xnn.cnn.models.spherical.SO3Transform#

class xnn.cnn.models.spherical.SO3Transform(b_grid, b_spec)[source]#

Bases: Module

Fourier transform between the SO(3) grid of bandwidth b_grid and spectra of bandwidth b_spec (b_spec <= b_grid).

A spectrum is a complex tensor (..., b_spec, 2 b_spec - 1, 2 b_spec - 1) holding f^l_{mn} at [l, m + b_spec - 1, n + b_spec - 1].

Parameters:

  • b_grid (int) – Bandwidth of the grid.

  • b_spec (int) – Bandwidth of the spectrum.

analyze(x)[source]#

Spectrum f^l_{mn} = int f conj(D^l_{mn}) dR of grid signals (..., 2b, 2b, 2b).

Parameters:

x (Tensor)

Return type:

Tensor

synthesize(f_hat, real=True)[source]#

Grid signal f = sum_l (2l + 1) sum_{mn} f^l_{mn} D^l_{mn} (eq 9).

Parameters:
Return type:

Tensor