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1250 lines
37 KiB
Python
1250 lines
37 KiB
Python
import pytest
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import numpy as np
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from numpy.testing import assert_equal, assert_array_almost_equal
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from numpy.testing import assert_allclose, assert_array_less
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from scipy.spatial.transform import Rotation, Slerp
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from scipy.stats import special_ortho_group
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from itertools import permutations
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def test_generic_quat_matrix():
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x = np.array([[3, 4, 0, 0], [5, 12, 0, 0]])
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r = Rotation.from_quat(x)
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expected_quat = x / np.array([[5], [13]])
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_from_single_1d_quaternion():
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x = np.array([3, 4, 0, 0])
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r = Rotation.from_quat(x)
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expected_quat = x / 5
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_from_single_2d_quaternion():
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x = np.array([[3, 4, 0, 0]])
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r = Rotation.from_quat(x)
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expected_quat = x / 5
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_from_square_quat_matrix():
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# Ensure proper norm array broadcasting
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x = np.array([
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[3, 0, 0, 4],
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[5, 0, 12, 0],
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[0, 0, 0, 1],
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[0, 0, 0, -1]
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])
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r = Rotation.from_quat(x)
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expected_quat = x / np.array([[5], [13], [1], [1]])
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_malformed_1d_from_quat():
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with pytest.raises(ValueError):
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Rotation.from_quat(np.array([1, 2, 3]))
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def test_malformed_2d_from_quat():
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with pytest.raises(ValueError):
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Rotation.from_quat(np.array([
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[1, 2, 3, 4, 5],
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[4, 5, 6, 7, 8]
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]))
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def test_zero_norms_from_quat():
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x = np.array([
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[3, 4, 0, 0],
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[0, 0, 0, 0],
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[5, 0, 12, 0]
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])
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with pytest.raises(ValueError):
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Rotation.from_quat(x)
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def test_as_matrix_single_1d_quaternion():
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quat = [0, 0, 0, 1]
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mat = Rotation.from_quat(quat).as_matrix()
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# mat.shape == (3,3) due to 1d input
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assert_array_almost_equal(mat, np.eye(3))
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def test_as_matrix_single_2d_quaternion():
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quat = [[0, 0, 1, 1]]
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mat = Rotation.from_quat(quat).as_matrix()
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assert_equal(mat.shape, (1, 3, 3))
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expected_mat = np.array([
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[0, -1, 0],
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[1, 0, 0],
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[0, 0, 1]
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])
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assert_array_almost_equal(mat[0], expected_mat)
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def test_as_matrix_from_square_input():
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quats = [
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[0, 0, 1, 1],
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[0, 1, 0, 1],
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[0, 0, 0, 1],
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[0, 0, 0, -1]
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]
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mat = Rotation.from_quat(quats).as_matrix()
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assert_equal(mat.shape, (4, 3, 3))
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expected0 = np.array([
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[0, -1, 0],
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[1, 0, 0],
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[0, 0, 1]
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])
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assert_array_almost_equal(mat[0], expected0)
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expected1 = np.array([
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[0, 0, 1],
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[0, 1, 0],
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[-1, 0, 0]
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])
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assert_array_almost_equal(mat[1], expected1)
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assert_array_almost_equal(mat[2], np.eye(3))
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assert_array_almost_equal(mat[3], np.eye(3))
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def test_as_matrix_from_generic_input():
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quats = [
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[0, 0, 1, 1],
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[0, 1, 0, 1],
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[1, 2, 3, 4]
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]
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mat = Rotation.from_quat(quats).as_matrix()
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assert_equal(mat.shape, (3, 3, 3))
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expected0 = np.array([
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[0, -1, 0],
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[1, 0, 0],
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[0, 0, 1]
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])
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assert_array_almost_equal(mat[0], expected0)
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expected1 = np.array([
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[0, 0, 1],
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[0, 1, 0],
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[-1, 0, 0]
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])
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assert_array_almost_equal(mat[1], expected1)
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expected2 = np.array([
