import pytest import numpy as np from numpy.testing import assert_equal, assert_array_almost_equal from numpy.testing import assert_allclose from scipy.spatial.transform import Rotation, Slerp from scipy.stats import special_ortho_group from itertools import permutations import pickle import copy def test_generic_quat_matrix(): x = np.array([[3, 4, 0, 0], [5, 12, 0, 0]]) r = Rotation.from_quat(x) expected_quat = x / np.array([[5], [13]]) assert_array_almost_equal(r.as_quat(), expected_quat) def test_from_single_1d_quaternion(): x = np.array([3, 4, 0, 0]) r = Rotation.from_quat(x) expected_quat = x / 5 assert_array_almost_equal(r.as_quat(), expected_quat) def test_from_single_2d_quaternion(): x = np.array([[3, 4, 0, 0]]) r = Rotation.from_quat(x) expected_quat = x / 5 assert_array_almost_equal(r.as_quat(), expected_quat) def test_from_square_quat_matrix(): # Ensure proper norm array broadcasting x = np.array([ [3, 0, 0, 4], [5, 0, 12, 0], [0, 0, 0, 1], [0, 0, 0, -1] ]) r = Rotation.from_quat(x) expected_quat = x / np.array([[5], [13], [1], [1]]) assert_array_almost_equal(r.as_quat(), expected_quat) def test_malformed_1d_from_quat(): with pytest.raises(ValueError): Rotation.from_quat(np.array([1, 2, 3])) def test_malformed_2d_from_quat(): with pytest.raises(ValueError): Rotation.from_quat(np.array([ [1, 2, 3, 4, 5], [4, 5, 6, 7, 8] ])) def test_zero_norms_from_quat(): x = np.array([ [3, 4, 0, 0], [0, 0, 0, 0], [5, 0, 12, 0] ]) with pytest.raises(ValueError): Rotation.from_quat(x) def test_as_matrix_single_1d_quaternion(): quat = [0, 0, 0, 1] mat = Rotation.from_quat(quat).as_matrix() # mat.shape == (3,3) due to 1d input assert_array_almost_equal(mat, np.eye(3)) def test_as_matrix_single_2d_quaternion(): quat = [[0, 0, 1, 1]] mat = Rotation.from_quat(quat).as_matrix() assert_equal(mat.shape, (1, 3, 3)) expected_mat = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) assert_array_almost_equal(mat[0], expected_mat) def test_as_matrix_from_square_input(): quats = [ [0, 0, 1, 1], [0, 1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1] ] mat = Rotation.from_quat(quats).as_matrix() assert_equal(mat.shape, (4, 3, 3)) expected0 = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) assert_array_almost_equal(mat[0], expected0) expected1 = np.array([ [0, 0, 1], [0, 1, 0], [-1, 0, 0] ]) assert_array_almost_equal(mat[1], expected1) assert_array_almost_equal(mat[2], np.eye(3)) assert_array_almost_equal(mat[3], np.eye(3)) def test_as_matrix_from_generic_input(): quats = [ [0, 0, 1, 1], [0, 1, 0, 1], [1, 2, 3, 4] ] mat = Rotation.from_quat(quats).as_matrix() assert_equal(mat.shape, (3, 3, 3)) expected0 = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) assert_array_almost_equal(mat[0], expected0) expected1 = np.array([ [0, 0, 1], [0, 1, 0], [-1, 0, 0] ]) assert_array_almost_equal(mat[1], expected1) expected2 = np.array([ [0.4, -2, 2.2], [2.8, 1, 0.4], [-1, 2, 2] ]) / 3 assert_array_almost_equal(mat[2], expected2) def test_from_single_2d_matrix(): mat = [ [0, 0, 1], [1, 0, 0], [0, 1, 0] ] expected_quat = [0.5, 0.5, 0.5, 0.5] assert_array_almost_equal( Rotation.from_matrix(mat).as_quat(), expected_quat) def test_from_single_3d_matrix(): mat = np.array([ [0, 0, 1], [1, 0, 0], [0, 1, 0] ]).reshape((1, 3, 3)) expected_quat = np.array([0.5, 0.5, 0.5, 0.5]).reshape((1, 4)) assert_array_almost_equal( Rotation.from_matrix(mat).as_quat(), expected_quat) def test_from_matrix_calculation(): expected_quat = np.array([1, 1, 6, 1]) / np.sqrt(39) mat = np.array([ [-0.8974359, -0.2564103, 0.3589744], [0.3589744, -0.8974359, 0.2564103], [0.2564103, 0.3589744, 0.8974359] ]) assert_array_almost_equal( Rotation.from_matrix(mat).as_quat(), expected_quat) assert_array_almost_equal( Rotation.from_matrix(mat.reshape((1, 3, 3))).as_quat(), expected_quat.reshape((1, 4))) def test_matrix_calculation_pipeline(): mat = special_ortho_group.rvs(3, size=10, random_state=0) assert_array_almost_equal(Rotation.from_matrix(mat).as_matrix(), mat) def test_from_matrix_ortho_output(): rnd = np.random.RandomState(0) mat = rnd.random_sample((100, 3, 3)) ortho_mat = Rotation.from_matrix(mat).as_matrix() mult_result = np.einsum('...ij,...jk->...ik', ortho_mat, ortho_mat.transpose((0, 2, 1))) eye3d = np.zeros((100, 3, 3)) for i in range(3): eye3d[:, i, i] = 1.0 assert_array_almost_equal(mult_result, eye3d) def test_from_1d_single_rotvec(): rotvec = [1, 0, 0] expected_quat = np.array([0.4794255, 0, 0, 0.8775826]) result = Rotation.from_rotvec(rotvec) assert_array_almost_equal(result.as_quat(), expected_quat) def test_from_2d_single_rotvec(): rotvec = [[1, 0, 0]] expected_quat = np.array([[0.4794255, 0, 0, 0.8775826]]) result = Rotation.from_rotvec(rotvec) assert_array_almost_equal(result.as_quat(), expected_quat) def test_from_generic_rotvec(): rotvec = [ [1, 2, 2], [1, -1, 0.5], [0, 0, 0] ] expected_quat = np.array([ [0.3324983, 0.6649967, 0.6649967, 0.0707372], [0.4544258, -0.4544258, 0.2272129, 0.7316889], [0, 0, 0, 1] ]) assert_array_almost_equal( Rotation.from_rotvec(rotvec).as_quat(), expected_quat) def test_from_rotvec_small_angle(): rotvec = np.array([ [5e-4 / np.sqrt(3), -5e-4 / np.sqrt(3), 5e-4 / np.sqrt(3)], [0.2, 0.3, 0.4], [0, 0, 0] ]) quat = Rotation.from_rotvec(rotvec).as_quat() # cos(theta/2) ~~ 1 for small theta assert_allclose(quat[0, 3], 1) # sin(theta/2) / theta ~~ 0.5 for small theta assert_allclose(quat[0, :3], rotvec[0] * 0.5) assert_allclose(quat[1, 3], 0.9639685) assert_allclose( quat[1, :3], np.array([ 0.09879603932153465, 0.14819405898230198, 0.19759207864306931 ])) assert_equal(quat[2], np.array([0, 0, 0, 1])) def test_degrees_from_rotvec(): rotvec1 = [1.0 / np.cbrt(3), 1.0 / np.cbrt(3), 1.0 / np.cbrt(3)] rot1 = Rotation.from_rotvec(rotvec1, degrees=True) quat1 = rot1.as_quat() rotvec2 = np.deg2rad(rotvec1) rot2 = Rotation.from_rotvec(rotvec2) quat2 = rot2.as_quat() assert_allclose(quat1, quat2) def test_malformed_1d_from_rotvec(): with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'): Rotation.from_rotvec([1, 2]) def test_malformed_2d_from_rotvec(): with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'): Rotation.from_rotvec([ [1, 2, 3, 4], [5, 6, 7, 8] ]) def test_as_generic_rotvec(): quat = np.array([ [1, 2, -1, 0.5], [1, -1, 1, 0.0003], [0, 0, 0, 1] ]) quat /= np.linalg.norm(quat, axis=1)[:, None] rotvec = Rotation.from_quat(quat).as_rotvec() angle = np.linalg.norm(rotvec, axis=1) assert_allclose(quat[:, 3], np.cos(angle/2)) assert_allclose(np.cross(rotvec, quat[:, :3]), np.zeros((3, 3))) def test_as_rotvec_single_1d_input(): quat = np.array([1, 2, -3, 2]) expected_rotvec = np.array([0.5772381, 1.1544763, -1.7317144]) actual_rotvec = Rotation.from_quat(quat).as_rotvec() assert_equal(actual_rotvec.shape, (3,)) assert_allclose(actual_rotvec, expected_rotvec) def test_as_rotvec_single_2d_input(): quat = np.array([[1, 2, -3, 2]]) expected_rotvec = np.array([[0.5772381, 1.1544763, -1.7317144]]) actual_rotvec = Rotation.from_quat(quat).as_rotvec() assert_equal(actual_rotvec.shape, (1, 3)) assert_allclose(actual_rotvec, expected_rotvec) def test_as_rotvec_degrees(): # x->y, y->z, z->x mat = [[0, 0, 1], [1, 0, 0], [0, 1, 0]] rot = Rotation.from_matrix(mat) rotvec = rot.as_rotvec(degrees=True) angle = np.linalg.norm(rotvec) assert_allclose(angle, 120.0) assert_allclose(rotvec[0], rotvec[1]) assert_allclose(rotvec[1], rotvec[2]) def test_rotvec_calc_pipeline(): # Include small angles rotvec = np.array([ [0, 0, 0], [1, -1, 2], [-3e-4, 3.5e-4, 7.5e-5] ]) assert_allclose(Rotation.from_rotvec(rotvec).as_rotvec(), rotvec) assert_allclose(Rotation.from_rotvec(rotvec, degrees=True).as_rotvec(degrees=True), rotvec) def test_from_1d_single_mrp(): mrp = [0, 0, 1.0] expected_quat = np.array([0, 0, 1, 0]) result = Rotation.from_mrp(mrp) assert_array_almost_equal(result.as_quat(), expected_quat) def test_from_2d_single_mrp(): mrp = [[0, 0, 1.0]] expected_quat = np.array([[0, 0, 1, 0]]) result = Rotation.from_mrp(mrp) assert_array_almost_equal(result.as_quat(), expected_quat) def test_from_generic_mrp(): mrp = np.array([ [1, 2, 2], [1, -1, 0.5], [0, 0, 0]]) expected_quat = np.array([ [0.2, 0.4, 0.4, -0.8], [0.61538462, -0.61538462, 0.30769231, -0.38461538], [0, 0, 0, 1]]) assert_array_almost_equal(Rotation.from_mrp(mrp).as_quat(), expected_quat) def