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# scipy.spatial.transform.Rotation.mean

Rotation.mean(self, weights=None)

  Get the mean of the rotations.

  The mean used is the chordal L2 mean (also called the projected or induced arithmetic mean) [1]. If `A` is a set of rotation matrices, then the mean `M` is the rotation matrix that minimizes the following loss function:

  \[L(M) = \sum_{i = 1}^{n} w_i \lVert \mathbf{A}_i - \mathbf{M} \rVert^2 ,\]

  where \(w_i\)’s are the weights corresponding to each matrix.

  Parameters:
    weights array_like shape (N,), optional

      Weights describing the relative importance of the rotations. If None (default), then all values in weights are assumed to be equal.

  Returns:
    mean `Rotation` instance

      Object containing the mean of the rotations in the current instance.

  References

  [1]

  Hartley, Richard, et al., “Rotation Averaging”, International Journal of Computer Vision 103, 2013, pp. 267-305.

  Examples

      >>> from scipy.spatial.transform import Rotation as R
      >>> r = R.from_euler('zyx', [[0, 0, 0],
      ...                          [1, 0, 0],
      ...                          [0, 1, 0],
      ...                          [0, 0, 1]], degrees=True)
      >>> r.mean().as_euler('zyx', degrees=True)
      array([0.24945696, 0.25054542, 0.24945696])