def test_mul_by_quat(self):
"""Quarternions should multiply correctly."""
# multiplication of quarternions is equivalent to the
# multiplication of corresponding rotation matrices.
other_quat = Quaternion(np.array([0.4, 0.2, -0.7, 0.8]))
other_mat = other_quat.to_matrix()
product_quat = self.quat_unnormalized * other_quat
product_mat = (self.quat_unnormalized.to_matrix()).dot(other_mat)
assert_allclose(product_quat.to_matrix(), product_mat)
class TestQuaternions(QiskitTestCase):
"""Tests qiskit.quantum_info.operators.quaternion"""
def setUp(self):
self.rnd_array = np.array([0.5, 0.8, 0.9, -0.3])
self.quat_unnormalized = Quaternion(self.rnd_array)
axes = ['x', 'y', 'z']
rnd = np.array([-0.92545003, -2.19985357, 6.01761209])
idx = np.array([0, 2, 1])
self.mat1 = rotation_matrix(rnd[0], axes[idx[0]]).dot(
rotation_matrix(rnd[1], axes[idx[1]]).dot(
rotation_matrix(rnd[2], axes[idx[2]])))
axes_str = ''.join(axes[i] for i in idx)
quat = quaternion_from_euler(rnd, axes_str)
self.mat2 = quat.to_matrix()
def test_str(self):
"""Quaternion should have a correct string representation."""
self.assertEqual(self.quat_unnormalized.__str__(),
self.rnd_array.__str__())
def test_repr(self):
"""Quaternion should have a correct string representation."""
self.assertEqual(self.quat_unnormalized.__repr__(),
self.rnd_array.__str__())
def test_norm(self):
"""Quaternions should give correct norm."""
norm = la.norm(self.rnd_array)
self.assertEqual(norm, self.quat_unnormalized.norm())
def test_normalize(self):
"""Quaternions should be normalizable"""
self.assertAlmostEqual(self.quat_unnormalized.normalize().norm(),
1,
places=5)
def test_random_euler(self):
"""Quaternion from Euler rotations."""
assert_allclose(self.mat1, self.mat2)
def test_orthogonality(self):
"""Quaternion rotation matrix orthogonality"""
assert_allclose(self.mat2.dot(self.mat2.T),
np.identity(3, dtype=float),
atol=1e-8)
def test_det(self):
"""Quaternion det = 1"""
assert_allclose(la.det(self.mat2), 1)
def test_equiv_quaternions(self):
"""Different Euler rotations give same quaternion, up to sign."""
# Check if euler angles from to_zyz return same quaternion
# up to a sign (2pi rotation)
rot = [
'xyz', 'xyx', 'xzy', 'xzx', 'yzx', 'yzy', 'yxz', 'yxy', 'zxy',
'zxz', 'zyx', 'zyz'
]
for value in rot:
rnd = np.array([-1.57657536, 5.66384302, 2.91532185])
quat1 = quaternion_from_euler(rnd, value)
euler = quat1.to_zyz()
quat2 = quaternion_from_euler(euler, 'zyz')
assert_allclose(abs(quat1.data.dot(quat2.data)), 1)
def test_mul_by_quat(self):
"""Quarternions should multiply correctly."""
# multiplication of quarternions is equivalent to the
# multiplication of corresponding rotation matrices.
other_quat = Quaternion(np.array([0.4, 0.2, -0.7, 0.8]))
other_mat = other_quat.to_matrix()
product_quat = self.quat_unnormalized * other_quat
product_mat = (self.quat_unnormalized.to_matrix()).dot(other_mat)
assert_allclose(product_quat.to_matrix(), product_mat)
def test_mul_by_array(self):
"""Quaternions cannot be multiplied with an array."""
other_array = np.array([0.1, 0.2, 0.3, 0.4])
self.assertRaises(Exception, self.quat_unnormalized.__mul__,
other_array)
def test_mul_by_scalar(self):
"""Quaternions cannot be multiplied with a scalar."""
other_scalar = 0.123456789
self.assertRaises(Exception, self.quat_unnormalized.__mul__,
other_scalar)
def test_rotation(self):
"""Multiplication by -1 should give the same rotation."""
neg_quat = Quaternion(self.quat_unnormalized.data * -1)
assert_allclose(neg_quat.to_matrix(),
self.quat_unnormalized.to_matrix())
def test_one_euler_angle(self):
"""Quaternion should return a correct sequence of zyz representation
in the case of rotations when there is only one non-zero Euler angle."""
rand_rot_angle = 0.123456789
some_quat = quaternion_from_axis_rotation(rand_rot_angle, "z")
assert_allclose(some_quat.to_zyz(), np.array([rand_rot_angle, 0, 0]))
def test_two_euler_angle_0123456789(self):
"""Quaternion should return a correct sequence of zyz representation
in the case of rotations when there are only two non-zero Euler angle.
angle = 0.123456789 """
rand_rot_angle = 0.123456789
some_quat = (quaternion_from_axis_rotation(rand_rot_angle, "z") *
quaternion_from_axis_rotation(np.pi, "y"))
assert_allclose(some_quat.to_zyz(),
np.array([rand_rot_angle, np.pi, 0]))
def test_two_euler_angle_0987654321(self):
"""Quaternion should return a correct sequence of zyz representation
in the case of rotations when there are only two non-zero Euler angle.
angle = 0.987654321 """
rand_rot_angle = 0.987654321
some_quat = (quaternion_from_axis_rotation(rand_rot_angle, "z") *
quaternion_from_axis_rotation(np.pi, "y"))
assert_allclose(some_quat.to_zyz(),
np.array([rand_rot_angle, np.pi, 0]))
def test_quaternion_from_rotation_invalid_axis(self):
"""Cannot generate quaternion from rotations around invalid axis."""
rand_axis = 'a'
rand_angle = 0.123456789
self.assertRaises(ValueError, quaternion_from_axis_rotation,
rand_angle, rand_axis)
def test_rotation(self):
"""Multiplication by -1 should give the same rotation."""
neg_quat = Quaternion(self.quat_unnormalized.data * -1)
assert_allclose(neg_quat.to_matrix(),
self.quat_unnormalized.to_matrix())