def test_wedge_vee():
xi = [1, 2, 3]
Xi = SE2.wedge(xi)
xis = np.array([[1, 2, 3], [4, 5, 6]])
Xis = SE2.wedge(xis)
assert np.array_equal(xi, SE2.vee(Xi))
assert np.array_equal(xis, SE2.vee(Xis))
def test_left_jacobian():
xi1 = [1, 2, 3]
assert np.allclose(
SE2.left_jacobian(xi1).dot(SE2.inv_left_jacobian(xi1)), np.identity(3))
xi2 = [0, 0, 0]
assert np.allclose(
SE2.left_jacobian(xi2).dot(SE2.inv_left_jacobian(xi2)), np.identity(3))
def test_odot_vectorized():
p1 = [1, 2]
p2 = [2, 3]
ps = np.array([p1, p2])
odot1 = SE2.odot(p1)
odot2 = SE2.odot(p2)
odots = SE2.odot(ps)
assert np.array_equal(odot1, odots[0, :, :])
assert np.array_equal(odot2, odots[1, :, :])
def test_odot():
p1 = [1, 2]
p2 = [1, 2, 1]
p3 = [1, 2, 0]
odot12 = np.vstack([SE2.odot(p1), np.zeros([1, 3])])
odot13 = np.vstack([SE2.odot(p1, directional=True), np.zeros([1, 3])])
odot2 = SE2.odot(p2)
odot3 = SE2.odot(p3)
assert np.array_equal(odot12, odot2)
assert np.array_equal(odot13, odot3)
def test_transform_vectorized():
T = SE2.exp([1, 2, 3])
pt1 = np.array([1, 2])
pt2 = np.array([4, 5])
pt3 = np.array([1, 2, 1])
pt4 = np.array([4, 5, 1])
pts12 = np.array([pt1, pt2]) # 2x2
pts34 = np.array([pt3, pt4]) # 2x3
Tpt1 = T.dot(pt1)
Tpt2 = T.dot(pt2)
Tpt3 = T.dot(pt3)
Tpt4 = T.dot(pt4)
Tpts12 = T.dot(pts12)
Tpts34 = T.dot(pts34)
assert np.allclose(Tpt1, Tpts12[0])
assert np.allclose(Tpt2, Tpts12[1])
assert np.allclose(Tpt3, Tpts34[0])
assert np.allclose(Tpt4, Tpts34[1])
def test_adjoint():
T = SE2.exp([1, 2, 3])
assert T.adjoint().shape == (3, 3)
def test_inv():
T = SE2.exp([1, 2, 3])
assert np.allclose((T.dot(T.inv())).as_matrix(), np.identity(3))
def test_identity():
T = SE2.identity()
assert isinstance(T, SE2)
def test_normalize():
T = SE2.exp([1, 2, 3])
T.rot.mat += 0.1
T.normalize()
assert SE2.is_valid_matrix(T.as_matrix())
def test_perturb():
T = SE2.exp([1, 2, 3])
T_copy = copy.deepcopy(T)
xi = [0.3, 0.2, 0.1]
T.perturb(xi)
assert np.allclose(T.as_matrix(), (SE2.exp(xi).dot(T_copy)).as_matrix())
def test_exp_log():
T = SE2.exp([1, 2, 3])
assert np.allclose(SE2.exp(SE2.log(T)).as_matrix(), T.as_matrix())
def test_dot():
T = np.array([[0, -1, -0.5], [1, 0, 0.5], [0, 0, 1]])
T2 = T.dot(T)
assert np.allclose(
(SE2.from_matrix(T).dot(SE2.from_matrix(T))).as_matrix(), T2)