aenet.torch_featurize.ChebyshevPolynomials

class aenet.torch_featurize.ChebyshevPolynomials(*args: Any, **kwargs: Any)

Vectorized Chebyshev polynomial evaluation using cosine form.

Uses T_n(x) = cos(n * arccos(x)) for numerical stability and efficient vectorization across all polynomial orders.

Parameters:

• max_order (int) – Maximum Chebyshev polynomial order to compute

• r_min (float) – Minimum distance (inner cutoff) in Angstroms

• r_max (float) – Maximum distance (outer cutoff) in Angstroms

• dtype (torch.dtype, optional) – Data type for computations (default: torch.float64)

Examples

>>> cheb = ChebyshevPolynomials(max_order=5, r_min=0.5, r_max=4.0)
>>> r = torch.tensor([1.0, 2.0, 3.0], dtype=torch.float64)
>>> T = cheb(r)  # Shape: (3, 6) for orders 0-5

__init__(max_order: int, r_min: float, r_max: float, dtype: torch.dtype = torch.float64)

Methods

__init__(max_order, r_min, r_max[, dtype])
cutoff_derivative(r, Rc)	Derivative of the cosine cutoff function.
cutoff_function(r, Rc)	Cosine cutoff function.
evaluate_with_derivatives(r)	Evaluate Chebyshev polynomials and their derivatives.
forward(r)	Evaluate Chebyshev polynomials for given distances.
rescale_distances(r)	Rescale distances from [r_min, r_max] to [-1, 1].