def test_right_jacobian_of_composition(self):
T1 = SE2.random()
T2 = SE2.random()
T3, Jr = T1.compose(T2, Jr=np.eye(3))
Jr_true = np.linalg.inv(T2.Adj)
np.testing.assert_allclose(Jr_true, Jr)
def test_boxminusl(self):
for i in range(100):
T1 = SE2.random()
T2 = SE2.random()
w = T1.boxminusl(T2)
T = T2.boxplusl(w)
np.testing.assert_allclose(T.T, T1.T)
def test_jacobians_of_exponential(self):
t = np.random.uniform(-10.0, 10.0, size=2)
theta = np.random.uniform(-np.pi, np.pi)
tau = np.array([*t, theta])
T, Jr = SE2.Exp(tau, Jr=np.eye(3))
_, Jl = SE2.Exp(-tau, Jl=np.eye(3))
np.testing.assert_allclose(Jr, Jl)
def test_jacobians_of_boxminusl(self):
for i in range(100):
T1, T2 = SE2.random(), SE2.random()
tau, Jr = T1.boxminusl(T2, Jr1=np.eye(3))
_, Jl = T1.boxminusl(T2, Jl1=np.eye(3))
Jl_true = np.eye(3) @ Jr @ np.linalg.inv(T1.Adj)
np.testing.assert_allclose(Jl_true, Jl)
def test_jacobians_of_boxminusl_second_element(self):
for i in range(100):
T1, T2 = SE2.random(), SE2.random()
tau, Jr2 = T1.boxminusl(T2, Jr2=np.eye(3))
_, Jl2 = T1.boxminusl(T2, Jl2=np.eye(3))
Jl_true = np.eye(3) @ Jr2 @ np.linalg.inv(T2.Adj)
np.testing.assert_allclose(Jl_true, Jl2)
def testTaylorExp(self):
for i in range(100):
v = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-1e-8, 1e-8)
arr = np.array([v[0], v[1], theta])
T = SE2.Exp(arr)
T_true = spl.expm(SE2.hat(arr))
np.testing.assert_allclose(T_true, T.arr)
def test_boxplusl(self):
for i in range(100):
T = SE2.random()
u = np.random.uniform(-10., 10., size=2)
theta = np.random.uniform(-np.pi, np.pi)
vec = np.array([*u, theta])
T2 = T.boxplusl(vec)
T2_true = SE2.Exp(vec) * T
np.testing.assert_allclose(T2_true.T, T2.T)
def testBoxPlusR(self):
for i in range(100):
T = SE2.random()
u = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
vec = np.array([*u, theta])
T3 = T.boxplusr(vec)
T3_true = T * SE2.Exp(vec)
np.testing.assert_allclose(T3_true.T, T3.T)
def test_jacobians_of_composition_second_element(self):
for i in range(100):
T1 = SE2.random()
T2 = SE2.random()
T3, Jr2 = T1.compose(T2, Jr2=np.eye(3))
_, Jl2 = T1.compose(T2, Jl2=np.eye(3))
Jl2_true = T3.Adj @ Jr2 @ np.linalg.inv(T2.Adj)
np.testing.assert_allclose(Jl2_true, Jl2)
def test_left_jacobian_of_composition(self):
for i in range(100):
T1 = SE2.random()
T2 = SE2.random()
T3, Jr = T1.compose(T2, Jr=np.eye(3))
_, Jl = T1.compose(T2, Jl=np.eye(3))
Jl_true = T3.Adj @ Jr @ T1.inv().Adj
np.testing.assert_allclose(Jl_true, Jl, atol=1e-10)
def test_right_jacobians_of_boxminusr(self):
for i in range(100):
T1, T2 = SE2.random(), SE2.random()
tau, Jr1 = T1.boxminusr(T2, Jr1=np.eye(3))
dT = T2.inv() * T1
_, Jr1_true = SE2.Log(dT, Jr=np.eye(3))
_, Jr2 = T1.boxminusr(T2, Jr2=np.eye(3))
_, Jr2_true = SE2.Log(dT, Jl=np.eye(3))
np.testing.assert_allclose(Jr1_true, Jr1)
np.testing.assert_allclose(-Jr2_true, Jr2)
def test_left_jacobians_of_boxminusr(self):
for i in range(100):
T1, T2 = SE2.random(), SE2.random()
tau, Jl1 = T1.boxminusr(T2, Jl1=np.eye(3))
_, Jr1 = T1.boxminusr(T2, Jr1=np.eye(3))
