|
import copy |
|
|
|
import torch |
|
|
|
from liegroups.torch import SE2, SO2, utils |
|
|
|
|
|
def test_from_matrix(): |
|
T_good = SE2.from_matrix(torch.eye(3)) |
|
assert isinstance(T_good, SE2) \ |
|
and isinstance(T_good.rot, SO2) \ |
|
and T_good.trans.shape == (2,) \ |
|
and SE2.is_valid_matrix(T_good.as_matrix()).all() |
|
|
|
T_bad = SE2.from_matrix(torch.eye(3).add_(1e-3), normalize=True) |
|
assert isinstance(T_bad, SE2) \ |
|
and isinstance(T_bad.rot, SO2) \ |
|
and T_bad.trans.shape == (2,) \ |
|
and SE2.is_valid_matrix(T_bad.as_matrix()).all() |
|
|
|
|
|
def test_from_matrix_batch(): |
|
T_good = SE2.from_matrix(torch.eye(3).repeat(5, 1, 1)) |
|
assert isinstance(T_good, SE2) \ |
|
and T_good.trans.shape == (5, 2) \ |
|
and SE2.is_valid_matrix(T_good.as_matrix()).all() |
|
|
|
T_bad = T_good.as_matrix() |
|
T_bad[3, :, :].add_(0.1) |
|
T_bad = SE2.from_matrix(T_bad, normalize=True) |
|
assert isinstance(T_bad, SE2) \ |
|
and T_bad.trans.shape == (5, 2) \ |
|
and SE2.is_valid_matrix(T_bad.as_matrix()).all() |
|
|
|
|
|
def test_identity(): |
|
T = SE2.identity() |
|
assert isinstance(T, SE2) \ |
|
and isinstance(T.rot, SO2) \ |
|
and T.rot.mat.dim() == 2 \ |
|
and T.trans.shape == (2,) |
|
|
|
|
|
def test_identity_batch(): |
|
T = SE2.identity(5) |
|
assert isinstance(T, SE2) \ |
|
and isinstance(T.rot, SO2) \ |
|
and T.rot.mat.dim() == 3 \ |
|
and T.trans.shape == (5, 2) |
|
|
|
|
|
def test_dot(): |
|
T = torch.Tensor([[0, -1, -0.5], |
|
[1, 0, 0.5], |
|
[0, 0, 1]]) |
|
T_SE2 = SE2.from_matrix(T) |
|
pt = torch.Tensor([1, 2]) |
|
pth = torch.Tensor([1, 2, 1]) |
|
|
|
TT = torch.mm(T, T) |
|
TT_SE2 = T_SE2.dot(T_SE2).as_matrix() |
|
assert utils.allclose(TT_SE2, TT) |
|
|
|
Tpt = torch.matmul(T[0:2, 0:2], pt) + T[0:2, 2] |
|
Tpt_SE2 = T_SE2.dot(pt) |
|
assert utils.allclose(Tpt_SE2, Tpt) |
|
|
|
Tpth = torch.matmul(T, pth) |
|
Tpth_SE2 = T_SE2.dot(pth) |
|
assert utils.allclose(Tpth_SE2, Tpth) and \ |
|
utils.allclose(Tpth_SE2[0:2], Tpt) |
|
|
|
|
|
def test_dot_batch(): |
|
T1 = torch.Tensor([[0, -1, -0.5], |
|
[1, 0, 0.5], |
|
[0, 0, 1]]).expand(5, 3, 3) |
|
T2 = torch.Tensor([[0, -1, -0.5], |
|
[1, 0, 0.5], |
|
[0, 0, 1]]) |
|
T1_SE2 = SE2.from_matrix(T1) |
|
T2_SE2 = SE2.from_matrix(T2) |
|
pt1 = torch.Tensor([1, 2]) |
|
pt2 = torch.Tensor([4, 5]) |
|
pt3 = torch.Tensor([7, 8]) |
|
pts = torch.cat([pt1.unsqueeze(dim=0), |
|
pt2.unsqueeze(dim=0), |
|
pt3.unsqueeze(dim=0)], dim=0) |
|
ptsbatch = pts.unsqueeze(dim=0).expand(5, 3, 2) |