test_malformed_1d_from_mrp(): with pytest.raises(ValueError, match='Expected `mrp` to have shape'): Rotation.from_mrp([1, 2]) def test_malformed_2d_from_mrp(): with pytest.raises(ValueError, match='Expected `mrp` to have shape'): Rotation.from_mrp([ [1, 2, 3, 4], [5, 6, 7, 8] ]) def test_as_generic_mrp(): quat = np.array([ [1, 2, -1, 0.5], [1, -1, 1, 0.0003], [0, 0, 0, 1]]) quat /= np.linalg.norm(quat, axis=1)[:, None] expected_mrp = np.array([ [0.33333333, 0.66666667, -0.33333333], [0.57725028, -0.57725028, 0.57725028], [0, 0, 0]]) assert_array_almost_equal(Rotation.from_quat(quat).as_mrp(), expected_mrp) def test_past_180_degree_rotation(): # ensure that a > 180 degree rotation is returned as a <180 rotation in MRPs # in this case 270 should be returned as -90 expected_mrp = np.array([-np.tan(np.pi/2/4), 0.0, 0]) assert_array_almost_equal(Rotation.from_euler('xyz', [270, 0, 0], degrees=True).as_mrp(), expected_mrp) def test_as_mrp_single_1d_input(): quat = np.array([1, 2, -3, 2]) expected_mrp = np.array([0.16018862, 0.32037724, -0.48056586]) actual_mrp = Rotation.from_quat(quat).as_mrp() assert_equal(actual_mrp.shape, (3,)) assert_allclose(actual_mrp, expected_mrp) def test_as_mrp_single_2d_input(): quat = np.array([[1, 2, -3, 2]]) expected_mrp = np.array([[0.16018862, 0.32037724, -0.48056586]]) actual_mrp = Rotation.from_quat(quat).as_mrp() assert_equal(actual_mrp.shape, (1, 3)) assert_allclose(actual_mrp, expected_mrp) def test_mrp_calc_pipeline(): actual_mrp = np.array([ [0, 0, 0], [1, -1, 2], [0.41421356, 0, 0], [0.1, 0.2, 0.1]]) expected_mrp = np.array([ [0, 0, 0], [-0.16666667, 0.16666667, -0.33333333], [0.41421356, 0, 0], [0.1, 0.2, 0.1]]) assert_allclose(Rotation.from_mrp(actual_mrp).as_mrp(), expected_mrp) def test_from_euler_single_rotation(): quat = Rotation.from_euler('z', 90, degrees=True).as_quat() expected_quat = np.array([0, 0, 1, 1]) / np.sqrt(2) assert_allclose(quat, expected_quat) def test_single_intrinsic_extrinsic_rotation(): extrinsic = Rotation.from_euler('z', 90, degrees=True).as_matrix() intrinsic = Rotation.from_euler('Z', 90, degrees=True).as_matrix() assert_allclose(extrinsic, intrinsic) def test_from_euler_rotation_order(): # Intrinsic rotation is same as extrinsic with order reversed rnd = np.random.RandomState(0) a = rnd.randint(low=0, high=180, size=(6, 3)) b = a[:, ::-1] x = Rotation.from_euler('xyz', a, degrees=True).as_quat() y = Rotation.from_euler('ZYX', b, degrees=True).as_quat() assert_allclose(x, y) def test_from_euler_elementary_extrinsic_rotation(): # Simple test to check if extrinsic rotations are implemented correctly mat = Rotation.from_euler('zx', [90, 90], degrees=True).as_matrix() expected_mat = np.array([ [0, -1, 0], [0, 0, -1], [1, 0, 0] ]) assert_array_almost_equal(mat, expected_mat) def test_from_euler_intrinsic_rotation_312(): angles = [ [30, 60, 45], [30, 60, 30], [45, 30, 60] ] mat = Rotation.from_euler('ZXY', angles, degrees=True).as_matrix() assert_array_almost_equal(mat[0], np.array([ [0.3061862, -0.2500000, 0.9185587], [0.8838835, 0.4330127, -0.1767767], [-0.3535534, 0.8660254, 0.3535534] ])) assert_array_almost_equal(mat[1], np.array([ [0.5334936, -0.2500000, 0.8080127], [0.8080127, 0.4330127, -0.3995191], [-0.2500000, 0.8660254, 0.4330127] ])) assert_array_almost_equal(mat[2], np.array([ [0.0473672, -0.6123725, 0.7891491], [0.6597396, 0.6123725, 0.4355958], [-0.7500000, 0.5000000, 0.4330127] ])) def test_from_euler_intrinsic_rotation_313(): angles = [ [30, 60, 45], [30, 60, 30], [45, 30, 60] ] mat = Rotation.from_euler('ZXZ', angles, degrees=True).as_matrix() assert_array_almost_equal(mat[0], np.array([ [0.43559574, -0.78914913, 0.4330127], [0.65973961, -0.04736717, -0.750000], [0.61237244, 0.61237244, 0.500000] ])) assert_array_almost_equal(mat[1], np.array([ [0.6250000, -0.64951905, 0.4330127], [0.64951905, 0.1250000, -0.750000], [0.4330127, 0.750000, 0.500000] ])) assert_array_almost_equal(mat[2], np.array([ [-0.1767767, -0.91855865, 0.35355339], [0.88388348, -0.30618622, -0.35355339], [0.4330127, 0.25000000, 0.8660254] ])) def test_from_euler_extrinsic_rotation_312(): angles = [ [30, 60, 45], [30, 60, 30], [45, 