BUG: Rotation matrix is changed with scipy.spatial.transform.Rotation

Describe your issue.

Greetings, I think I encountered some bug in processing a 3D rotation matrix. I tried to retrieve Euler angles, but they made the wrong rotation. Even when I retrieve the matrix back, it is altered incorrectly. I think this failure has something to do with the internal storage of rotation objects as quaternions. But I don’t have expertise enough to debug through the source code, and I haven’t found description in the documentation about conversion limitations between rotation formats, except gimbal lock. There is a code example of the initial rotation matrix and the wrong output during conversions. Even the first retrieved matrix rotmatrix11 (without conversions) is wrong. I dubbed my question on StackOverflow https://stackoverflow.com/questions/74265765/rotation-matrix-is-changed-with-scipy-spatial-transform-rotation The rotation matrix seems correct in terms of orthonormality and the determinant.

Reproducing Code Example

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

rotmatrix1 = np.array([[ 0.86345719, -0.48700394,  0.13141101],
       [ 0.02362667, -0.221185  , -0.97494563],
       [-0.5038685 , -0.84492861,  0.1794775 ]])

print(f"rotmatrix1:\n  {rotmatrix1}")

r1 = R.from_matrix(rotmatrix1)
rotmatrix11 = r1.as_matrix()
angles1 = r1.as_euler("xyz")
print(f"angles1:  {angles1}")
print(f"rotmatrix11:\n  {rotmatrix11}")
print("-------------------------------")

r2 = R.from_euler("xyz", angles1)
rotmatrix2 = r2.as_matrix()
print(f"rotmatrix2:\n  {rotmatrix2}")

r3 = R.from_matrix(rotmatrix2)
angles2 = r3.as_euler("xyz")
print(f"angles2:  {angles2}")
r4 = R.from_euler("xyz", angles2)
rotmatrix3 = r4.as_matrix()
print(f"rotmatrix3:\n  {rotmatrix3}")

Error message

Output (all matrices are expected to be the same or at least do the same rotation job, but they differ):
rotmatrix1:
  [[ 0.86345719 -0.48700394  0.13141101]
 [ 0.02362667 -0.221185   -0.97494563]
 [-0.5038685  -0.84492861  0.1794775 ]]
angles1:  [ 2.91754028  0.33066594 -0.51471512]
rotmatrix11:
  [[ 0.82327846 -0.4171921  -0.3849199 ]
 [-0.46561791 -0.88418854 -0.03755775]
 [-0.32467296  0.21014609 -0.9221855 ]]
-------------------------------
rotmatrix2:
  [[ 0.82327846 -0.4171921  -0.3849199 ]
 [-0.46561791 -0.88418854 -0.03755775]
 [-0.32467296  0.21014609 -0.9221855 ]]
angles2:  [ 2.91754028  0.33066594 -0.51471512]
rotmatrix3:
  [[ 0.82327846 -0.4171921  -0.3849199 ]
 [-0.46561791 -0.88418854 -0.03755775]
 [-0.32467296  0.21014609 -0.9221855 ]]

SciPy/NumPy/Python version information

1.7.3 1.21.6 sys.version_info(major=3, minor=7, micro=15, releaselevel=‘final’, serial=0)

[rkern]

rotmatrix1 is not a rotation matrix. It incorporates a reflection.

|2> np.linalg.det(rotmatrix1)                                                                                                                                                                                        
-1.0000000047994289

[akvilonBrown]

Thank you for your clarification and for your time. My knowledge gap didn’t allow me to reveal it in time. I was misled by some custom code snippets on the web which can handle negative determinants and stated that it was OK for rotation. Now I see that in scipy documentation that determinant +1 is a mandatory condition. Indeed reflection is quite likely to occur when I use PCA results as a basis for the rotational matrix.