Tweak some params

app.py

@@ -284,8 +284,8 @@ def train_coefficients(m, method, quality, rand_or_det):
     else:
         theta = np.column_stack(
             (
-                np.linspace(-0.5, 0.5, m),  # Nonlinear spacing for x
-                np.linspace(-2.5, 2.5, m),  # Nonlinear spacing for y
+                np.linspace(-5, 5, m),  # Linear spacing for x
+                np.linspace(-25, 25, m),  # Linear spacing for y
             )
         )
 
@@ -304,26 +304,26 @@ def train_coefficients(m, method, quality, rand_or_det):
         theta=theta,
     )
 
-    # Create grids for x and t
-    # x_random = np.random.uniform(0, 1, 10 * n_x)  # Spatial grid
-    # t_random = np.random.uniform(0, 5, 10 * n_t)  # Temporal grid
-    # X, T = np.meshgrid(x_random, t_random)  # Create the mesh grid
+    # Compute the average error
+    #
+    x = np.linspace(0, 1, n_x)  # Spatial grid
+    t = np.linspace(0, 5, n_t)  # Temporal grid
+    X, T = np.meshgrid(x, t)
+
     # Compute the real solution over the grid
-    # U_real = complex_heat_eq_solution(X, T, glob_k, glob_a, glob_b, glob_c)
-    # print(U_real.shape)
-    # print(U_real)
+    U_real = complex_heat_eq_solution(X, T, glob_k, glob_a, glob_b, glob_c)
+
     # Compute the selected approximation
-    # U_approx = np.zeros_like(U_real)
-    # for i, xpos in enumerate(x_random):
-    #    for j, tpos in enumerate(t_random):
-    #        Phi_at_x_t = test_approx([xpos, tpos], theta, method)
-    #        U_approx[j, i] = np.dot(Phi_at_x_t, alpha)
+    U_approx = np.zeros_like(U_real)
+    for i, t_val in enumerate(t):
+        Phi_at_t = Phi[i * n_x : (i + 1) * n_x]
+        U_approx[i, :] = np.dot(Phi_at_t, alpha)
 
     # Compute average error
-    # avg_err = np.mean(np.abs(U_real - U_approx))
+    avg_err = np.mean(np.abs(U_real - U_approx))
 
     return (
-        f"Training completed in {end_time} seconds."  # The average error is {avg_err}."
+        f"Training completed in {end_time} seconds. The average error is {avg_err}."
     )