def test_jacobian_Y_ominus_X_wrt_Y():
X = SO2(np.pi / 4)
Y = SO2(np.pi / 3)
J_ominus_Y = Y.jac_Y_ominus_X_wrt_Y(X)
# Should be J_r_inv.
np.testing.assert_equal(J_ominus_Y, SO2.jac_right_inverse(Y - X))
# Test the Jacobian numerically.
delta = 1e-3 * np.ones((1, 1))
taylor_diff = Y.oplus(delta).ominus(X) - (Y.ominus(X) +
(J_ominus_Y @ delta))
np.testing.assert_almost_equal(taylor_diff, 0.0, 6)
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_inverse():
theta = np.pi / 4
# Should have J_l_inv(theta) == J_r_inv(theta).T
np.testing.assert_almost_equal(SO2.jac_left_inverse(theta),
SO2.jac_right_inverse(theta).T, 14)