|
pt1h = torch.Tensor([1, 2, 1]) |
|
pt2h = torch.Tensor([4, 5, 1]) |
|
pt3h = torch.Tensor([7, 8, 1]) |
|
ptsh = torch.cat([pt1h.unsqueeze(dim=0), |
|
pt2h.unsqueeze(dim=0), |
|
pt3h.unsqueeze(dim=0)], dim=0) |
|
ptshbatch = ptsh.unsqueeze(dim=0).expand(5, 3, 3) |
|
|
|
T1T1 = torch.bmm(T1, T1) |
|
T1T1_SE2 = T1_SE2.dot(T1_SE2).as_matrix() |
|
assert T1T1_SE2.shape == T1.shape and utils.allclose(T1T1_SE2, T1T1) |
|
|
|
T1T2 = torch.matmul(T1, T2) |
|
T1T2_SE2 = T1_SE2.dot(T2_SE2).as_matrix() |
|
assert T1T2_SE2.shape == T1.shape and utils.allclose(T1T2_SE2, T1T2) |
|
|
|
T1pt1 = torch.matmul(T1[:, 0:2, 0:2], pt1) + T1[:, 0:2, 2] |
|
T1pt1_SE2 = T1_SE2.dot(pt1) |
|
assert T1pt1_SE2.shape == (T1.shape[0], pt1.shape[0]) \ |
|
and utils.allclose(T1pt1_SE2, T1pt1) |
|
|
|
T1pt1h = torch.matmul(T1, pt1h) |
|
T1pt1h_SE2 = T1_SE2.dot(pt1h) |
|
assert T1pt1h_SE2.shape == (T1.shape[0], pt1h.shape[0]) \ |
|
and utils.allclose(T1pt1h_SE2, T1pt1h) \ |
|
and utils.allclose(T1pt1h_SE2[:, 0:2], T1pt1_SE2) |
|
|
|
T1pt2 = torch.matmul(T1[:, 0:2, 0:2], pt2) + T1[:, 0:2, 2] |
|
T1pt2_SE2 = T1_SE2.dot(pt2) |
|
assert T1pt2_SE2.shape == (T1.shape[0], pt2.shape[0]) \ |
|
and utils.allclose(T1pt2_SE2, T1pt2) |
|
|
|
T1pt2h = torch.matmul(T1, pt2h) |
|
T1pt2h_SE2 = T1_SE2.dot(pt2h) |
|
assert T1pt2h_SE2.shape == (T1.shape[0], pt2h.shape[0]) \ |
|
and utils.allclose(T1pt2h_SE2, T1pt2h) \ |
|
and utils.allclose(T1pt2h_SE2[:, 0:2], T1pt2_SE2) |
|
|
|
T1pts = torch.bmm(T1[:, 0:2, 0:2], |
|
pts.unsqueeze(dim=0).expand( |
|
T1.shape[0], |
|
pts.shape[0], |
|
pts.shape[1]).transpose(2, 1)).transpose(2, 1) + \ |
|
T1[:, 0:2, 2].unsqueeze(dim=1).expand( |
|
T1.shape[0], pts.shape[0], pts.shape[1]) |
|
T1pts_SE2 = T1_SE2.dot(pts) |
|
assert T1pts_SE2.shape == (T1.shape[0], pts.shape[0], pts.shape[1]) \ |
|
and utils.allclose(T1pts_SE2, T1pts) \ |
|
and utils.allclose(T1pt1, T1pts[:, 0, :]) \ |
|
and utils.allclose(T1pt2, T1pts[:, 1, :]) |
|
|
|
T1ptsh = torch.bmm(T1, ptsh.unsqueeze(dim=0).expand( |
|
T1.shape[0], |
|
ptsh.shape[0], |
|
ptsh.shape[1]).transpose(2, 1)).transpose(2, 1) |
|
T1ptsh_SE2 = T1_SE2.dot(ptsh) |
|
assert T1ptsh_SE2.shape == (T1.shape[0], ptsh.shape[0], ptsh.shape[1]) \ |
|
and utils.allclose(T1ptsh_SE2, T1ptsh) \ |
|
and utils.allclose(T1pt1h, T1ptsh[:, 0, :]) \ |
|
and utils.allclose(T1pt2h, T1ptsh[:, 1, :]) \ |
|
and utils.allclose(T1ptsh_SE2[:, :, 0:2], T1pts_SE2) |
|
|
|
T1ptsbatch = torch.bmm(T1[:, 0:2, 0:2], |
|
ptsbatch.transpose(2, 1)).transpose(2, 1) + \ |
