def test_jacobian_right_inverse(): theta = 3 * np.pi / 4 X = SO2.Exp(theta) J_r_inv = SO2.jac_right_inverse(theta) # Should have J_l * J_r_inv = Exp(theta).adjoint(). J_l = SO2.jac_left(theta) np.testing.assert_almost_equal(J_l @ J_r_inv, SO2.Exp(theta).adjoint(), 14) # Test the Jacobian numerically. delta = 1e-3 * np.ones((1, 1)) taylor_diff = X.oplus(delta).Log() - (X.Log() + J_r_inv @ delta) np.testing.assert_almost_equal(taylor_diff, 0.0, 5)
def test_jacobian_left(): theta = np.pi / 4 # Should have J_l(theta) == J_r(-theta). np.testing.assert_almost_equal(SO2.jac_left(theta), SO2.jac_right(-theta), 14)