def test_multiply(self):
# Single
rot = rotmodule.random()
inv = rotmodule.inverse(rot)
identity = numpy.array((1., 0., 0., 0.))
numpy.testing.assert_array_almost_equal(rotmodule.multiply(rot, inv),
identity)
# Array
rot = rotmodule.random(number_of_quaternions=10)
inv = rotmodule.inverse(rot)
identity = numpy.zeros((10, 4))
identity[:, 0] = 1.
numpy.testing.assert_array_almost_equal(rotmodule.multiply(rot, inv),
identity)
def test_perturbation_no_symmetry_absolute(self):
nrots = 100
rotations_1 = rotmodule.random(number_of_quaternions=nrots)
overall_rot = rotmodule.random()
perturbation = 0.000001
rotations_2 = rotmodule.normalize(rotations_1 + perturbation *
numpy.random.random((nrots, 4)))
repeated_overall_rot = numpy.repeat(overall_rot.reshape((1, 4)),
nrots,
axis=0)
rotations_2 = rotmodule.multiply(repeated_overall_rot, rotations_2)
avg_absolute = compare_rotations.absolute_orientation_error(
rotations_1, rotations_2)
self.assertLess(avg_absolute, 4. * numpy.pi / 180.)
def test_perturbation_with_symmetry_relative(self):
nrots = 100
rotations_1 = rotmodule.random(number_of_quaternions=nrots)
overall_rot = rotmodule.random()
perturbation = 0.000001
rotations_2 = rotmodule.normalize(rotations_1 + perturbation *
numpy.random.random((nrots, 4)))
symmetry_operations = ((1., 0., 0., 0.), (0., 1., 0., 0.))
symmetry_version = numpy.random.randint(2, size=nrots)
for i in range(nrots):
rotations_2[i, :] = rotmodule.multiply(
symmetry_operations[symmetry_version[i]], rotations_2[i, :])
repeated_overall_rot = numpy.repeat(overall_rot.reshape((1, 4)),
nrots,
axis=0)
rotations_2 = rotmodule.multiply(repeated_overall_rot, rotations_2)
avg_relative = compare_rotations.relative_orientation_error(
rotations_1, rotations_2, symmetry_operations)
self.assertLess(avg_relative, 5. * numpy.pi / 180.)
def test_random(self):
"""Check that all quaternions have non-negative x-component and that
the average is close to the x-axis"""
nrots = 100
rots = rotmodule.random(number_of_quaternions=nrots)
self.assertGreaterEqual(rots[:, 0].min(), 0)
numpy.testing.assert_array_almost_equal(rots.mean(axis=0)[1:],
numpy.array((
0.,
0.,
0.,
)),
decimal=1)
def test_fix_sign(self):
# Single
rot = numpy.array([-1., 0., 0., 0.])
rotmodule.fix_sign(rot)
self.assertGreaterEqual(rot[0], 0)
rot = numpy.array([0., 0., 0., -1.])
rotmodule.fix_sign(rot)
numpy.testing.assert_array_almost_equal(rot,
numpy.array([0., 0., 0., 1.]))
# Array
rots = rotmodule.random(100, fix_sign=False)
rotmodule.fix_sign(rots)
self.assertGreaterEqual(rots[:, 0].min(), 0)
def test_inverse(self):
# Single
rot_1 = rotmodule.from_angle_and_dir(numpy.pi / 8., (1., 0., 0.))
rot_2 = rotmodule.from_angle_and_dir(-numpy.pi / 8., (1., 0., 0.))
rot_1_inv = rotmodule.inverse(rot_1)
numpy.testing.assert_array_almost_equal(rot_1_inv, rot_2)
# Array
rots = rotmodule.random(number_of_quaternions=10)
inv_1 = rotmodule.inverse(rots)
inv_2 = rots.copy()
inv_2[:, 0] = -inv_2[:, 0]
rotmodule.fix_sign(inv_2)
numpy.testing.assert_array_almost_equal(inv_1, inv_2)