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Wavelet Filters#

s2ball.wavelets.tiling.compute_wav_lmp(L: int, N: int, P: int, lam_l: float, lam_p: float) → Tuple[List[List[ndarray]], ndarray]#

Compute multiresolution wavelet and scaling filters.

Parameters:

  • L (int) – Harmonic band-limit.

  • N (int) – Directional band-limit. Must be < L.

  • P (int) – Radial band-limit.

  • lam_l (float) – Wavelet angular scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

  • lam_p (float) – Wavelet radial scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

Returns:

List of wavelet filters for each

wavelet scale, and an array scaling coefficients.

Return type:

Tuple[List[List[np.ndarray]], np.ndarray]

s2ball.wavelets.tiling.construct_f_wav(L: int, N: int, P: int, lam_l: float, lam_p: float) → List[List[ndarray]]#

Generate multiresolution wavelet Wigner-Laguerre coefficients for Numpy.

Parameters:

  • L (int) – Harmonic band-limit.

  • N (int) – Directional band-limit. Must be < L.

  • P (int) – Radial band-limit.

  • lam_l (float) – Wavelet angular scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

  • lam_p (float) – Wavelet radial scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

Returns:

List of wavelet pixel-space coefficients for each scale.

Return type:

List[List[np.ndarray]]

s2ball.wavelets.tiling.construct_f_wav_lmnp(L: int, N: int, P: int, lam_l: float, lam_p: float) → List[List[ndarray]]#

Generate multiresolution wavelet Wigner-Laguerre coefficients for Numpy.

Parameters:

  • L (int) – Harmonic band-limit.

  • N (int) – Directional band-limit. Must be < L.

  • P (int) – Radial band-limit.

  • lam_l (float) – Wavelet angular scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

  • lam_p (float) – Wavelet radial scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

Returns:

List of wavelet Wigner-Laguerre coefficients.

Return type:

List[List[np.ndarray]]

s2ball.wavelets.tiling.construct_f_wav_lmnp_jax(L: int, N: int, P: int, lam_l: float, lam_p: float) → List[List[Array]]#

Generate multiresolution wavelet Wigner-Laguerre coefficients for JAX.

Parameters:

  • L (int) – Harmonic band-limit.

  • N (int) – Directional band-limit. Must be < L.

  • P (int) – Radial band-limit.

  • lam_l (float) – Wavelet angular scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

  • lam_p (float) – Wavelet radial scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

Returns:

List of wavelet Wigner-Laguerre coefficients.

Return type:

List[List[jnp.ndarray]]

s2ball.wavelets.tiling.construct_wav_lmp(L: int, P: int, lam_l: float, lam_p: float) → List[List[ndarray]]#

Generate multiresolution wavelet filters

Parameters:

  • L (int) – Harmonic band-limit.

  • P (int) – Radial band-limit.

  • lam_l (float) – Wavelet angular scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

  • lam_p (float) – Wavelet radial scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

Returns:

List of wavelet filters for each wavelet scale.

Return type:

List[List[np.ndarray]]

s2ball.wavelets.tiling.tiling_axisym(L: int, P: int, lam_l: float, lam_p: float) → Tuple[ndarray, ndarray]#

Axisymmetric tiling functions

Parameters:

  • L (int) – Harmonic band-limit.

  • P (int) – Radial band-limit.

  • lam_l (float) – Wavelet angular scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

  • lam_p (float) – Wavelet radial scaling factor. \(\lambda = 2.0\) indicates dyadic wavelets.

Returns:

Tuple of axisymmetric tiling functions.

Return type:

Tuple[np.ndarray, np.ndarray]