30, 60] ] mat = Rotation.from_euler('zxy', angles, degrees=True).as_matrix() assert_array_almost_equal(mat[0], np.array([ [0.91855865, 0.1767767, 0.35355339], [0.25000000, 0.4330127, -0.8660254], [-0.30618622, 0.88388348, 0.35355339] ])) assert_array_almost_equal(mat[1], np.array([ [0.96650635, -0.0580127, 0.2500000], [0.25000000, 0.4330127, -0.8660254], [-0.0580127, 0.89951905, 0.4330127] ])) assert_array_almost_equal(mat[2], np.array([ [0.65973961, -0.04736717, 0.7500000], [0.61237244, 0.61237244, -0.5000000], [-0.43559574, 0.78914913, 0.4330127] ])) def test_from_euler_extrinsic_rotation_313(): angles = [ [30, 60, 45], [30, 60, 30], [45, 30, 60] ] mat = Rotation.from_euler('zxz', angles, degrees=True).as_matrix() assert_array_almost_equal(mat[0], np.array([ [0.43559574, -0.65973961, 0.61237244], [0.78914913, -0.04736717, -0.61237244], [0.4330127, 0.75000000, 0.500000] ])) assert_array_almost_equal(mat[1], np.array([ [0.62500000, -0.64951905, 0.4330127], [0.64951905, 0.12500000, -0.750000], [0.4330127, 0.75000000, 0.500000] ])) assert_array_almost_equal(mat[2], np.array([ [-0.1767767, -0.88388348, 0.4330127], [0.91855865, -0.30618622, -0.250000], [0.35355339, 0.35355339, 0.8660254] ])) def test_as_euler_asymmetric_axes(): rnd = np.random.RandomState(0) n = 10 angles = np.empty((n, 3)) angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) angles[:, 1] = rnd.uniform(low=-np.pi / 2, high=np.pi / 2, size=(n,)) angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) for seq_tuple in permutations('xyz'): # Extrinsic rotations seq = ''.join(seq_tuple) assert_allclose(angles, Rotation.from_euler(seq, angles).as_euler(seq)) # Intrinsic rotations seq = seq.upper() assert_allclose(angles, Rotation.from_euler(seq, angles).as_euler(seq)) def test_as_euler_symmetric_axes(): rnd = np.random.RandomState(0) n = 10 angles = np.empty((n, 3)) angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,)) angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) for axis1 in ['x', 'y', 'z']: for axis2 in ['x', 'y', 'z']: if axis1 == axis2: continue # Extrinsic rotations seq = axis1 + axis2 + axis1 assert_allclose( angles, Rotation.from_euler(seq, angles).as_euler(seq)) # Intrinsic rotations seq = seq.upper() assert_allclose( angles, Rotation.from_euler(seq, angles).as_euler(seq)) def test_as_euler_degenerate_asymmetric_axes(): # Since we cannot check for angle equality, we check for rotation matrix # equality angles = np.array([ [45, 90, 35], [35, -90, 20], [35, 90, 25], [25, -90, 15] ]) with pytest.warns(UserWarning, match="Gimbal lock"): for seq_tuple in permutations('xyz'): # Extrinsic rotations seq = ''.join(seq_tuple) rotation = Rotation.from_euler(seq, angles, degrees=True) mat_expected = rotation.as_matrix() angle_estimates = rotation.as_euler(seq, degrees=True) mat_estimated = Rotation.from_euler( seq, angle_estimates, degrees=True ).as_matrix() assert_array_almost_equal(mat_expected, mat_estimated) # Intrinsic rotations seq = seq.upper() rotation = Rotation.from_euler(seq, angles, degrees=True) mat_expected = rotation.as_matrix() angle_estimates = rotation.as_euler(seq, degrees=True) mat_estimated = Rotation.from_euler( seq, angle_estimates, degrees=True ).as_matrix() assert_array_almost_equal(mat_expected, mat_estimated) def test_as_euler_degenerate_symmetric_axes(): # Since we cannot check for angle equality, we check for rotation matrix # equality angles = np.array([ [15, 0, 60], [35, 0, 75], [60, 180, 35], [15, -180, 25], ]) with pytest.warns(UserWarning, match="Gimbal lock"): for axis1 in ['x', 'y', 'z']: for axis2 in ['x', 'y', 'z']: if axis1 == axis2: continue # Extrinsic rotations seq = axis1 + axis2 + axis1 rotation = Rotation.from_euler(seq, angles, degrees=True) mat_expected = rotation.as_matrix() angle_estimates = rotation.as_euler(seq, degrees=True) mat_estimated = Rotation.from_euler( seq, angle_estimates, degrees=True ).as_matrix() assert_array_almost_equal(mat_expected, mat_estimated) # Intrinsic rotations seq = seq.upper() rotation = Rotation.from_euler(seq, angles, degrees=True) mat_expected = rotation.as_matrix() angle_estimates = rotation.as_euler(seq, degrees=True) mat_estimated = Rotation.from_euler( seq, angle_estimates, degrees=True ).as_matrix() assert_array_almost_equal(mat_expected, mat_estimated) def test_inv(): rnd = np.random.RandomState(0) n = 10 p = Rotation.from_quat(rnd.normal(size=(n, 4))) q = p.inv() p_mat = p.as_matrix() q_mat = q.as_matrix() result1 = np.einsum('...ij,...jk->...ik', p_mat, q_mat) result2 = np.einsum('...ij,...jk->...ik', q_mat, p_mat) eye3d = np.empty((n, 3, 3)) eye3d[:] = np.eye(3) assert_array_almost_equal(result1, eye3d) assert_array_almost_equal(result2, eye3d) def test_inv_single_rotation(): rnd = np.random.RandomState(0) p = Rotation.from_quat(rnd.normal(size=(4,))) q = p.inv() p_mat = p.as_matrix() q_mat = q.as_matrix() res1 = np.dot(p_mat, q_mat) res2 = np.dot(q_mat, p_mat) eye = np.eye(3) assert_array_almost_equal(res1, eye) assert_array_almost_equal(res2, eye) x = Rotation.from_quat(rnd.normal(size=(1, 4))) y = x.inv() x_matrix = x.as_matrix() y_matrix = y.as_matrix() result1 = np.einsum('...ij,...jk->...ik', x_matrix, y_matrix) result2 = np.einsum('...ij,...jk->...ik', y_matrix, x_matrix) eye3d = np.empty((1, 3, 3)) eye3d[:] = np.eye(3) assert_array_almost_equal(result1, eye3d) assert_array_almost_equal(result2, eye3d) def test_identity_magnitude(): n = 10 assert_allclose(Rotation.identity(n).magnitude(), 0) assert_allclose(Rotation.identity(n).inv().magnitude(), 0) def test_single_identity_magnitude(): assert Rotation.identity().magnitude() == 0 assert Rotation.identity().inv().magnitude() == 0 def test_identity_invariance(): n = 10 p = Rotation.random(n, random_state=0) result = p * Rotation.identity(n) assert_array_almost_equal(p.as_quat(), result.as_quat()) result = result * p.inv() assert_array_almost_equal(result.magnitude(), np.zeros(n)) def test_single_identity_invariance(): n = 10 p = Rotation.random(n, random_state=0) result = p * Rotation.identity() assert_array_almost_equal(p.as_quat(), result.as_quat()) result = result * p.inv() assert_array_almost_equal(result.magnitude(), np.zeros(n)) def test_magnitude(): r = Rotation.from_quat(np.eye(4)) result = r.magnitude() assert_array_almost_equal(result, [np.pi, np.pi, np.pi, 0]) r = Rotation.from_quat(-np.eye(4)) result = r.magnitude() assert_array_almost_equal(result, [np.pi, np.pi, np.pi, 0]) def test_magnitude_single_rotation(): r = Rotation.from_quat(np.eye(4)) result1 = r[0].magnitude() assert_allclose(result1, np.pi) result2 = r[3].magnitude() assert_allclose(result2, 0) def test_mean(): axes = np.concatenate((-np.eye(3), np.eye(3))) thetas = np.linspace(0, np.pi / 2, 100) for t in thetas: r = Rotation.from_rotvec(t * axes) assert_allclose(r.mean().magnitude(), 0, atol=1E-10) def test_weighted_mean(): # test that doubling a weight is equivalent to including a rotation twice. axes = np.array([[0, 0, 0], [1, 0, 0], [1, 0, 0]]) thetas = np.linspace(0, np.pi / 2, 100) for t in thetas: rw = Rotation.from_rotvec(t * axes[:2]) mw = rw.mean(weights=[1, 2]) r = Rotation.from_rotvec(t * axes) m = r.mean() assert_allclose((m * mw.inv()).magnitude(), 0, atol=1E-10) def test_mean_invalid_weights(): with pytest.raises(ValueError, match="non-negative"): r = Rotation.from_quat(np.eye(4)) r.mean(weights=-np.ones(4)) def test_reduction_no_indices(): result = Rotation.identity().reduce(return_indices=False) assert isinstance(result, Rotation) def test_reduction_none_indices(): result = Rotation.identity().reduce(return_indices=True) assert type(result) == tuple assert len(result) == 3 reduced, left_best, right_best = result assert left_best is None assert right_best is None def test_reduction_scalar_calculation(): rng = np.random.RandomState(0) l = Rotation.random(5, random_state=rng) r = Rotation.random(10, random_state=rng) p = Rotation.random(7, random_state=rng) reduced, left_best, right_best = p.reduce(l, r, return_indices=True) # Loop implementation of the vectorized calculation in Rotation.reduce scalars = np.zeros((len(l), len(p), len(r))) for i, li in enumerate(l): for j, pj in enumerate(p): for k, rk in enumerate(r): scalars[i, j, k] = np.abs((li * pj * rk).as_quat()[3]) scalars = np.reshape(np.rollaxis(scalars, 