Add tests to methods of Quaternion.

tests/test_quaternions.py

@@ -5,13 +5,16 @@
 
 class TestQuaternion(unittest.TestCase):
     def setUp(self) -> None:
+        # Identity Quaternion
         self.q0 = ahrs.Quaternion()
+        # Versor from 3D array
         self.vector3 = np.random.random(3)-0.5
-        self.vector3 /= np.linalg.norm(self.vector3)
         self.q3 = ahrs.Quaternion(self.vector3)
+        self.vector3 /= np.linalg.norm(self.vector3)
+        # Versor from 4D array
         self.vector4 = np.random.random(4)-0.5
-        self.vector4 /= np.linalg.norm(self.vector4)
         self.q4 = ahrs.Quaternion(self.vector4)
+        self.vector4 /= np.linalg.norm(self.vector4)
         self.decimal_precision = 15
 
     def test_identity_quaternion(self):
@@ -21,6 +24,58 @@ def test_identity_quaternion(self):
         self.assertEqual(self.q0.z, 0.0)
         np.testing.assert_equal(self.q0.v, np.zeros(3))
 
+    def test_conjugate(self):
+        qc = self.q4.conjugate
+        self.assertAlmostEqual(qc[0], self.q4.w, places=self.decimal_precision)
+        self.assertAlmostEqual(qc[1], -self.q4.x, places=self.decimal_precision)
+        self.assertAlmostEqual(qc[2], -self.q4.y, places=self.decimal_precision)
+        self.assertAlmostEqual(qc[3], -self.q4.z, places=self.decimal_precision)
+        np.testing.assert_almost_equal(qc[1:], -self.q4.v, decimal=self.decimal_precision)
+
+    def test_conj(self):
+        qc = self.q4.conj
+        self.assertAlmostEqual(qc[0], self.q4.w, places=self.decimal_precision)
+        self.assertAlmostEqual(qc[1], -self.q4.x, places=self.decimal_precision)
+        self.assertAlmostEqual(qc[2], -self.q4.y, places=self.decimal_precision)
+        self.assertAlmostEqual(qc[3], -self.q4.z, places=self.decimal_precision)
+        np.testing.assert_almost_equal(qc[1:], -self.q4.v, decimal=self.decimal_precision)
+
+    def test_inverse(self):
+        qi = self.q4.inverse
+        self.assertAlmostEqual(qi[0], self.q4.w, places=self.decimal_precision)
+        self.assertAlmostEqual(qi[1], -self.q4.x, places=self.decimal_precision)
+        self.assertAlmostEqual(qi[2], -self.q4.y, places=self.decimal_precision)
+        self.assertAlmostEqual(qi[3], -self.q4.z, places=self.decimal_precision)
+        np.testing.assert_almost_equal(qi[1:], -self.q4.v, decimal=self.decimal_precision)
+
+    def test_inv(self):
+        qi = self.q4.inv
+        self.assertAlmostEqual(qi[0], self.q4.w, places=self.decimal_precision)
+        self.assertAlmostEqual(qi[1], -self.q4.x, places=self.decimal_precision)
+        self.assertAlmostEqual(qi[2], -self.q4.y, places=self.decimal_precision)
+        self.assertAlmostEqual(qi[3], -self.q4.z, places=self.decimal_precision)
+        np.testing.assert_almost_equal(qi[1:], -self.q4.v, decimal=self.decimal_precision)
+
+    def test_is_pure(self):
+        self.assertFalse(self.q0.is_pure())
+        self.assertTrue(self.q3.is_pure())
+        self.assertFalse(self.q4.is_pure())
+
+    def test_is_real(self):
+        self.assertTrue(self.q0.is_real())
+        self.assertFalse(self.q3.is_real())
+        self.assertFalse(self.q4.is_real())
+
+    def test_is_versor(self):
+        self.assertTrue(self.q0.is_versor())
+        self.assertTrue(self.q3.is_versor())
+        self.assertTrue(self.q4.is_versor())
+
+    def test_is_identity(self):
+        self.assertTrue(self.q0.is_identity())
+        self.assertFalse(self.q3.is_identity())
+        self.assertFalse(self.q4.is_identity())
+
     def test_versor_from_3d_array(self):
         self.assertAlmostEqual(self.q3.w, 0.0, places=self.decimal_precision)
         self.assertAlmostEqual(self.q3.x, self.vector3[0], places=self.decimal_precision)
@@ -73,8 +128,9 @@ def test_4_by_4_array(self):
         np.testing.assert_equal(self.Q1.v, np.identity(4)[:, 1:])
 
     def test_quaternion_average(self):
-        # Create 10 continuous quaternions between 0 and 90 degrees and average
-        # them. Must be, naturally, equal to the 45 degree quaternion.
+        # Create 10 continuous quaternions representing rotations around the
+        # Z-axis between 0 and 90 degrees and average them. The mean quaternion
+        # must be, naturally, equal to the 45 degree quaternion.
         Q = ahrs.QuaternionArray([ahrs.Quaternion(rpy=np.array([0.0, 0.0, x])*ahrs.DEG2RAD) for x in range(0, 100, 10)])
         np.testing.assert_almost_equal(Q.average(), ahrs.Quaternion(rpy=np.array([0.0, 0.0, 45.0])*ahrs.DEG2RAD), decimal=self.decimal_precision)