xnn.cnn.models.spherical.quadrature_weights#

xnn.cnn.models.spherical.quadrature_weights(b)[source]#

Quadrature weights w_j of the SO(3) grid for the normalized Haar measure (eq 11): int f dR = sum_{j,k,l} w_j f(beta_j, alpha_k, gamma_l).

The Driscoll-Healy weights (2/b) sin(beta_j) sum_{k<b} sin((2k+1) beta_j) / (2k+1) integrate every polynomial of degree below 2b in cos beta exactly over sin(beta) d beta; they are normalized by the 2 (2b)^2 of the measure and of the alpha / gamma sums.

Parameters:: b (int) – Bandwidth of the grid.
Returns:: Shape (2b,), float64, summing to 1 / (2b)^2.
Return type:: Tensor