fix project 1 q3

project1/Project1_Q3.py

@@ -135,6 +135,32 @@ def f2(n:int, t: float) -> float:
     """
     return sum([t**i for i in range(n + 1)])
 
+def question_3d():
+    Ns = [25, 50, 100]
+    ns = Ns
+    t = np.linspace(-5, 5, 1000)
+    f_t = f1(t)
+    plt.figure(figsize=(15, 10))
+    for i in range(len(Ns)):
+        N = Ns[i]
+        n = ns[i]
+        A = np.zeros((N + 1, n + 1), dtype=float)
+        A, b = build_A(N, n, f1)
+        x = householder_lstsq(A, b)
+        p_t = sum([x[j] * t**j for j in range(n + 1)])
+        plt.subplot(1, 3, i + 1)
+        plt.plot(t, f_t, label='f(t)', color='blue')
+        plt.plot(t, p_t, label='p(t)', color='red', linestyle='--')
+        plt.title(f'N={N}, n={n}')
+        plt.xlabel('t')
+        plt.ylabel('y')
+        plt.legend()
+        plt.grid(True, alpha=0.3)
+    plt.suptitle('Least Squares Polynomial Approximation using Householder QR')
+    plt.tight_layout(rect=[0, 0.03, 1, 0.95])
+    plt.savefig('Project1_A3d_least_squares_approximation.png')
+    #plt.show()
+
 def question_3e():
     # n = 4, 6, 8, 10, ..., 20
     ns = list(range(4, 21, 2))
@@ -161,6 +187,7 @@ def question_3e():
 
 if __name__ == "__main__":
     question_3c()
+    question_3d()
     question_3e()