import torch


def qrot(q, v):
    """
    Rotate vector(s) v about the rotation described by quaternion(s) q.
    Expects a tensor of shape (*, 4) for q and a tensor of shape (*, 3) for v,
    where * denotes any number of dimensions.
    Returns a tensor of shape (*, 3).
    """
    assert q.shape[-1] == 4
    assert v.shape[-1] == 3
    assert q.shape[:-1] == v.shape[:-1]

    qvec = q[..., 1:]
    uv = torch.cross(qvec, v, dim=len(q.shape)-1)
    uuv = torch.cross(qvec, uv, dim=len(q.shape)-1)
    return (v + 2 * (q[..., :1] * uv + uuv))