# scipy.spatial.transform.Rotation.from_matrix

Rotation.from_matrix()

  Initialize from rotation matrix.

  Rotations in 3 dimensions can be represented with 3 x 3 proper orthogonal matrices [1]. If the input is not proper orthogonal, an approximation is created using the method described in [2].

  Parameters
    matrix array_like, shape (N, 3, 3) or (3, 3)

      A single matrix or a stack of matrices, where `matrix[i]` is the i-th matrix.

  Returns
    rotation `Rotation` instance

      Object containing the rotations represented by the rotation matrices.

  Notes

  This function was called from_dcm before.

  New in version 1.4.0.

  References

  1

    https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions

  2

    F. Landis Markley, “Unit Quaternion from Rotation Matrix”, Journal of guidance, control, and dynamics vol. 31.2, pp. 440-442, 2008.

  Examples

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

  Initialize a single rotation:

      >>> r = R.from_matrix([
      ... [0, -1, 0],
      ... [1, 0, 0],
      ... [0, 0, 1]])
      >>> r.as_matrix().shape
      (3, 3)

  Initialize multiple rotations in a single object:

      >>> r = R.from_matrix([
      ... [
      ...     [0, -1, 0],
      ...     [1, 0, 0],
      ...     [0, 0, 1],
      ... ],
      ... [
      ...     [1, 0, 0],
      ...     [0, 0, -1],
      ...     [0, 1, 0],
      ... ]])
      >>> r.as_matrix().shape
      (2, 3, 3)

  If input matrices are not special orthogonal (orthogonal with determinant equal to +1), then a special orthogonal estimate is stored:

      >>> a = np.array([
      ... [0, -0.5, 0],
      ... [0.5, 0, 0],
      ... [0, 0, 0.5]])
      >>> np.linalg.det(a)
      0.12500000000000003
      >>> r = R.from_matrix(a)
      >>> matrix = r.as_matrix()
      >>> matrix
      array([[-0.38461538, -0.92307692,  0.        ],
             [ 0.92307692, -0.38461538,  0.        ],
             [ 0.        ,  0.        ,  1.        ]])
      >>> np.linalg.det(matrix)
      1.0000000000000002

  It is also possible to have a stack containing a single rotation:

      >>> r = R.from_matrix([[
      ... [0, -1, 0],
      ... [1, 0, 0],
      ... [0, 0, 1]]])
      >>> r.as_matrix()
      array([[[ 0., -1.,  0.],
              [ 1.,  0.,  0.],
              [ 0.,  0.,  1.]]])
      >>> r.as_matrix().shape
      (1, 3, 3)