import numpy as np


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 = np.cross(qvec, v)
  uuv = np.cross(qvec, uv)

  return (v + 2 * (q[..., :1] * uv + uuv))


def qinverse(q, inplace=False):
  # We assume the quaternion to be normalized
  if inplace:
    q[..., 1:] *= -1
    return q
  else:
    w = q[..., :1]
    xyz = q[..., 1:]
    return np.hstack((w, -xyz))