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import copy |
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import torch |
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import numpy as np |
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from liegroups.torch import SO2, utils |
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def test_from_matrix(): |
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C_good = SO2.from_matrix(torch.eye(2)) |
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assert isinstance(C_good, SO2) \ |
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and C_good.mat.dim() == 2 \ |
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and C_good.mat.shape == (2, 2) \ |
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and SO2.is_valid_matrix(C_good.mat).all() |
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C_bad = SO2.from_matrix(torch.eye(2).add_(1e-3), normalize=True) |
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assert isinstance(C_bad, SO2) \ |
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and C_bad.mat.dim() == 2 \ |
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and C_bad.mat.shape == (2, 2) \ |
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and SO2.is_valid_matrix(C_bad.mat).all() |
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def test_from_matrix_batch(): |
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C_good = SO2.from_matrix(torch.eye(2).repeat(5, 1, 1)) |
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assert isinstance(C_good, SO2) \ |
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and C_good.mat.dim() == 3 \ |
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and C_good.mat.shape == (5, 2, 2) \ |
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and SO2.is_valid_matrix(C_good.mat).all() |
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C_bad = copy.deepcopy(C_good.mat) |
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C_bad[3].add_(0.1) |
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C_bad = SO2.from_matrix(C_bad, normalize=True) |
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assert isinstance(C_bad, SO2) \ |
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and C_bad.mat.dim() == 3 \ |
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and C_bad.mat.shape == (5, 2, 2) \ |
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and SO2.is_valid_matrix(C_bad.mat).all() |
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def test_identity(): |
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C = SO2.identity() |
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assert isinstance(C, SO2) \ |
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and C.mat.dim() == 2 \ |
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and C.mat.shape == (2, 2) |
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def test_identity_batch(): |
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C = SO2.identity(5) |
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assert isinstance(C, SO2) \ |
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and C.mat.dim() == 3 \ |
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and C.mat.shape == (5, 2, 2) |
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C_copy = SO2.identity(5, copy=True) |
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assert isinstance(C_copy, SO2) \ |
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and C_copy.mat.dim() == 3 \ |
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and C_copy.mat.shape == (5, 2, 2) |
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def test_from_angle_to_angle(): |
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angle = torch.Tensor([np.pi / 2.]) |
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assert utils.allclose(SO2.from_angle(angle).to_angle(), angle) |
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def test_from_angle_to_angle_batch(): |
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angles = torch.Tensor([-1., 0, 1.]) |
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assert utils.allclose(SO2.from_angle(angles).to_angle(), angles) |
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def test_dot(): |
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C = SO2(torch.Tensor([[0, -1], |
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[1, 0]])) |
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pt = torch.Tensor([1, 2]) |
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CC = C.mat.mm(C.mat) |
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assert utils.allclose(C.dot(C).mat, CC) |
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Cpt = C.mat.matmul(pt) |
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assert utils.allclose(C.dot(pt), Cpt) |
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def test_dot_batch(): |
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C1 = SO2(torch.Tensor([[0, -1], |
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[1, 0]]).expand(5, 2, 2)) |
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C2 = SO2(torch.Tensor([[-1, 0], |
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[0, -1]])) |
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pt1 = torch.Tensor([1, 2]) |
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pt2 = torch.Tensor([4, 5]) |
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pt3 = torch.Tensor([7, 8]) |
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pts = torch.cat([pt1.unsqueeze(dim=0), |
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pt2.unsqueeze(dim=0), |
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pt3.unsqueeze(dim=0)], dim=0) |
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ptsbatch = pts.unsqueeze(dim=0).expand(5, 3, 2) |
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C1C1 = torch.bmm(C1.mat, C1.mat) |
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C1C1_SO2 = C1.dot(C1).mat |
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assert C1C1_SO2.shape == C1.mat.shape and utils.allclose(C1C1_SO2, C1C1) |
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C1C2 = torch.matmul(C1.mat, C2.mat) |
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C1C2_SO2 = C1.dot(C2).mat |
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assert C1C2_SO2.shape == C1.mat.shape and utils.allclose(C1C2_SO2, C1C2) |
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C1pt1 = torch.matmul(C1.mat, pt1) |
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C1pt1_SO2 = C1.dot(pt1) |
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assert C1pt1_SO2.shape == (C1.mat.shape[0], pt1.shape[0]) \ |
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and utils.allclose(C1pt1_SO2, C1pt1) |
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C1pt2 = torch.matmul(C1.mat, pt2) |
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C1pt2_SO2 = C1.dot(pt2) |
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assert C1pt2_SO2.shape == (C1.mat.shape[0], pt2.shape[0]) \ |
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and utils.allclose(C1pt2_SO2, C1pt2) |
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C1pts = torch.matmul(C1.mat, pts.transpose(1, 0)).transpose(2, 1) |
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C1pts_SO2 = C1.dot(pts) |
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assert C1pts_SO2.shape == (C1.mat.shape[0], pts.shape[0], pts.shape[1]) \ |
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and utils.allclose(C1pts_SO2, C1pts) \ |
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and utils.allclose(C1pt1, C1pts[:, 0, :]) \ |
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and utils.allclose(C1pt2, C1pts[:, 1, :]) |
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C1ptsbatch = torch.bmm(C1.mat, ptsbatch.transpose(2, 1)).transpose(2, 1) |
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C1ptsbatch_SO2 = C1.dot(ptsbatch) |
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assert C1ptsbatch_SO2.shape == ptsbatch.shape \ |
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and utils.allclose(C1ptsbatch_SO2, C1ptsbatch) \ |
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and utils.allclose(C1pt1, C1ptsbatch[:, 0, :]) \ |
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and utils.allclose(C1pt2, C1ptsbatch[:, 1, :]) |
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C2ptsbatch = torch.matmul(C2.mat, ptsbatch.transpose(2, 1)).transpose(2, 1) |