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[0.4, -2, 2.2],
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[2.8, 1, 0.4],
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[-1, 2, 2]
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]) / 3
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assert_array_almost_equal(mat[2], expected2)
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def test_from_single_2d_matrix():
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mat = [
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[0, 0, 1],
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[1, 0, 0],
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[0, 1, 0]
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]
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expected_quat = [0.5, 0.5, 0.5, 0.5]
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assert_array_almost_equal(
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Rotation.from_matrix(mat).as_quat(),
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expected_quat)
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def test_from_single_3d_matrix():
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mat = np.array([
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[0, 0, 1],
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[1, 0, 0],
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[0, 1, 0]
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]).reshape((1, 3, 3))
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expected_quat = np.array([0.5, 0.5, 0.5, 0.5]).reshape((1, 4))
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assert_array_almost_equal(
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Rotation.from_matrix(mat).as_quat(),
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expected_quat)
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def test_from_matrix_calculation():
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expected_quat = np.array([1, 1, 6, 1]) / np.sqrt(39)
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mat = np.array([
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[-0.8974359, -0.2564103, 0.3589744],
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[0.3589744, -0.8974359, 0.2564103],
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[0.2564103, 0.3589744, 0.8974359]
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])
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assert_array_almost_equal(
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Rotation.from_matrix(mat).as_quat(),
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expected_quat)
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assert_array_almost_equal(
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Rotation.from_matrix(mat.reshape((1, 3, 3))).as_quat(),
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expected_quat.reshape((1, 4)))
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def test_matrix_calculation_pipeline():
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mat = special_ortho_group.rvs(3, size=10, random_state=0)
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assert_array_almost_equal(Rotation.from_matrix(mat).as_matrix(), mat)
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def test_from_matrix_ortho_output():
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np.random.seed(0)
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mat = np.random.random((100, 3, 3))
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ortho_mat = Rotation.from_matrix(mat).as_matrix()
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mult_result = np.einsum('...ij,...jk->...ik', ortho_mat,
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ortho_mat.transpose((0, 2, 1)))
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eye3d = np.zeros((100, 3, 3))
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for i in range(3):
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eye3d[:, i, i] = 1.0
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assert_array_almost_equal(mult_result, eye3d)
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def test_from_1d_single_rotvec():
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rotvec = [1, 0, 0]
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expected_quat = np.array([0.4794255, 0, 0, 0.8775826])
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result = Rotation.from_rotvec(rotvec)
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assert_array_almost_equal(result.as_quat(), expected_quat)
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def test_from_2d_single_rotvec():
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rotvec = [[1, 0, 0]]
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expected_quat = np.array([[0.4794255, 0, 0, 0.8775826]])
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result = Rotation.from_rotvec(rotvec)
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assert_array_almost_equal(result.as_quat(), expected_quat)
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def test_from_generic_rotvec():
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rotvec = [
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[1, 2, 2],
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[1, -1, 0.5],
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[0, 0, 0]
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]
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expected_quat = np.array([
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[0.3324983, 0.6649967, 0.6649967, 0.0707372],
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[0.4544258, -0.4544258, 0.2272129, 0.7316889],
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[0, 0, 0, 1]
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])
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assert_array_almost_equal(
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Rotation.from_rotvec(rotvec).as_quat(),
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expected_quat)
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def test_from_rotvec_small_angle():
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rotvec = np.array([
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[5e-4 / np.sqrt(3), -5e-4 / np.sqrt(3), 5e-4 / np.sqrt(3)],
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[0.2, 0.3, 0.4],
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[0, 0, 0]
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])
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quat = Rotation.from_rotvec(rotvec).as_quat()
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# cos(theta/2) ~~ 1 for small theta
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assert_allclose(quat[0, 3], 1)
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# sin(theta/2) / theta ~~ 0.5 for small theta
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assert_allclose(quat[0, :3], rotvec[0] * 0.5)
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assert_allclose(quat[1, 3], 0.9639685)
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assert_allclose(
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quat[1, :3],
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np.array([
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0.09879603932153465,
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0.14819405898230198,
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0.19759207864306931
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]))
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assert_equal(quat[2], np.array([0, 0, 0, 1]))
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def test_malformed_1d_from_rotvec():
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with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'):
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Rotation.from_rotvec([1, 2])
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def test_malformed_2d_from_rotvec():
