From 323f757b142dc6e82248f56ea056f12d8e2b02bd Mon Sep 17 00:00:00 2001 From: Zhe Yuan Date: Tue, 21 Oct 2025 16:49:59 -0400 Subject: [PATCH] fix project1 q3 bug --- ...oject1_A3c_least_squares_approximation.png | Bin 72403 -> 72377 bytes ...oject1_A3d_least_squares_approximation.png | Bin 91320 -> 93241 bytes project1/Project1_A3e_coefficient_error.png | Bin 38823 -> 38637 bytes project1/Project1_Q3.py | 14 +++++++------- 4 files changed, 7 insertions(+), 7 deletions(-) diff --git a/project1/Project1_A3c_least_squares_approximation.png b/project1/Project1_A3c_least_squares_approximation.png index 874382baacf1052b20a2c7317e47f798a7700e81..f6d6f8c09f2375b3575a134e097f013c7451fac6 100644 GIT binary patch literal 72377 zcmeFZWmJ}3|2Bw;fheKUD59uHBOL}3ii9XgNQZQH*`N}F(xs9Dg3=92iGZl6G)RlU zg@AO;ar(^jpP6^oe0skQYq{=QxniID-23-CYM&2Pl;rm8V%SASMz%*mUgioJ*|u&n zvQ2+?Y{$QF+@Csy|A;wVxbCE8YwF}`;9x>_*}%!p%GSxs-0+Z#iG!oLt&IRTA1}A? zsY5rNoa`LMczCS;=M~(x4rV-xZ;xEXr|h(o*K{N!+iO7l*_0-oYEHI^j7&l1>{Yke 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SJ>f$4z>?p;J89S9v;QBIji?p? diff --git a/project1/Project1_Q3.py b/project1/Project1_Q3.py index 474dcda..2125899 100644 --- a/project1/Project1_Q3.py +++ b/project1/Project1_Q3.py @@ -73,18 +73,18 @@ def f1(t: float) -> float: """ return 1.0 / (1.0 + t**2) -def build_A(N: int, n: int, f: callable) -> tuple[np.ndarray, np.ndarray]: +def build_A(N: int, n: int, f: callable, f_range: tuple) -> tuple[np.ndarray, np.ndarray]: """ Build the matrix A for the least squares problem. Parameters: n + 1 (int): The number of columns in the matrix A. - + f_range (tuple): The range of the function f. Returns: np.ndarray: The constructed matrix A. """ """ - {t_j}j=0->N, t_0=-5, t_N=5, t_j divides [-5, 5] equally + {t_j}j=0->N, t_0=f_range[0], t_N=f_range[1], t_j divides [f_range[0], f_range[1]] equally A = [[1, t_0, t_0^2, t_0^3, ..., t_0^n], [1, t_1, t_1^2, t_1^3, ..., t_1^n], ... @@ -95,7 +95,7 @@ def build_A(N: int, n: int, f: callable) -> tuple[np.ndarray, np.ndarray]: Ax = b, x is the coeffs of the polynomial """ A = np.zeros((N + 1, n + 1), dtype=float) - t = np.linspace(-5, 5, N + 1) + t = np.linspace(f_range[0], f_range[1], N + 1) for i in range(N + 1): A[i, :] = [t[i]**j for j in range(n + 1)] b = np.array([f(t_i) for t_i in t]) @@ -113,7 +113,7 @@ def question_3c(): N = Ns[i] n = ns[i] A = np.zeros((N + 1, n + 1), dtype=float) - A, b = build_A(N, n, f1) + A, b = build_A(N, n, f1, (-5, 5)) x = householder_lstsq(A, b) p_t = sum([x[j] * t**j for j in range(n + 1)]) plt.subplot(1, 3, i + 1) @@ -145,7 +145,7 @@ def question_3d(): N = Ns[i] n = ns[i] A = np.zeros((N + 1, n + 1), dtype=float) - A, b = build_A(N, n, f1) + A, b = build_A(N, n, f1, (-5, 5)) x = householder_lstsq(A, b) p_t = sum([x[j] * t**j for j in range(n + 1)]) plt.subplot(1, 3, i + 1) @@ -169,7 +169,7 @@ def question_3e(): losses = [] for n in ns: N = 2 * n - A, b = build_A(N, n, lambda t: f2(n, t)) + A, b = build_A(N, n, lambda t: f2(n, t), (0, 1)) x = householder_lstsq(A, b) true_coeffs = np.array([1.0 for _ in range(n + 1)]) loss = np.linalg.norm(x - true_coeffs)