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C2ptsbatch_SO2 = C2.dot(ptsbatch) |
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assert C2ptsbatch_SO2.shape == ptsbatch.shape \ |
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and utils.allclose(C2ptsbatch_SO2, C2ptsbatch) \ |
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and utils.allclose(C2.dot(pt1), C2ptsbatch[:, 0, :]) \ |
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and utils.allclose(C2.dot(pt2), C2ptsbatch[:, 1, :]) |
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def test_wedge(): |
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phi = torch.Tensor([1]) |
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Phi = SO2.wedge(phi) |
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assert (Phi == -Phi.t()).all() |
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def test_wedge_batch(): |
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phis = torch.Tensor([1, 2]) |
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Phis = SO2.wedge(phis) |
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assert (Phis[0, :, :] == SO2.wedge(torch.Tensor([phis[0]]))).all() |
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assert (Phis[1, :, :] == SO2.wedge(torch.Tensor([phis[1]]))).all() |
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def test_wedge_vee(): |
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phi = torch.Tensor([1]) |
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Phi = SO2.wedge(phi) |
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assert (phi == SO2.vee(Phi)).all() |
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def test_wedge_vee_batch(): |
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phis = torch.Tensor([1, 2]) |
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Phis = SO2.wedge(phis) |
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assert (phis == SO2.vee(Phis)).all() |
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def test_left_jacobians(): |
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phi_small = torch.Tensor([0.]) |
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phi_big = torch.Tensor([np.pi / 2]) |
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left_jacobian_small = SO2.left_jacobian(phi_small) |
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inv_left_jacobian_small = SO2.inv_left_jacobian(phi_small) |
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assert utils.allclose( |
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torch.mm(left_jacobian_small, inv_left_jacobian_small), |
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torch.eye(2)) |
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left_jacobian_big = SO2.left_jacobian(phi_big) |
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inv_left_jacobian_big = SO2.inv_left_jacobian(phi_big) |
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assert utils.allclose( |
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torch.mm(left_jacobian_big, inv_left_jacobian_big), |
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torch.eye(2)) |
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def test_left_jacobians_batch(): |
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phis = torch.Tensor([0., np.pi / 2]) |
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left_jacobian = SO2.left_jacobian(phis) |
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inv_left_jacobian = SO2.inv_left_jacobian(phis) |
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assert utils.allclose(torch.bmm(left_jacobian, inv_left_jacobian), |
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torch.eye(2).unsqueeze_(dim=0).expand(2, 2, 2)) |
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def test_exp_log(): |
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C_big = SO2.exp(torch.Tensor([np.pi / 4])) |
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assert utils.allclose(SO2.exp(SO2.log(C_big)).mat, C_big.mat) |
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C_small = SO2.exp(torch.Tensor([0])) |
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assert utils.allclose(SO2.exp(SO2.log(C_small)).mat, C_small.mat) |
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def test_exp_log_batch(): |
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C = SO2.exp(torch.Tensor([-1., 0., 1.])) |
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assert utils.allclose(SO2.exp(SO2.log(C)).mat, C.mat) |
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def test_perturb(): |
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C = SO2.exp(torch.Tensor([np.pi / 4])) |
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C_copy = copy.deepcopy(C) |
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phi = torch.Tensor([0.1]) |
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C.perturb(phi) |
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assert utils.allclose( |
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C.as_matrix(), (SO2.exp(phi).dot(C_copy)).as_matrix()) |
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def test_perturb_batch(): |
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C = SO2.exp(torch.Tensor([-1., 0., 1.])) |
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C_copy1 = copy.deepcopy(C) |
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C_copy2 = copy.deepcopy(C) |
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phi = torch.Tensor([0.1]) |
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C_copy1.perturb(phi) |
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assert utils.allclose(C_copy1.as_matrix(), |
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(SO2.exp(phi).dot(C)).as_matrix()) |
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phis = torch.Tensor([0.1, 0.2, 0.3]) |
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C_copy2.perturb(phis) |
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assert utils.allclose(C_copy2.as_matrix(), |
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(SO2.exp(phis).dot(C)).as_matrix()) |
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def test_normalize(): |
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C = SO2.exp(torch.Tensor([np.pi / 4])) |
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C.mat.add_(0.1) |
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C.normalize() |
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assert SO2.is_valid_matrix(C.mat).all() |
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def test_normalize_batch(): |
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C = SO2.exp(torch.Tensor([-1., 0., 1.])) |
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assert SO2.is_valid_matrix(C.mat).all() |
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C.mat.add_(0.1) |
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assert (SO2.is_valid_matrix(C.mat) == torch.ByteTensor([0, 0, 0])).all() |
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C.normalize(inds=[0, 2]) |
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assert (SO2.is_valid_matrix(C.mat) == torch.ByteTensor([1, 0, 1])).all() |
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C.normalize() |
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assert SO2.is_valid_matrix(C.mat).all() |
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def test_inv(): |
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C = SO2.exp(torch.Tensor([np.pi / 4])) |
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assert utils.allclose(C.dot(C.inv()).mat, SO2.identity().mat) |
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def test_inv_batch(): |
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C = SO2.exp(torch.Tensor([-1., 0., 1.])) |
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assert utils.allclose(C.dot(C.inv()).mat, SO2.identity(C.mat.shape[0]).mat) |
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def test_adjoint(): |
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C = SO2.exp(torch.Tensor([np.pi / 4])) |
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assert (C.adjoint() == torch.Tensor([1.])).all() |
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def test_adjoint_batch(): |
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C = SO2.exp(torch.Tensor([-1., 0., 1.])) |
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assert (C.adjoint() == torch.ones(C.mat.shape[0])).all() |
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