# scipy.spatial.transform.Rotation.__mul__

Rotation.__mul__()

  Compose this rotation with the other.

  If p and q are two rotations, then the composition of ‘q followed by p’ is equivalent to p * q. In terms of rotation matrices, the composition can be expressed as `p.as_matrix().dot(q.as_matrix())`.

  Parameters:
    other `Rotation` instance

      Object containing the rotations to be composed with this one. Note that rotation compositions are not commutative, so `p * q` is different from `q * p`.

  Returns:
    composition `Rotation` instance

      This function supports composition of multiple rotations at a time. The following cases are possible:

      - Either `p` or `q` contains a single rotation. In this case composition contains the result of composing each rotation in the other object with the single rotation.

      - Both `p` and `q` contain `N` rotations. In this case each rotation `p[i]` is composed with the corresponding rotation `q[i]` and output contains `N` rotations.

  Examples

      >>> from scipy.spatial.transform import Rotation as R
      >>> import numpy as np

  Composition of two single rotations:

      >>> p = R.from_quat([0, 0, 1, 1])
      >>> q = R.from_quat([1, 0, 0, 1])
      >>> p.as_matrix()
      array([[ 0., -1.,  0.],
             [ 1.,  0.,  0.],
             [ 0.,  0.,  1.]])
      >>> q.as_matrix()
      array([[ 1.,  0.,  0.],
             [ 0.,  0., -1.],
             [ 0.,  1.,  0.]])
      >>> r = p * q
      >>> r.as_matrix()
      array([[0., 0., 1.],
             [1., 0., 0.],
             [0., 1., 0.]])

  Composition of two objects containing equal number of rotations:

      >>> p = R.from_quat([[0, 0, 1, 1], [1, 0, 0, 1]])
      >>> q = R.from_rotvec([[np.pi/4, 0, 0], [-np.pi/4, 0, np.pi/4]])
      >>> p.as_quat()
      array([[0.        , 0.        , 0.70710678, 0.70710678],
             [0.70710678, 0.        , 0.        , 0.70710678]])
      >>> q.as_quat()
      array([[ 0.38268343,  0.        ,  0.        ,  0.92387953],
             [-0.37282173,  0.        ,  0.37282173,  0.84971049]])
      >>> r = p * q
      >>> r.as_quat()
      array([[ 0.27059805,  0.27059805,  0.65328148,  0.65328148],
             [ 0.33721128, -0.26362477,  0.26362477,  0.86446082]])