Wavelet Matrices

s2ball.construct.wavelet_constructor.wavelet_laguerre_kernels(P: int, lam: float, tau: float) → List[List[ndarray]]

Constructs a collection of Laguerre polynomial kernel for multiresolution

directional wavelet transforms.

Parameters:

• P (int) – Radial band-limit.

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

• tau (float) – Laguerre polynomial scale factor.

Returns:

List of Laguerre polynomial kernels for each radial wavelet scale.

Return type:

List[List[np.ndarray]]

s2ball.construct.wavelet_constructor.wavelet_wigner_kernels(L: int, N: int, lam: float, save_dir: str = '.matrices') → List[List[ndarray]]

Constructs a collection of Wigner kernels for multiresolution directional wavelet

transforms.

Parameters:

• L (int) – Harmonic band-limit.

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

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

• save_dir (str, optional) – Directory in which to save precomputed matrices. Defaults to “.matrices”.

Returns:

List of Wigner transform kernels for each angular wavelet scale.

Return type:

List[List[np.ndarray]]

Note

Currently only McEwen-Wauix sampling on the sphere is supported, though this approach can be extended to alternate sampling schemes, e.g. HEALPix.