Jl1_true = np.eye(3) @ Jr1 @ np.linalg.inv(T1.Adj)
_, Jl2 = T1.boxminusr(T2, Jl2=np.eye(3))
_, Jr2 = T1.boxminusr(T2, Jr2=np.eye(3))
Jl2_true = np.eye(3) @ Jr2 @ np.linalg.inv(T2.Adj)
np.testing.assert_allclose(Jl1_true, Jl1)
np.testing.assert_allclose(Jl2_true, Jl2)
def testTaylorLog(self):
for i in range(100): #Test taylor series
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-1e-8, 1e-8)
T = SE2.fromAngleAndt(theta, t)
logT = SE2.log(T)
logT_true = spl.logm(T.arr)
if np.linalg.norm(logT_true - logT, ord='fro') > 1e-8:
Pdb().set_trace()
debug = 1
temp = SE2.log(T)
np.testing.assert_allclose(logT_true, logT, atol=1e-7)
def test_right_jacobian_or_transp(self):
for i in range(100):
T = SE2.random()
v = np.random.uniform(-10, 10, size=2)
vp, Jr = T.transp(v, Jr=np.eye(3))
one_x = np.array([[0, -1], [1, 0]])
Jr_true = np.block(
[np.eye(2), (one_x @ T.R.T @ (T.t - v))[:, None]])
def testLog(self):
for i in range(100):
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
ct = np.cos(theta)
st = np.sin(theta)
R = np.array([[ct, -st], [st, ct]])
T = SE2.fromRandt(R, t)
logT = SE2.log(T)
logT_true = spl.logm(T.arr)
if np.linalg.norm(logT_true - logT, ord='fro') > 1e-3:
Pdb().set_trace()
debug = 1
temp = SE2.log(T)
np.testing.assert_allclose(logT_true, logT, atol=1e-7)
def testHat(self):
for i in range(100):
u = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
arr = np.array([u[0], u[1], theta])
X_true = np.array([[0, -theta, u[0]], [theta, 0, u[1]], [0, 0, 0]])
X = SE2.hat(arr)
np.testing.assert_allclose(X_true, X)
def test_left_jacobian_of_transp(self):
for i in range(100):
T = SE2.random()
v = np.random.uniform(-10, 10, size=2)
vp, Jl = T.transp(v, Jl=np.eye(3))
one_x = np.array([[0, -1], [1, 0]])
Jl_true = np.block([-T.R.T, -(T.R.T @ one_x @ v)[:, None]])
np.testing.assert_allclose(Jl_true, Jl)
def test_right_jacobian_of_transformation(self):
for i in range(100):
T = SE2.random()
v = np.random.uniform(-10, 10, size=2)
vp, Jr = T.transa(v, Jr=np.eye(3))
vx = np.array([-v[1], v[0]])
Jr_true = np.block([T.R, (T.R @ vx)[:, None]])
np.testing.assert_allclose(Jr_true, Jr)
def testVee(self):
for i in range(100):
u = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
# arr_true = np.array([theta, u[0], u[1]])
arr_true = np.array([u[0], u[1], theta])
X = np.array([[0, -theta, u[0]], [theta, 0, u[1]], [0, 0, 0]])
arr = SE2.vee(X)
np.testing.assert_allclose(arr_true, arr)
def testAdjoint(self):
for i in range(100):
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
u = np.random.uniform(-1, 1, size=2)
phi = np.random.uniform(-np.pi, np.pi)
# delta = np.array([phi, u[0], u[1]])
delta = np.array([u[0], u[1], phi])
ct = np.cos(theta)
st = np.sin(theta)
R = np.array([[ct, -st], [st, ct]])
T = SE2.fromRandt(R, t)
adj = T.Adj
T2_true = T * SE2.Exp(delta)
T2 = SE2.Exp(adj @ delta) * T
np.testing.assert_allclose(T2_true.arr, T2.arr)
def test_left_jacobian_of_transformation(self):
for i in range(100):
T = SE2.random()
v = np.random.uniform(-10, 10, size=2)