|
T1[:, 0:2, 2].unsqueeze(dim=1).expand(ptsbatch.shape) |
|
T1ptsbatch_SE2 = T1_SE2.dot(ptsbatch) |
|
assert T1ptsbatch_SE2.shape == ptsbatch.shape \ |
|
and utils.allclose(T1ptsbatch_SE2, T1ptsbatch) \ |
|
and utils.allclose(T1pt1, T1ptsbatch[:, 0, :]) \ |
|
and utils.allclose(T1pt2, T1ptsbatch[:, 1, :]) |
|
|
|
T1ptshbatch = torch.bmm(T1, ptshbatch.transpose(2, 1)).transpose(2, 1) |
|
T1ptshbatch_SE2 = T1_SE2.dot(ptshbatch) |
|
assert T1ptshbatch_SE2.shape == ptshbatch.shape \ |
|
and utils.allclose(T1ptshbatch_SE2, T1ptshbatch) \ |
|
and utils.allclose(T1pt1h, T1ptshbatch[:, 0, :]) \ |
|
and utils.allclose(T1pt2h, T1ptshbatch[:, 1, :]) \ |
|
and utils.allclose(T1ptshbatch_SE2[:, :, 0:2], T1ptsbatch_SE2) |
|
|
|
T2ptsbatch = torch.matmul(T2[0:2, 0:2], |
|
ptsbatch.transpose(2, 1)).transpose(2, 1) + \ |
|
T1[:, 0:2, 2].unsqueeze(dim=1).expand(ptsbatch.shape) |
|
T2ptsbatch_SE2 = T2_SE2.dot(ptsbatch) |
|
assert T2ptsbatch_SE2.shape == ptsbatch.shape \ |
|
and utils.allclose(T2ptsbatch_SE2, T2ptsbatch) \ |
|
and utils.allclose(T2_SE2.dot(pt1), T2ptsbatch[:, 0, :]) \ |
|
and utils.allclose(T2_SE2.dot(pt2), T2ptsbatch[:, 1, :]) |
|
|
|
T2ptshbatch = torch.matmul(T2, ptshbatch.transpose(2, 1)).transpose(2, 1) |
|
T2ptshbatch_SE2 = T2_SE2.dot(ptshbatch) |
|
assert T2ptshbatch_SE2.shape == ptshbatch.shape \ |
|
and utils.allclose(T2ptshbatch_SE2, T2ptshbatch) \ |
|
and utils.allclose(T2_SE2.dot(pt1h), T2ptshbatch[:, 0, :]) \ |
|
and utils.allclose(T2_SE2.dot(pt2h), T2ptshbatch[:, 1, :]) \ |
|
and utils.allclose(T2ptshbatch_SE2[:, :, 0:2], T2ptsbatch_SE2) |
|
|
|
|
|
def test_wedge_vee(): |
|
xi = torch.Tensor([1, 2, 3]) |
|
Xi = SE2.wedge(xi) |
|
assert (xi == SE2.vee(Xi)).all() |
|
|
|
|
|
def test_wedge_vee_batch(): |
|
xis = torch.Tensor([[1, 2, 3], [4, 5, 6]]) |
|
Xis = SE2.wedge(xis) |
|
assert (xis == SE2.vee(Xis)).all() |
|
|
|
|
|
def test_odot(): |
|
p1 = torch.Tensor([1, 2]) |
|
p2 = torch.Tensor([1, 2, 1]) |
|
p3 = torch.Tensor([1, 2, 0]) |
|
|
|
odot12 = torch.cat([SE2.odot(p1), torch.zeros(3).unsqueeze_(dim=0)], dim=0) |
|
odot13 = torch.cat([SE2.odot(p1, directional=True), |
|
torch.zeros(3).unsqueeze_(dim=0)], dim=0) |
|
odot2 = SE2.odot(p2) |
|
odot3 = SE2.odot(p3) |
|
|
|
assert (odot12 == odot2).all() |
|
assert (odot13 == odot3).all() |
|
|
|
|
|
def test_odot_batch(): |
|
p1 = torch.Tensor([1, 2]) |
|
p2 = torch.Tensor([2, 3]) |
|
ps = torch.cat([p1.unsqueeze(dim=0), |
|
p2.unsqueeze(dim=0)], dim=0) |
|
|
|
