def test_left_jacobian_of_exponential(self):
tau = np.random.uniform(-np.pi, np.pi)
R, Jr = SO2.Exp(tau, Jr=True)
_, Jl = SO2.Exp(tau, Jl=True)
Ad_R = Jl * (1.0 / Jr)
self.assertEqual(1.0, Jl)
self.assertEqual(Ad_R, R.Adj)
def testAdjoint(self):
for i in range(100):
theta = np.random.uniform(-np.pi, np.pi)
R = SO2.fromAngle(theta)
delta = np.random.uniform(-np.pi, np.pi)
Adj_R = R.Adj
Rf = R * SO2.Exp(delta)
Rf_true = SO2.Exp(Adj_R * delta) * R
np.testing.assert_allclose(Rf_true.R, Rf.R)
def test_right_jacobian_of_boxplusr(self):
for i in range(100):
R = SO2.random()
theta = np.random.uniform(-np.pi, np.pi)
R2, Jr = R.boxplusr(theta, Jr=1)
_, Jr_true = SO2.Exp(theta, Jr=1)
np.testing.assert_allclose(Jr_true, Jr)
def test_left_jacobian_of_logarithm(self):
R = SO2.random()
logR, Jl_inv = SO2.Log(R, Jl=True)
_, Jl = SO2.Exp(logR, Jl=True)
self.assertEqual(1/Jl, Jl_inv)
def test_right_jacobian_of_logarithm(self):
R = SO2.random()
logR, Jr_inv = SO2.Log(R, Jr=True)
_, Jr = SO2.Exp(logR, Jr=True)
self.assertEqual(1/Jr, Jr_inv)
def test_right_jacobian_of_exponential(self):
tau = np.random.uniform(-np.pi, np.pi)
R, Jr = SO2.Exp(tau, Jr=True)
self.assertEqual(1.0, Jr)