Major fixes to pipeline.

Error now are close in plot. Still Lanczos orthogonalization selection
must be fixed.

tests/test_main.py

@@ -1,17 +1,31 @@
 import numpy as np
 import numpy.linalg as LA
+from afgl.ex_1 import compute_g_M, filter_signal_with_fourier, g
 from afgl.util.build_T_matrix import build_T_matrix
 from afgl.util.lanczos import lanczos
-
-"""
-Todo: better test case
-"""
+from pygsp import graphs
 
 
-def test_lanczos_return_correct_solution():
+def g_evaluation_should_respect_chi():
+    A = np.array([[1, 0, 1], [0, 0, 0], [1, 0, 0]])
+    expected_gA = np.array([[0, 1, 0], [1, 1, 1], [0, 1, 1]])
+    assert (expected_gA == g(A).astype(int)).all()
+
+
+def g_evaluation_should_return_matrix_of_zeros():
+    A = 1 / 2 * np.array([[1, 1, 1], [1, 1, 1], [1, 1, 1]])
+
+    assert (g(A).astype(int) == np.zeros((3, 3))).all()
+
+
+def test_lanczos_return_correct_solution_with_dense():
+    """Tests correctness of solution of Lx=s comparing Lanczos projected
+    solution with numpy solve function.
+    """
     N = 1000
     M = 999
 
+    # Generate a good conditioned matrix
     eigvals = np.random.uniform(10000, 100000, N)
     Q, _ = LA.qr(np.random.randn(N, N))
     L = Q @ np.diag(eigvals) @ Q.T
@@ -28,3 +42,35 @@ def test_lanczos_return_correct_solution():
     x_lanczos = V @ y
 
     assert LA.norm(x - x_lanczos) < 1e-10
+
+
+def test_function_g_with_graph_laplacian():
+    N = 1000
+    p = 0.04
+    j = 3
+
+    n = 5
+    M_VALS = 25 * (2 ** np.arange(n))
+    M_VALS = [200]
+
+    for M in M_VALS:
+        s = np.random.randint(1, 10000, N).astype(float)
+        # Normalize s as in request
+        s /= LA.norm(s)
+
+        GRAPHS = [graphs.ErdosRenyi(N, p), graphs.Sensor(N)]
+
+        for G in GRAPHS:
+            G.compute_laplacian()
+            L = G.L
+            V, alp, beta = lanczos(L, s, M + j)
+
+            GLs = filter_signal_with_fourier(G, s)
+
+            g_M = compute_g_M(V[:, 0:M], alp[0:M], beta[0 : M - 1], s)
+            g_Mj = compute_g_M(V[:, 0 : M + j], alp[0 : M + j], beta[0 : M + j - 1], s)
+
+            diff = LA.norm(g_Mj - g_M)
+            e_M = LA.norm(GLs - g_M)
+
+            assert abs(diff - e_M) < 1e-2