Fourier-Wigner Transform#
- s2fft.precompute_transforms.fourier_wigner.forward_transform(f: np.ndarray, L: int, N: int, precomps: tuple[np.ndarray, np.ndarray] | None = None, reality: bool = False, sampling: str = 'mw') np.ndarray #
Computes the forward Wigner transform using the Fourier decomposition algorithm.
- Parameters:
f (np.ndarray) – Function sampled on the rotation group.
L (int) – Harmonic band-limit.
N (int) – Azimuthal band-limit.
precomps (tuple[np.ndarray, np.ndarray], optional) – Fourier coefficients of the reduced Wigner d-functions and the corresponding upsampled quadrature weights. Defaults to None.
reality (bool, optional) – Whether the signal on the sphere is real. If so, conjugate symmetry is exploited to reduce computational costs. Defaults to False.
sampling (str, optional) – Sampling scheme. Supported sampling schemes include {“mw”, “mwss”}. Defaults to “mw”.
- Returns:
Wigner coefficients of function f.
- Return type:
np.ndarray
- s2fft.precompute_transforms.fourier_wigner.forward_transform_jax(f: jnp.ndarray, L: int, N: int, precomps: tuple[jnp.ndarray, jnp.ndarray] | None = None, reality: bool = False, sampling: str = 'mw') jnp.ndarray #
Computes the forward Wigner transform using the Fourier decomposition algorithm (JAX).
- Parameters:
f (jnp.ndarray) – Function sampled on the rotation group.
L (int) – Harmonic band-limit.
N (int) – Azimuthal band-limit.
precomps (tuple[np.ndarray, np.ndarray], optional) – Fourier coefficients of the reduced Wigner d-functions and the corresponding upsampled quadrature weights. Defaults to None.
reality (bool, optional) – Whether the signal on the sphere is real. If so, conjugate symmetry is exploited to reduce computational costs. Defaults to False.
sampling (str, optional) – Sampling scheme. Supported sampling schemes include {“mw”, “mwss”}. Defaults to “mw”.
- Returns:
Wigner coefficients of function f.
- Return type:
jnp.ndarray
- s2fft.precompute_transforms.fourier_wigner.inverse_transform(flmn: np.ndarray, L: int, N: int, precomps: tuple[np.ndarray, np.ndarray] | None = None, reality: bool = False, sampling: str = 'mw') np.ndarray #
Computes the inverse Wigner transform using the Fourier decomposition algorithm.
- Parameters:
flmn (np.ndarray) – Wigner coefficients.
L (int) – Harmonic band-limit.
N (int) – Azimuthal band-limit.
precomps (tuple[np.ndarray, np.ndarray], optional) – Fourier coefficients of the reduced Wigner d-functions and the corresponding upsampled quadrature weights. Defaults to None.
reality (bool, optional) – Whether the signal on the sphere is real. If so, conjugate symmetry is exploited to reduce computational costs. Defaults to False.
sampling (str, optional) – Sampling scheme. Supported sampling schemes include {“mw”, “mwss”}. Defaults to “mw”.
- Returns:
Pixel-space function sampled on the rotation group.
- Return type:
np.ndarray
- s2fft.precompute_transforms.fourier_wigner.inverse_transform_jax(flmn: jnp.ndarray, L: int, N: int, precomps: tuple[jnp.ndarray, jnp.ndarray] | None = None, reality: bool = False, sampling: str = 'mw') jnp.ndarray #
Computes the inverse Wigner transform using the Fourier decomposition algorithm (JAX).
- Parameters:
flmn (jnp.ndarray) – Wigner coefficients.
L (int) – Harmonic band-limit.
N (int) – Azimuthal band-limit.
precomps (tuple[np.ndarray, np.ndarray], optional) – Fourier coefficients of the reduced Wigner d-functions and the corresponding upsampled quadrature weights. Defaults to None.
reality (bool, optional) – Whether the signal on the sphere is real. If so, conjugate symmetry is exploited to reduce computational costs. Defaults to False.
sampling (str, optional) – Sampling scheme. Supported sampling schemes include {“mw”, “mwss”}. Defaults to “mw”.
- Returns:
Pixel-space function sampled on the rotation group.
- Return type:
jnp.ndarray