def test_coordinate_conversion(self):
x = rd.random((self.n, 3))
r1, alpha1, gamma1 = math.cart2inter(x)
y = math.inter2cart(r1, alpha1, gamma1)
r2, alpha2, gamma2 = math.cart2inter(y)
z = math.inter2cart(r2, alpha2, gamma2)
self.assertTrue(np.allclose(r1, r2))
self.assertTrue(np.allclose(alpha1, alpha2))
self.assertTrue(np.allclose(gamma1, gamma2))
self.assertTrue(np.allclose(x, math.kabsch(x, z)[0]))
def test_random_transformation(self):
x = rd.random((self.n, 3))
theta = rd.random(1)
random_rotation = np.array([[1, 0, 0],
[0, np.cos(theta), -np.sin(theta)],
[0, np.sin(theta), np.cos(theta)]])
random_traslation = rd.random(3)
y = np.dot(x, random_rotation.T) + np.tile(
random_traslation, (self.n, 1))
z, restored_rotation = math.kabsch(x, y)
self.assertTrue(np.allclose(x, z))
self.assertTrue(np.allclose(restored_rotation,
random_rotation))
def test_different_dimentions(self):
x = np.ones((3, 2))
y = np.ones((3, 4))
with self.assertRaises(exception.MathError):
math.kabsch(x, y)
def test_reflected_matrix(self):
x = rd.random((self.n, 3))
y = np.vstack((x[:, 1], x[:, 0], x[:, 2])).T
math.kabsch(x, y)
def test_same_matrix(self):
x = rd.random((self.n, 3))
z, q = math.kabsch(x, x)
self.assertTrue(np.allclose(x, z))
self.assertTrue(np.allclose(q, np.eye(3)))
