src/misc/sh_rotation.py

from math import isqrt

import torch
from e3nn.o3 import matrix_to_angles, wigner_D
from einops import einsum
from jaxtyping import Float
from torch import Tensor


def rotate_sh(
    sh_coefficients: Float[Tensor, "*#batch n"],
    rotations: Float[Tensor, "*#batch 3 3"],
) -> Float[Tensor, "*batch n"]:
    device = sh_coefficients.device
    dtype = sh_coefficients.dtype

    # change the basis from YZX -> XYZ to fit the convention of e3nn
    P = torch.tensor([[0, 0, 1], [1, 0, 0], [0, 1, 0]],
                     dtype=sh_coefficients.dtype, device=sh_coefficients.device)
    inversed_P = torch.tensor([[0, 1, 0], [0, 0, 1], [1, 0, 0], ],
                              dtype=sh_coefficients.dtype, device=sh_coefficients.device)
    permuted_rotation_matrix = inversed_P @ rotations @ P

    *_, n = sh_coefficients.shape
    alpha, beta, gamma = matrix_to_angles(permuted_rotation_matrix)
    result = []
    for degree in range(isqrt(n)):
        with torch.device(device):
            sh_rotations = wigner_D(degree, alpha, -beta, gamma).type(dtype)
        sh_rotated = einsum(
            sh_rotations,
            sh_coefficients[..., degree**2 : (degree + 1) ** 2],
            "... i j, ... j -> ... i",
        )
        result.append(sh_rotated)

    return torch.cat(result, dim=-1)


# def rotate_sh(
#     sh_coefficients: Float[Tensor, "*#batch n"],
#     rotations: Float[Tensor, "*#batch 3 3"],
# ) -> Float[Tensor, "*batch n"]:
#     device = sh_coefficients.device
#     dtype = sh_coefficients.dtype
#
#     *_, n = sh_coefficients.shape
#     alpha, beta, gamma = matrix_to_angles(rotations)
#     result = []
#     for degree in range(isqrt(n)):
#         with torch.device(device):
#             sh_rotations = wigner_D(degree, alpha, beta, gamma).type(dtype)
#         sh_rotated = einsum(
#             sh_rotations,
#             sh_coefficients[..., degree**2 : (degree + 1) ** 2],
#             "... i j, ... j -> ... i",
#         )
#         result.append(sh_rotated)
#
#     return torch.cat(result, dim=-1)


if __name__ == "__main__":
    from pathlib import Path

    import matplotlib.pyplot as plt
    from e3nn.o3 import spherical_harmonics
    from matplotlib import cm
    from scipy.spatial.transform.rotation import Rotation as R

    device = torch.device("cuda")

    # Generate random spherical harmonics coefficients.
    degree = 4
    coefficients = torch.rand((degree + 1) ** 2, dtype=torch.float32, device=device)

    def plot_sh(sh_coefficients, path: Path) -> None:
        phi = torch.linspace(0, torch.pi, 100, device=device)
        theta = torch.linspace(0, 2 * torch.pi, 100, device=device)
        phi, theta = torch.meshgrid(phi, theta, indexing="xy")
        x = torch.sin(phi) * torch.cos(theta)
        y = torch.sin(phi) * torch.sin(theta)
        z = torch.cos(phi)
        xyz = torch.stack([x, y, z], dim=-1)
        sh = spherical_harmonics(list(range(degree + 1)), xyz, True)
        result = einsum(sh, sh_coefficients, "... n, n -> ...")
        result = (result - result.min()) / (result.max() - result.min())

        # Set the aspect ratio to 1 so our sphere looks spherical
        fig = plt.figure(figsize=plt.figaspect(1.0))
        ax = fig.add_subplot(111, projection="3d")
        ax.plot_surface(
            x.cpu().numpy(),
            y.cpu().numpy(),
            z.cpu().numpy(),
            rstride=1,
            cstride=1,
            facecolors=cm.seismic(result.cpu().numpy()),
        )
        # Turn off the axis planes
        ax.set_axis_off()
        path.parent.mkdir(exist_ok=True, parents=True)
        plt.savefig(path)

    for i, angle in enumerate(torch.linspace(0, 2 * torch.pi, 30)):
        rotation = torch.tensor(
            R.from_euler("x", angle.item()).as_matrix(), device=device
        )
        plot_sh(rotate_sh(coefficients, rotation), Path(f"sh_rotation/{i:0>3}.png"))

    print("Done!")