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import torch
from e3nn.util.jit import compile_mode
from ._wigner import wigner_D
from ._s2grid import _quadrature_weights, s2_grid
def flat_wigner(lmax: int, alpha: torch.Tensor, beta: torch.Tensor, gamma: torch.Tensor) -> torch.Tensor:
return torch.cat([(2 * l + 1) ** 0.5 * wigner_D(l, alpha, beta, gamma).flatten(-2) for l in range(lmax + 1)], dim=-1)
@compile_mode("script")
class SO3Grid(torch.nn.Module): # pylint: disable=abstract-method
r"""Apply non linearity on the signal on SO(3)
Parameters
----------
lmax : int
irreps representation ``[(2 * l + 1, (l, p_val)) for l in [0, ..., lmax]]``
resolution : int
SO(3) grid resolution
normalization : {'norm', 'component'}
aspect_ratio : float
default value (2) should be optimal
"""
def __init__(self, lmax, resolution, *, normalization: str = "component", aspect_ratio: int = 2) -> None:
super().__init__()
assert normalization == "component"
nb = 2 * resolution
na = round(2 * aspect_ratio * resolution)
b, a = s2_grid(nb, na)
self.register_buffer("D", flat_wigner(lmax, a[:, None, None], b[None, :, None], a[None, None, :]))
qw = _quadrature_weights(nb // 2) * nb**2 / na**2
self.register_buffer("qw", qw)
self.register_buffer("alpha", a)
self.register_buffer("beta", b)
self.register_buffer("gamma", a)
self.res_alpha = na
self.res_beta = nb
self.res_gamma = na
def __repr__(self) -> str:
return f"{self.__class__.__name__} ({self.lmax})"
def to_grid(self, features) -> torch.Tensor:
r"""evaluate
Parameters
----------
features : `torch.Tensor`
tensor of shape ``(..., self.irreps.dim)``
Returns
-------
`torch.Tensor`
tensor of shape ``(..., self.res_alpha, self.res_beta, self.res_gamma)``
"""
return torch.einsum("...i,abci->...abc", features, self.D) / self.D.shape[-1] ** 0.5
def from_grid(self, features) -> torch.Tensor:
r"""evaluate
Parameters
----------
features : `torch.Tensor`
tensor of shape ``(..., self.res_alpha, self.res_beta, self.res_gamma)``
Returns
-------
`torch.Tensor`
tensor of shape ``(..., self.irreps.dim)``
"""
return torch.einsum("...abc,abci,b->...i", features, self.D, self.qw) * self.D.shape[-1] ** 0.5
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