vp, Jl = T.transa(v, Jl=np.eye(3))
_, Jr = T.transa(v, Jr=np.eye(3))
Jl_true = np.eye(2) @ Jr @ np.linalg.inv(T.Adj)
np.testing.assert_allclose(Jl_true, Jl, atol=1e-10)
def test_left_jacobian_of_inversion(self):
T = SE2.random()
T_inv, Jr = T.inv(Jr=np.eye(3))
_, Jl = T.inv(Jl=np.eye(3))
Adj_T = T.Adj
Adj_Tinv = T_inv.Adj
Jl_true = Adj_Tinv @ Jr @ np.linalg.inv(Adj_T)
np.testing.assert_allclose(Jl_true, Jl)
def test_jacobians_for_boxplusl(self):
for i in range(100):
T1 = SE2.random()
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
tau = np.array([*t, theta])
T2, Jr = T1.boxplusl(tau, Jr=np.eye(3))
_, Jl = T1.boxplusl(tau, Jl=np.eye(3))
Jl_true = T2.Adj @ Jr @ np.eye(3)
np.testing.assert_allclose(Jl_true, Jl)
def testExp(self):
for i in range(100):
v = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
logT = np.array([[0, -theta, v[0]], [theta, 0, v[1]], [0, 0, 0]])
T = SE2.exp(logT)
T_true = spl.expm(logT)
np.testing.assert_allclose(T_true, T.arr)
def testGroupOperator(self):
for i in range(100):
t1 = np.random.uniform(-10, 10, size=2)
theta1 = np.random.uniform(-np.pi, np.pi)
t2 = np.random.uniform(-10, 10, size=2)
theta2 = np.random.uniform(-np.pi, np.pi)
ct1 = np.cos(theta1)
ct2 = np.cos(theta2)
st1 = np.sin(theta1)
st2 = np.sin(theta2)
R1 = np.array([[ct1, -st1], [st1, ct1]])
R2 = np.array([[ct2, -st2], [st2, ct2]])
T1 = SE2.fromRandt(R1, t1)
T2 = SE2.fromRandt(R2, t2)
T = T1 * T2
R_true = R1 @ R2
t_true = R1 @ t2 + t1
T_true = SE2.fromRandt(R_true, t_true)
np.testing.assert_allclose(T_true.arr, T.arr)
def testActionOnVector(self):
for i in range(100):
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
T = SE2.fromAngleAndt(theta, t)
vec = np.random.uniform(-5, 5, size=2)
pt = T.transa(vec)
pt_true = T.R @ vec + T.t
np.testing.assert_allclose(pt_true, pt)
for i in range(100):
T = SE2.random()
vec = np.random.uniform(-5, 5, size=2)
pt = T.transp(vec)
pt_true = T.R.T @ vec - T.R.T @ T.t
np.testing.assert_allclose(pt_true, pt)
def testFromAngle(self):
for i in range(100):
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
T = SE2.fromAngleAndt(theta, t)
ct = np.cos(theta)
st = np.sin(theta)
R = np.array([[ct, -st], [st, ct]])
T_true = np.eye(3)
T_true[:2, :2] = R
T_true[:2, 2] = t
np.testing.assert_allclose(T_true, T.arr)
def testInv(self):
for i in range(100):
t = np.random.uniform(-10, 10, size=2)
theta = np.random.uniform(-np.pi, np.pi)
ct = np.cos(theta)
st = np.sin(theta)
R = np.array([[ct, -st], [st, ct]])
T = SE2.fromRandt(R, t)
T_inv = T.inv()
T_inv_true = np.eye(3)
T_inv_true[:2, :2] = R.T
T_inv_true[:2, 2] = -R.T @ t
np.testing.assert_allclose(T_inv_true, T_inv.arr)
def test_right_jacobian_of_logarithm(self):
T = SE2.random()
tau, Jr_inv = SE2.Log(T, Jr=np.eye(3))
_, Jr = SE2.Exp(tau, Jr=np.eye(3))
np.testing.assert_allclose(np.linalg.inv(Jr), Jr_inv)
def test_left_jacobian_or_logarithm(self):
T = SE2.random()
tau, Jl_inv = SE2.Log(T, Jl=np.eye(3))
_, Jl = SE2.Exp(tau, Jl=np.eye(3))
np.testing.assert_allclose(np.linalg.inv(Jl), Jl_inv)