odot1 = SE2.odot(p1) |
|
odot2 = SE2.odot(p2) |
|
odots = SE2.odot(ps) |
|
|
|
assert (odot1 == odots[0, :, :]).all() |
|
assert (odot2 == odots[1, :, :]).all() |
|
|
|
|
|
def test_exp_log(): |
|
T = SE2.exp(torch.Tensor([1, 2, 3])) |
|
assert utils.allclose(SE2.exp(SE2.log(T)).as_matrix(), T.as_matrix()) |
|
|
|
|
|
def test_exp_log_batch(): |
|
T = SE2.exp(0.1 * torch.Tensor([[1, 2, 3], |
|
[4, 5, 6]])) |
|
assert utils.allclose(SE2.exp(SE2.log(T)).as_matrix(), T.as_matrix()) |
|
|
|
|
|
def test_perturb(): |
|
T = SE2.exp(torch.Tensor([1, 2, 3])) |
|
T_copy = copy.deepcopy(T) |
|
xi = torch.Tensor([0.3, 0.2, 0.1]) |
|
T.perturb(xi) |
|
assert utils.allclose(T.as_matrix(), (SE2.exp(xi).dot(T_copy)).as_matrix()) |
|
|
|
|
|
def test_perturb_batch(): |
|
T = SE2.exp(0.1 * torch.Tensor([[1, 2, 3], |
|
[4, 5, 6]])) |
|
T_copy1 = copy.deepcopy(T) |
|
T_copy2 = copy.deepcopy(T) |
|
|
|
xi = torch.Tensor([0.3, 0.2, 0.1]) |
|
T_copy1.perturb(xi) |
|
assert utils.allclose(T_copy1.as_matrix(), |
|
(SE2.exp(xi).dot(T)).as_matrix()) |
|
|
|
xis = torch.Tensor([[0.3, 0.2, 0.1], |
|
[-0.1, -0.2, -0.3]]) |
|
T_copy2.perturb(xis) |
|
assert utils.allclose(T_copy2.as_matrix(), |
|
(SE2.exp(xis).dot(T)).as_matrix()) |
|
|
|
|
|
def test_normalize(): |
|
T = SE2.exp(torch.Tensor([1, 2, 3])) |
|
T.rot.mat.add_(0.1) |
|
T.normalize() |
|
assert SE2.is_valid_matrix(T.as_matrix()).all() |
|
|
|
|
|
def test_normalize_batch(): |
|
T = SE2.exp(0.1 * torch.Tensor([[1, 2, 3], |
|
[4, 5, 6], |
|
[7, 8, 9]])) |
|
assert SE2.is_valid_matrix(T.as_matrix()).all() |
|
|
|
T.rot.mat.add_(0.1) |
|
assert (SE2.is_valid_matrix(T.as_matrix()) |
|
== torch.ByteTensor([0, 0, 0])).all() |
|
|
|
T.normalize(inds=[0, 2]) |
|
assert (SE2.is_valid_matrix(T.as_matrix()) |
|
== torch.ByteTensor([1, 0, 1])).all() |
|
|
|
T.normalize() |
|
assert SE2.is_valid_matrix(T.as_matrix()).all() |
|
|
|
|
|
def test_inv(): |
|
T = SE2.exp(torch.Tensor([1, 2, 3])) |
|
assert utils.allclose((T.dot(T.inv())).as_matrix(), torch.eye(3)) |
|
|
|
|
|
def test_inv_batch(): |
|
T = SE2.exp(0.1 * torch.Tensor([[1, 2, 3], |
|
[4, 5, 6], |
|
[7, 8, 9]])) |
|
assert utils.allclose(T.dot(T.inv()).as_matrix(), |
|
SE2.identity(T.trans.shape[0]).as_matrix()) |
|
|
|
|
|
def test_adjoint(): |
|
T = SE2.exp(torch.Tensor([1, 2, 3])) |
|
assert T.adjoint().shape == (3, 3) |
|
|
|
|
|
def test_adjoint_batch(): |
|
T = SE2.exp(0.1 * torch.Tensor([[1, 2, 3], |
|
[4, 5, 6]])) |
|
assert T.adjoint().shape == (2, 3, 3) |
|
|
