added task 1.3

A2.py

@@ -86,3 +86,79 @@ plt.tight_layout()
 plt.show()
 
 #__________________________________________________________________________________
+#1.3 Model fitting
+#for now I used the whole data but idk we that's what they asked for that part
+class GaussianRegression:
+    """Linear Regression with Gaussian Basis Functions"""
+    
+    def __init__(self, sigma=1.0):
+        self.sigma = sigma
+        self.weights = None
+        self.mus = None
+        self.D = None
+    
+    def fit(self, x_train, y_train, D):
+        # Store D for later use in predict
+        self.D = D
+        
+        # create features for training and fit using least squares
+        X_train_basis = gaussian_features(x_train, D, self.sigma)
+        self.weights = np.linalg.lstsq(X_train_basis, y_train, rcond=None)[0]
+        
+        return self
+    
+
+    def predict(self, x_predict):
+        # create features for prediction and predict
+        X_predict_basis = gaussian_features(x_predict, self.D, self.sigma)
+        y_pred = X_predict_basis @ self.weights
+        
+        return y_pred
+    
+    
+
+def true_function(x):
+    return (np.log(x + 1e-10) + 1) * np.cos(x) + np.sin(2*x)
+
+# fit models with different numbers of basis functions and plot
+D_i = [0, 2, 5, 10, 13, 15, 17, 20, 25, 30, 35, 45]
+x_plot = np.linspace(0, 10, 300) 
+
+plt.figure(figsize=(18, 12))
+
+for i, D in enumerate(D_i):
+    plt.subplot(4, 3, i+1)
+    
+    # Create new model for each D value, fit and get predictions 
+    model = GaussianRegression(sigma=1.0)
+    model.fit(x, y_noisy, D)
+    y_hat = model.predict(x_plot)
+    
+    # Ensure y_hat is 1D and has same length as x_plot
+    y_hat = y_hat.flatten() if y_hat.ndim > 1 else y_hat
+    
+    # Plot
+    plt.plot(x_plot, true_function(x_plot), 'b-', label='True Function', linewidth=2, alpha=0.7)
+    plt.plot(x, y_noisy, 'ro', label='Noisy Data', alpha=0.4, markersize=3)
+    plt.plot(x_plot, y_hat, 'g-', label=f'Fitted (D={D})', linewidth=2)
+    
+    plt.ylim(-6, 6)
+    plt.title(f'D = {D}')
+    plt.grid(True, alpha=0.3)
+    plt.legend(fontsize=8)
+
+    # x and y labels
+    if i % 3 == 0:  
+        plt.ylabel('y')
+    if i >= 9:  
+        plt.xlabel('x')
+        
+
+
+plt.tight_layout()
+plt.show()
+
+
+
+#__________________________________________________________________________________
+#1.4 Model Selection