that the McEwen & Wiaux sampling theorem reduces the Nyquist rate on the sphere by a factor of two compared to the Driscoll & Healy approach, halving the number of spherical samples required.
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The equiangular sampling schemes of `McEwen & Wiaux (2012) <https://arxiv.org/abs/1110.6298>`_,
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`Driscoll & Healy (1995) <https://www.sciencedirect.com/science/article/pii/S0196885884710086>`_, and `Gauss-Legendre (1986) <https://link.springer.com/article/10.1007/BF02519350>`_ are supported, which exhibit associated sampling theorems and so harmonic transforms can be computed to machine precision. Note that the McEwen & Wiaux sampling theorem reduces the Nyquist rate on the sphere by a factor of two compared to the Driscoll & Healy approach, halving the number of spherical samples required.
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The popular `HEALPix <https://healpix.jpl.nasa.gov>`_ sampling scheme (`Gorski et al. 2005 <https://arxiv.org/abs/astro-ph/0409513>`_) is also supported. The HEALPix sampling does not exhibit a sampling theorem and so the corresponding harmonic transforms do not achieve machine precision but exhibit some error. However, the HEALPix sampling provides pixels of equal areas, which has many practical advantages.
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‎requirements/requirements-core.txt‎

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@@ -3,4 +3,7 @@ numpy>=1.20
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colorlog
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pyyaml
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jax>=0.3.13
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jaxlib
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jaxlib
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# Remove when subpackage functionality is fixed.
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torch

‎s2fft/_version.py‎

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# file generated by setuptools_scm
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# don't change, don't track in version control
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TYPE_CHECKING = False
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if TYPE_CHECKING:
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from typing import Tuple, Union
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VERSION_TUPLE = Tuple[Union[int, str], ...]
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else:
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VERSION_TUPLE = object
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version: str
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__version__: str
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__version_tuple__: VERSION_TUPLE
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version_tuple: VERSION_TUPLE
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__version__ = version = '1.0.1.dev12'
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__version_tuple__ = version_tuple = (1, 0, 1, 'dev12')

‎s2fft/base_transforms/spherical.py‎

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@@ -27,7 +27,7 @@ def inverse(
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spin (int, optional): Harmonic spin. Defaults to 0.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int, optional): HEALPix Nside resolution parameter. Only required
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if sampling="healpix". Defaults to None.

‎s2fft/base_transforms/wigner.py‎

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@@ -33,7 +33,7 @@ def inverse(
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L_lower (int, optional): Harmonic lower bound. Defaults to 0.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl"}. Defaults to "mw".
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs. Defaults to

‎s2fft/precompute_transforms/construct.py‎

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@@ -34,7 +34,7 @@ def spin_spherical_kernel(
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Defaults to False.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int): HEALPix Nside resolution parameter. Only required
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if sampling="healpix".
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Defaults to False.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int): HEALPix Nside resolution parameter. Only required
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if sampling="healpix".
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Defaults to False.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int): HEALPix Nside resolution parameter. Only required
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if sampling="healpix".
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Defaults to False.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int): HEALPix Nside resolution parameter. Only required
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if sampling="healpix".

‎s2fft/precompute_transforms/spherical.py‎

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@@ -32,7 +32,7 @@ def inverse(
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kernel (np.ndarray, optional): Wigner-d kernel. Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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L (int): Harmonic band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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L (int): Harmonic band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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kernel (np.ndarray, optional): Wigner-d kernel. Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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L (int): Harmonic band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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L (int): Harmonic band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.

‎s2fft/precompute_transforms/wigner.py‎

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@@ -32,7 +32,7 @@ def inverse(
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kernel (np.ndarray, optional): Wigner-d kernel. Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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N (int): Directional band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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N (int): Directional band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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kernel (np.ndarray, optional): Wigner-d kernel. Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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N (int): Directional band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.
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N (int): Directional band-limit.
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sampling (str): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}.
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{"mw", "mwss", "dh", "gl", "healpix"}.
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reality (bool, optional): Whether the signal on the sphere is real. If so,
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conjugate symmetry is exploited to reduce computational costs.

‎s2fft/sampling/s2_samples.py‎

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@@ -10,7 +10,7 @@ def ntheta(L: int = None, sampling: str = "mw", nside: int = None) -> int:
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Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int, optional): HEALPix Nside resolution parameter. Only required
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if sampling="healpix". Defaults to None.
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f"Sampling scheme sampling={sampling} with L={L} not supported"
3232
)
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34-
if sampling.lower() == "mw":
34+
if sampling.lower() in ["mw", "gl"]:
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return L
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3737
elif sampling.lower() == "mwss":
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L (int): Harmonic band-limit.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl"}. Defaults to "mw".
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Raises:
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ValueError: HEALPix sampling scheme.
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int: Number of :math:`\phi` samples.
105105
"""
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if sampling.lower() == "mw":
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if sampling.lower() in ["mw", "gl"]:
108108
return 2 * L - 1
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110110
elif sampling.lower() == "mwss":
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129129
L (int): Harmonic band-limit.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int, optional): HEALPix Nside resolution parameter.
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144144
if sampling.lower() in ["mwss", "healpix"]:
145145
return ntheta(L, sampling, nside), 2 * L
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147-
elif sampling.lower() in ["mw", "dh"]:
147+
elif sampling.lower() in ["mw", "dh", "gl"]:
148148
return ntheta(L, sampling, nside), 2 * L - 1
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150150
else:
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203203
Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int, optional): HEALPix Nside resolution parameter. Only required
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if sampling="healpix". Defaults to None.
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"""
214+
if sampling.lower() == "gl":
215+
return np.flip(np.arccos(np.polynomial.legendre.leggauss(L)[0]))
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t = np.arange(0, ntheta(L=L, sampling=sampling, nside=nside)).astype(np.float64)
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Defaults to None.
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int, optional): HEALPix Nside resolution parameter. Only required
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L (int, optional): Harmonic band-limit.
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sampling (str, optional): Sampling scheme. Supported equiangular sampling
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schemes include {"mw", "mwss", "dh"}. Defaults to "mw".
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schemes include {"mw", "mwss", "dh", "gl"}. Defaults to "mw".
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sampling (str, optional): Sampling scheme. Supported equiangular sampling
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schemes include {"mw", "mwss", "dh"}. Defaults to "mw".
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schemes include {"mw", "mwss", "dh", "gl"}. Defaults to "mw".
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376379
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377380
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378381

379-
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382+
if sampling.lower() in ["mw", "gl"]:
380383
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382385
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431434
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sampling (str, optional): Sampling scheme. Supported sampling schemes include
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{"mw", "mwss", "dh", "healpix"}. Defaults to "mw".
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{"mw", "mwss", "dh", "gl", "healpix"}. Defaults to "mw".
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nside (int, optional): HEALPix Nside resolution parameter. Only required
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if sampling="healpix". Defaults to None.

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