1), (scalars.shape[1], -1)) max_ind = np.argmax(np.reshape(scalars, (len(p), -1)), axis=1) left_best_check = max_ind // len(r) right_best_check = max_ind % len(r) assert (left_best == left_best_check).all() assert (right_best == right_best_check).all() reduced_check = l[left_best_check] * p * r[right_best_check] mag = (reduced.inv() * reduced_check).magnitude() assert_array_almost_equal(mag, np.zeros(len(p))) def test_apply_single_rotation_single_point(): mat = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) r_1d = Rotation.from_matrix(mat) r_2d = Rotation.from_matrix(np.expand_dims(mat, axis=0)) v_1d = np.array([1, 2, 3]) v_2d = np.expand_dims(v_1d, axis=0) v1d_rotated = np.array([-2, 1, 3]) v2d_rotated = np.expand_dims(v1d_rotated, axis=0) assert_allclose(r_1d.apply(v_1d), v1d_rotated) assert_allclose(r_1d.apply(v_2d), v2d_rotated) assert_allclose(r_2d.apply(v_1d), v2d_rotated) assert_allclose(r_2d.apply(v_2d), v2d_rotated) v1d_inverse = np.array([2, -1, 3]) v2d_inverse = np.expand_dims(v1d_inverse, axis=0) assert_allclose(r_1d.apply(v_1d, inverse=True), v1d_inverse) assert_allclose(r_1d.apply(v_2d, inverse=True), v2d_inverse) assert_allclose(r_2d.apply(v_1d, inverse=True), v2d_inverse) assert_allclose(r_2d.apply(v_2d, inverse=True), v2d_inverse) def test_apply_single_rotation_multiple_points(): mat = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) r1 = Rotation.from_matrix(mat) r2 = Rotation.from_matrix(np.expand_dims(mat, axis=0)) v = np.array([[1, 2, 3], [4, 5, 6]]) v_rotated = np.array([[-2, 1, 3], [-5, 4, 6]]) assert_allclose(r1.apply(v), v_rotated) assert_allclose(r2.apply(v), v_rotated) v_inverse = np.array([[2, -1, 3], [5, -4, 6]]) assert_allclose(r1.apply(v, inverse=True), v_inverse) assert_allclose(r2.apply(v, inverse=True), v_inverse) def test_apply_multiple_rotations_single_point(): mat = np.empty((2, 3, 3)) mat[0] = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) mat[1] = np.array([ [1, 0, 0], [0, 0, -1], [0, 1, 0] ]) r = Rotation.from_matrix(mat) v1 = np.array([1, 2, 3]) v2 = np.expand_dims(v1, axis=0) v_rotated = np.array([[-2, 1, 3], [1, -3, 2]]) assert_allclose(r.apply(v1), v_rotated) assert_allclose(r.apply(v2), v_rotated) v_inverse = np.array([[2, -1, 3], [1, 3, -2]]) assert_allclose(r.apply(v1, inverse=True), v_inverse) assert_allclose(r.apply(v2, inverse=True), v_inverse) def test_apply_multiple_rotations_multiple_points(): mat = np.empty((2, 3, 3)) mat[0] = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) mat[1] = np.array([ [1, 0, 0], [0, 0, -1], [0, 1, 0] ]) r = Rotation.from_matrix(mat) v = np.array([[1, 2, 3], [4, 5, 6]]) v_rotated = np.array([[-2, 1, 3], [4, -6, 5]]) assert_allclose(r.apply(v), v_rotated) v_inverse = np.array([[2, -1, 3], [4, 6, -5]]) assert_allclose(r.apply(v, inverse=True), v_inverse) def test_getitem(): mat = np.empty((2, 3, 3)) mat[0] = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) mat[1] = np.array([ [1, 0, 0], [0, 0, -1], [0, 1, 0] ]) r = Rotation.from_matrix(mat) assert_allclose(r[0].as_matrix(), mat[0], atol=1e-15) assert_allclose(r[1].as_matrix(), mat[1], atol=1e-15) assert_allclose(r[:-1].as_matrix(), np.expand_dims(mat[0], axis=0), atol=1e-15) def test_n_rotations(): mat = np.empty((2, 3, 3)) mat[0] = np.array([ [0, -1, 0], [1, 0, 0], [0, 0, 1] ]) mat[1] = np.array([ [1, 0, 0], [0, 0, -1], [0, 1, 0] ]) r = Rotation.from_matrix(mat) assert_equal(len(r), 2) assert_equal(len(r[:-1]), 1) def test_align_vectors_no_rotation(): x = np.array([[1, 2, 3], [4, 5, 6]]) y = x.copy() r, rmsd = Rotation.align_vectors(x, y) assert_array_almost_equal(r.as_matrix(), np.eye(3)) assert_allclose(rmsd, 0, atol=1e-6) def test_align_vectors_no_noise(): rnd = np.random.RandomState(0) c = Rotation.from_quat(rnd.normal(size=4)) b = rnd.normal(size=(5, 3)) a = c.apply(b) est, rmsd = Rotation.align_vectors(a, b) assert_allclose(c.as_quat(), est.as_quat()) assert_allclose(rmsd, 0, atol=1e-7) def test_align_vectors_improper_rotation(): # Tests correct logic for issue #10444 x = np.array([[0.89299824, -0.44372674, 0.0752378], [0.60221789, -0.47564102, -0.6411702]]) y = np.array([[0.02386536, -0.82176463, 