Laguerre Sampling

s2ball.sampling.laguerre_sampling.nodes_and_weights(P: int, tau: float) → Tuple[ndarray]

Evaluates nodes and corresponding weights for zeros of the Laguerre polynomials.

Parameters:

• P (int) – Radial band-limit.

• tau (float) – Laguerre polynomial scale factor.

Returns:

Nodes scaled by \(\tau\) and corresponding weights.

Return type:

Tuple[np.ndarray]

s2ball.sampling.laguerre_sampling.polynomials(P: int, tau: float, forward: bool = True) → ndarray

Computes Laguerre polynomials, sampled at nodes coincident with zeros.

Parameters:

• P (int) – Radial band-limit.

• tau (float) – Laguerre polynomial scale factor.

• forward (bool, optional) – Whether to load the forward or inverse matrices. Defaults to True.

Returns:

Array containing Laguerre polynomials sampled at zeros.

Return type:

np.ndarray

s2ball.sampling.laguerre_sampling.quadrature(P: int) → ndarray

Compute Gauss-Laguerre quadrature over the positive half-line.

Parameters:

P (int) – Radial band-limit.

Returns:

Gauss-Laguerre quadrature weights.

Return type:

np.ndarray