Add unit tests for null_space()

scripts/generate_field_test_vectors.py

@@ -587,7 +587,7 @@ def make_luts(field, sub_folder, seed, sparse=False):
             z = np.array([[I(e) for e in row] for row in z], dtype)
         Z.append(z)
 
-        # Reduce the row space by 1 by copying the 0th row to the jth row
+        # Reduce the left null space by 1 by copying the 0th row to the jth row
         for j in range(1, shapes[i][0]):
             x = copy(x)
             x[j,:] = F(random.randint(0, order-1)) * x[0,:]
@@ -616,6 +616,53 @@ def make_luts(field, sub_folder, seed, sparse=False):
     d = {"X": X, "Z": Z}
     save_pickle(d, folder, "left_null_space.pkl")
 
+    set_seed(seed + 211)
+    shapes = [(2,2), (2,3), (2,4), (3,2), (4,2), (3,3)]
+    X = []
+    Z = []
+    for i in range(len(shapes)):
+        deg = shapes[i][1]  # The degree of the vector space
+
+        # Random matrix
+        x = randint_matrix(0, order, shapes[i])
+        X.append(x)
+        x = matrix(FIELD, [[F(e) for e in row] for row in x])
+        z = x.right_kernel()
+        if z.dimension() == 0:
+            z = randint_matrix(0, 1, (0, deg))
+        else:
+            z = z.basis_matrix()
+            z = np.array([[I(e) for e in row] for row in z], dtype)
+        Z.append(z)
+
+        # Reduce the null space by 1 by copying the 0th column to the jth column
+        for j in range(1, shapes[i][1]):
+            x = copy(x)
+            x[:,j] = F(random.randint(0, order-1)) * x[:,0]
+
+            z = x.right_kernel()
+            if z.dimension() == 0:
+                z = randint_matrix(0, 1, (0, deg))
+            else:
+                z = z.basis_matrix()
+                z = np.array([[I(e) for e in row] for row in z], dtype)
+            X.append(np.array([[I(e) for e in row] for row in x], dtype))
+            Z.append(z)
+
+        # Zero matrix
+        x = copy(x)
+        x[:] = F(0)
+        z = x.right_kernel()
+        if z.dimension() == 0:
+            z = randint_matrix(0, 1, (0, deg))
+        else:
+            z = z.basis_matrix()
+            z = np.array([[I(e) for e in row] for row in z], dtype)
+        X.append(np.array([[I(e) for e in row] for row in x], dtype))
+        Z.append(z)
+
+    d = {"X": X, "Z": Z}
+    save_pickle(d, folder, "null_space.pkl")
 
     ###############################################################################
     # Polynomial arithmetic

tests/fields/conftest.py

@@ -353,6 +353,15 @@ def field_left_null_space(field_folder):
     return d
 
 
+@pytest.fixture(scope="session")
+def field_null_space(field_folder):
+    GF, d = read_pickle(field_folder, "null_space.pkl")
+    d["GF"] = GF
+    d["X"] = [GF(x) for x in d["X"]]
+    d["Z"] = [GF(z) for z in d["Z"]]
+    return d
+
+
 ###############################################################################
 # Fixtures for arithmetic methods over finite fields
 ###############################################################################

tests/fields/test_linalg.py

@@ -489,3 +489,24 @@ def test_left_null_space(field_left_null_space):
         z = x.left_null_space()
         assert np.array_equal(z, Z[i])
         assert type(z) is GF
+
+
+def test_null_space_exceptions():
+    GF = galois.GF(2**8)
+    with pytest.raises(ValueError):
+        A = GF.Random(5)
+        A.null_space()
+    with pytest.raises(ValueError):
+        A = GF.Random((2,2,2))
+        A.null_space()
+
+
+def test_null_space(field_null_space):
+    GF, X, Z = field_null_space["GF"], field_null_space["X"], field_null_space["Z"]
+
+    for i in range(len(X)):
+        dtype = random.choice(GF.dtypes)
+        x = X[i].astype(dtype)
+        z = x.null_space()
+        assert np.array_equal(z, Z[i])
+        assert type(z) is GF