0.5693271], [-0.27654929, -0.95191427, -0.1318321]]) est, rmsd = Rotation.align_vectors(x, y) assert_allclose(x, est.apply(y), atol=1e-6) assert_allclose(rmsd, 0, atol=1e-7) def test_align_vectors_scaled_weights(): rng = np.random.RandomState(0) c = Rotation.random(random_state=rng) b = rng.normal(size=(5, 3)) a = c.apply(b) est1, rmsd1, cov1 = Rotation.align_vectors(a, b, np.ones(5), True) est2, rmsd2, cov2 = Rotation.align_vectors(a, b, 2 * np.ones(5), True) assert_allclose(est1.as_matrix(), est2.as_matrix()) assert_allclose(np.sqrt(2) * rmsd1, rmsd2) assert_allclose(cov1, cov2) def test_align_vectors_noise(): rnd = np.random.RandomState(0) n_vectors = 100 rot = Rotation.from_euler('xyz', rnd.normal(size=3)) vectors = rnd.normal(size=(n_vectors, 3)) result = rot.apply(vectors) # The paper adds noise as independently distributed angular errors sigma = np.deg2rad(1) tolerance = 1.5 * sigma noise = Rotation.from_rotvec( rnd.normal( size=(n_vectors, 3), scale=sigma ) ) # Attitude errors must preserve norm. Hence apply individual random # rotations to each vector. noisy_result = noise.apply(result) est, rmsd, cov = Rotation.align_vectors(noisy_result, vectors, return_sensitivity=True) # Use rotation compositions to find out closeness error_vector = (rot * est.inv()).as_rotvec() assert_allclose(error_vector[0], 0, atol=tolerance) assert_allclose(error_vector[1], 0, atol=tolerance) assert_allclose(error_vector[2], 0, atol=tolerance) # Check error bounds using covariance matrix cov *= sigma assert_allclose(cov[0, 0], 0, atol=tolerance) assert_allclose(cov[1, 1], 0, atol=tolerance) assert_allclose(cov[2, 2], 0, atol=tolerance) assert_allclose(rmsd, np.sum((noisy_result - est.apply(vectors))**2)**0.5) def test_align_vectors_single_vector(): with pytest.warns(UserWarning, match="Optimal rotation is not"): r_estimate, rmsd = Rotation.align_vectors([[1, -1, 1]], [[1, 1, -1]]) assert_allclose(rmsd, 0, atol=1e-16) def test_align_vectors_invalid_input(): with pytest.raises(ValueError, match="Expected input `a` to have shape"): Rotation.align_vectors([1, 2, 3], [[1, 2, 3]]) with pytest.raises(ValueError, match="Expected input `b` to have shape"): Rotation.align_vectors([[1, 2, 3]], [1, 2, 3]) with pytest.raises(ValueError, match="Expected inputs `a` and `b` " "to have same shapes"): Rotation.align_vectors([[1, 2, 3],[4, 5, 6]], [[1, 2, 3]]) with pytest.raises(ValueError, match="Expected `weights` to be 1 dimensional"): Rotation.align_vectors([[1, 2, 3]], [[1, 2, 3]], weights=[[1]]) with pytest.raises(ValueError, match="Expected `weights` to have number of values"): Rotation.align_vectors([[1, 2, 3]], [[1, 2, 3]], weights=[1, 2]) def test_random_rotation_shape(): rnd = np.random.RandomState(0) assert_equal(Rotation.random(random_state=rnd).as_quat().shape, (4,)) assert_equal(Rotation.random(None, random_state=rnd).as_quat().shape, (4,)) assert_equal(Rotation.random(1, random_state=rnd).as_quat().shape, (1, 4)) assert_equal(Rotation.random(5, random_state=rnd).as_quat().shape, (5, 4)) def test_slerp(): rnd = np.random.RandomState(0) key_rots = Rotation.from_quat(rnd.uniform(size=(5, 4))) key_quats = key_rots.as_quat() key_times = [0, 1, 2, 3, 4] interpolator = Slerp(key_times, key_rots) times = [0, 0.5, 0.25, 1, 1.5, 2, 2.75, 3, 3.25, 3.60, 4] interp_rots = interpolator(times) interp_quats = interp_rots.as_quat() # Dot products are affected by sign of quaternions interp_quats[interp_quats[:, -1] < 0] *= -1 # Checking for quaternion equality, perform same operation key_quats[key_quats[:, -1] < 0] *= -1 # Equality at keyframes, including both endpoints assert_allclose(interp_quats[0], key_quats[0]) assert_allclose(interp_quats[3], key_quats[1]) assert_allclose(interp_quats[5], key_quats[2]) assert_allclose(interp_quats[7], key_quats[3]) assert_allclose(interp_quats[10], key_quats[4]) # Constant angular velocity between keyframes. Check by equating # cos(theta) between quaternion pairs with equal time difference. cos_theta1 = np.sum(interp_quats[0] * interp_quats[2]) cos_theta2 = np.sum(interp_quats[2] * interp_quats[1]) assert_allclose(cos_theta1, cos_theta2) cos_theta4 = np.sum(interp_quats[3] * interp_quats[4]) cos_theta5 = np.sum(interp_quats[4] * interp_quats[5]) assert_allclose(cos_theta4, cos_theta5) # theta1: 0 -> 0.25, theta3 : 0.5 -> 1 # Use double angle formula for double the time difference cos_theta3 = np.sum(interp_quats[1] * interp_quats[3]) assert_allclose(cos_theta3, 2 * (cos_theta1**2) - 1) # Miscellaneous checks assert_equal(len(interp_rots), len(times)) def test_slerp_single_rot(): with pytest.raises(ValueError, match="must be a sequence of rotations"): r = Rotation.from_quat([1, 2, 3, 4]) Slerp([1], r) def test_slerp_time_dim_mismatch(): with pytest.raises(ValueError, match="times to be specified in a 1 dimensional array"): rnd = np.random.RandomState(0) r = Rotation.from_quat(rnd.uniform(size=(2, 4))) t = np.array([[1], [2]]) Slerp(t, r) def test_slerp_num_rotations_mismatch(): with pytest.raises(ValueError, match="number of rotations to be equal to " "number of timestamps"): rnd = np.random.RandomState(0) r = Rotation.from_quat(rnd.uniform(size=(5, 4))) t = np.arange(7) Slerp(t, r) def test_slerp_equal_times(): with pytest.raises(ValueError, match="strictly increasing order"): rnd = np.random.RandomState(0) r = Rotation.from_quat(rnd.uniform(size=(5, 4))) t = [0, 1, 2, 2, 4] Slerp(t, r) def test_slerp_decreasing_times(): with pytest.raises(ValueError, match="strictly increasing order"): rnd = np.random.RandomState(0) r = Rotation.from_quat(rnd.uniform(size=(5, 4))) t = [0, 1, 3, 2, 4] Slerp(t, r) def test_slerp_call_time_dim_mismatch(): rnd = np.random.RandomState(0) r = Rotation.from_quat(rnd.uniform(size=(5, 4))) t = np.arange(5) s = Slerp(t, r) with pytest.raises(ValueError, match="`times` must be at most 1-dimensional."): interp_times = np.array([[3.5], [4.2]]) s(interp_times) def test_slerp_call_time_out_of_range(): rnd = np.random.RandomState(0) r = Rotation.from_quat(rnd.uniform(size=(5, 4))) t = np.arange(5) + 1 s = Slerp(t, r) with pytest.raises(ValueError, match="times must be within the range"): s([0, 1, 2]) with pytest.raises(ValueError, match="times must be within the range"): s([1, 2, 6]) def test_slerp_call_scalar_time(): r = Rotation.from_euler('X', [0, 80], degrees=True) s = Slerp([0, 1], r) r_interpolated = s(0.25) r_interpolated_expected = Rotation.from_euler('X', 20, degrees=True) delta = r_interpolated * r_interpolated_expected.inv() assert_allclose(delta.magnitude(), 0, atol=1e-16) def test_multiplication_stability(): qs = Rotation.random(50, random_state=0) rs = Rotation.random(1000, random_state=1) for q in qs: rs *= q * rs assert_allclose(np.linalg.norm(rs.as_quat(), axis=1), 1) def test_rotation_within_numpy_array(): single = Rotation.random(random_state=0) multiple = Rotation.random(2, random_state=1) array = np.array(single) assert_equal(array.shape, ()) array = np.array(multiple) assert_equal(array.shape, (2,)) assert_allclose(array[0].as_matrix(), multiple[0].as_matrix()) assert_allclose(array[1].as_matrix(), multiple[1].as_matrix()) array = np.array([single]) assert_equal(array.shape, (1,)) assert_equal(array[0], single) array = np.array([multiple]) assert_equal(array.shape, (1, 2)) assert_allclose(array[0, 0].as_matrix(), multiple[0].as_matrix()) assert_allclose(array[0, 1].as_matrix(), multiple[1].as_matrix()) array = np.array([single, multiple], dtype=object) assert_equal(array.shape, (2,)) assert_equal(array[0], single) assert_equal(array[1], multiple) array = np.array([multiple, multiple, multiple]) assert_equal(array.shape, (3, 2)) def test_pickling(): r = Rotation.from_quat([0, 0, np.sin(np.pi/4), np.cos(np.pi/4)]) pkl = pickle.dumps(r) unpickled = pickle.loads(pkl) assert_allclose(r.as_matrix(), unpickled.as_matrix(), atol=1e-15) def test_deepcopy(): r = Rotation.from_quat([0, 0, np.sin(np.pi/4), np.cos(np.pi/4)]) r1 = copy.deepcopy(r) assert_allclose(r.as_matrix(), r1.as_matrix(), atol=1e-15) def test_as_euler_contiguous(): r = Rotation.from_quat([0, 0, 0, 1]) e1 = r.as_euler('xyz') # extrinsic euler rotation e2 = r.as_euler('XYZ') # intrinsic assert e1.flags['C_CONTIGUOUS'] is True assert e2.flags['C_CONTIGUOUS'] is True assert all(i >= 0 for i in e1.strides) assert all(i >= 0 for i in e2.strides)