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with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'):
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Rotation.from_rotvec([
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[1, 2, 3, 4],
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[5, 6, 7, 8]
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])
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def test_as_generic_rotvec():
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quat = np.array([
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[1, 2, -1, 0.5],
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[1, -1, 1, 0.0003],
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[0, 0, 0, 1]
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])
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quat /= np.linalg.norm(quat, axis=1)[:, None]
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rotvec = Rotation.from_quat(quat).as_rotvec()
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angle = np.linalg.norm(rotvec, axis=1)
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assert_allclose(quat[:, 3], np.cos(angle/2))
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assert_allclose(np.cross(rotvec, quat[:, :3]), np.zeros((3, 3)))
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def test_as_rotvec_single_1d_input():
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quat = np.array([1, 2, -3, 2])
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expected_rotvec = np.array([0.5772381, 1.1544763, -1.7317144])
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actual_rotvec = Rotation.from_quat(quat).as_rotvec()
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assert_equal(actual_rotvec.shape, (3,))
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assert_allclose(actual_rotvec, expected_rotvec)
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def test_as_rotvec_single_2d_input():
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quat = np.array([[1, 2, -3, 2]])
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expected_rotvec = np.array([[0.5772381, 1.1544763, -1.7317144]])
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actual_rotvec = Rotation.from_quat(quat).as_rotvec()
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assert_equal(actual_rotvec.shape, (1, 3))
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assert_allclose(actual_rotvec, expected_rotvec)
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def test_rotvec_calc_pipeline():
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# Include small angles
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rotvec = np.array([
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[0, 0, 0],
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[1, -1, 2],
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[-3e-4, 3.5e-4, 7.5e-5]
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])
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assert_allclose(Rotation.from_rotvec(rotvec).as_rotvec(), rotvec)
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def test_from_1d_single_mrp():
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mrp = [0, 0, 1.0]
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expected_quat = np.array([0, 0, 1, 0])
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result = Rotation.from_mrp(mrp)
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assert_array_almost_equal(result.as_quat(), expected_quat)
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def test_from_2d_single_mrp():
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mrp = [[0, 0, 1.0]]
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expected_quat = np.array([[0, 0, 1, 0]])
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result = Rotation.from_mrp(mrp)
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assert_array_almost_equal(result.as_quat(), expected_quat)
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def test_from_generic_mrp():
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mrp = np.array([
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[1, 2, 2],
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[1, -1, 0.5],
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[0, 0, 0]])
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expected_quat = np.array([
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[0.2, 0.4, 0.4, -0.8],
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[0.61538462, -0.61538462, 0.30769231, -0.38461538],
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[0, 0, 0, 1]])
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assert_array_almost_equal(Rotation.from_mrp(mrp).as_quat(), expected_quat)
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def test_malformed_1d_from_mrp():
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with pytest.raises(ValueError, match='Expected `mrp` to have shape'):
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Rotation.from_mrp([1, 2])
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def test_malformed_2d_from_mrp():
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with pytest.raises(ValueError, match='Expected `mrp` to have shape'):
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Rotation.from_mrp([
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[1, 2, 3, 4],
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[5, 6, 7, 8]
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])
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def test_as_generic_mrp():
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quat = np.array([
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[1, 2, -1, 0.5],
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[1, -1, 1, 0.0003],
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[0, 0, 0, 1]])
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quat /= np.linalg.norm(quat, axis=1)[:, None]
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expected_mrp = np.array([
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[0.33333333, 0.66666667, -0.33333333],
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[0.57725028, -0.57725028, 0.57725028],
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[0, 0, 0]])
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assert_array_almost_equal(Rotation.from_quat(quat).as_mrp(), expected_mrp)
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def test_past_180_degree_rotation():
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# ensure that a > 180 degree rotation is returned as a <180 rotation in MRPs
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# in this case 270 should be returned as -90
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expected_mrp = np.array([-np.tan(np.pi/2/4), 0.0, 0])
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assert_array_almost_equal(Rotation.from_euler('xyz', [270, 0, 0], degrees=True).as_mrp(), expected_mrp)
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def test_as_mrp_single_1d_input():
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quat = np.array([1, 2, -3, 2])
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expected_mrp = np.array([0.16018862, 0.32037724, -0.48056586])
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actual_mrp = Rotation.from_quat(quat).as_mrp()
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assert_equal(actual_mrp.shape, (3,))
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assert_allclose(actual_mrp, expected_mrp)
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def test_as_mrp_single_2d_input():
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quat = np.array([[1, 2, -3, 2]])
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expected_mrp = np.array([[0.16018862, 0.32037724, -0.48056586]])
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actual_mrp = Rotation.from_quat(quat).as_mrp()
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assert_equal(actual_mrp.shape, (1, 3))
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assert_allclose(actual_mrp, expected_mrp)
