Fix lanczos test.

Matrix was badly conditioned.

tests/test_main.py

@@ -8,20 +8,22 @@ Todo: better test case
 
 
 def test_lanczos_return_correct_solution():
-    N = 6
-    M = 4
+    N = 1000
+    M = 999
+
+    eigvals = np.random.uniform(10000, 100000, N)
+    Q, _ = LA.qr(np.random.randn(N, N))
+    L = Q @ np.diag(eigvals) @ Q.T
 
-    A = np.random.randint(1, 10, size=(N, N))
-    L = (A + A.T) / 2
     s = np.random.randint(1, 10, N)
     [V, alp, beta] = lanczos(L, s, M)
 
     T = np.diag(alp) + np.diag(beta, -1) + np.diag(beta, 1)
 
-    x = LA.solve(A, s)
+    x = LA.solve(L, s)
     e_1 = np.zeros(M)
     e_1[0] = 1
     y = (LA.inv(T) @ e_1) * LA.norm(s)
     x_lanczos = V @ y
 
-    assert LA.norm(x - x_lanczos) < 1e-3
+    assert LA.norm(x - x_lanczos) < 1e-10