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def test_mrp_calc_pipeline():
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actual_mrp = np.array([
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[0, 0, 0],
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[1, -1, 2],
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[0.41421356, 0, 0],
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[0.1, 0.2, 0.1]])
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expected_mrp = np.array([
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[0, 0, 0],
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[-0.16666667, 0.16666667, -0.33333333],
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[0.41421356, 0, 0],
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[0.1, 0.2, 0.1]])
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assert_allclose(Rotation.from_mrp(actual_mrp).as_mrp(), expected_mrp)
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def test_from_euler_single_rotation():
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quat = Rotation.from_euler('z', 90, degrees=True).as_quat()
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expected_quat = np.array([0, 0, 1, 1]) / np.sqrt(2)
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assert_allclose(quat, expected_quat)
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def test_single_intrinsic_extrinsic_rotation():
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extrinsic = Rotation.from_euler('z', 90, degrees=True).as_matrix()
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intrinsic = Rotation.from_euler('Z', 90, degrees=True).as_matrix()
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assert_allclose(extrinsic, intrinsic)
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def test_from_euler_rotation_order():
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# Intrinsic rotation is same as extrinsic with order reversed
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np.random.seed(0)
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a = np.random.randint(low=0, high=180, size=(6, 3))
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b = a[:, ::-1]
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x = Rotation.from_euler('xyz', a, degrees=True).as_quat()
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y = Rotation.from_euler('ZYX', b, degrees=True).as_quat()
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assert_allclose(x, y)
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def test_from_euler_elementary_extrinsic_rotation():
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# Simple test to check if extrinsic rotations are implemented correctly
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mat = Rotation.from_euler('zx', [90, 90], degrees=True).as_matrix()
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expected_mat = np.array([
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[0, -1, 0],
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[0, 0, -1],
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[1, 0, 0]
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])
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assert_array_almost_equal(mat, expected_mat)
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def test_from_euler_intrinsic_rotation_312():
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angles = [
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[30, 60, 45],
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[30, 60, 30],
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[45, 30, 60]
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]
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mat = Rotation.from_euler('ZXY', angles, degrees=True).as_matrix()
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assert_array_almost_equal(mat[0], np.array([
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[0.3061862, -0.2500000, 0.9185587],
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[0.8838835, 0.4330127, -0.1767767],
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[-0.3535534, 0.8660254, 0.3535534]
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]))
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assert_array_almost_equal(mat[1], np.array([
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[0.5334936, -0.2500000, 0.8080127],
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[0.8080127, 0.4330127, -0.3995191],
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[-0.2500000, 0.8660254, 0.4330127]
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]))
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assert_array_almost_equal(mat[2], np.array([
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[0.0473672, -0.6123725, 0.7891491],
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[0.6597396, 0.6123725, 0.4355958],
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[-0.7500000, 0.5000000, 0.4330127]
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]))
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|
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():
|
|
np.random.seed(0)
|
|
n = 10
|
|
angles = np.empty((n, 3))
|
|
angles[:, 0] = np.random.uniform(low=-np.pi, high=np.pi, size=(n,))
|
|
angles[:, 1] = np.random.uniform(low=-np.pi / 2, high=np.pi / 2, size=(n,))
|
|
angles[:, 2] = np.random.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():
|
|
np.random.seed(0)
|
|
n = 10
|
|
angles = np.empty((n, 3))
|
|
angles[:, 0] = np.random.uniform(low=-np.pi, high=np.pi, size=(n,))
|
|
angles[:, 1] = np.random.uniform(low=0, high=np.pi, size=(n,))
|
|
angles[:, 2] = np.random.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():
|
|
np.random.seed(0)
|
|
n = 10
|
|
p = Rotation.from_quat(np.random.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():
|
|
np.random.seed(0)
|
|
p = Rotation.from_quat(np.random.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(np.random.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)
|
|
|
|
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)
|
|
|
|
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():
|
|
np.random.seed(0)
|
|
c = Rotation.from_quat(np.random.normal(size=4))
|
|
b = np.random.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():
|
|
np.random.seed(0)
|
|
n_vectors = 100
|
|
rot = Rotation.from_euler('xyz', np.random.normal(size=3))
|
|
vectors = np.random.normal(size=(n_vectors, 3))
|
|
result = rot.apply(vectors)
|
|
|
|
# The paper adds noise as indepedently distributed angular errors
|
|
sigma = np.deg2rad(1)
|
|
tolerance = 1.5 * sigma
|
|
noise = Rotation.from_rotvec(
|
|
np.random.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():
|
|
assert_equal(Rotation.random().as_quat().shape, (4,))
|
|
assert_equal(Rotation.random(None).as_quat().shape, (4,))
|
|
|
|
assert_equal(Rotation.random(1).as_quat().shape, (1, 4))
|
|
assert_equal(Rotation.random(5).as_quat().shape, (5, 4))
|
|
|
|
|
|
def test_slerp():
|
|
np.random.seed(0)
|
|
|
|
key_rots = Rotation.from_quat(np.random.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"):
|
|
np.random.seed(0)
|
|
r = Rotation.from_quat(np.random.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"):
|
|
np.random.seed(0)
|
|
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
|
t = np.arange(7)
|
|
Slerp(t, r)
|
|
|
|
|
|
def test_slerp_equal_times():
|
|
with pytest.raises(ValueError, match="strictly increasing order"):
|
|
np.random.seed(0)
|
|
r = Rotation.from_quat(np.random.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"):
|
|
np.random.seed(0)
|
|
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
|
t = [0, 1, 3, 2, 4]
|
|
Slerp(t, r)
|
|
|
|
|
|
def test_slerp_call_time_dim_mismatch():
|
|
np.random.seed(0)
|
|
r = Rotation.from_quat(np.random.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():
|
|
np.random.seed(0)
|
|
r = Rotation.from_quat(np.random.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()
|
|
multiple = Rotation.random(2)
|
|
|
|
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))
|