From 7208e0284000725b5bf25a40b0397f5ef57dd8a1 Mon Sep 17 00:00:00 2001 From: p11menova Date: Wed, 26 Feb 2025 21:18:49 +0300 Subject: [PATCH 01/10] lab passed --- .../pimenova_409342/lab1/gauss-zeidel.py" | 205 ++++++++++++++++++ .../pimenova_409342/lab1/matrix.txt" | 6 + ...\320\260\320\225\320\220_\320\2403213.pdf" | Bin 0 -> 896573 bytes 3 files changed, 211 insertions(+) create mode 100644 "\320\2403213/pimenova_409342/lab1/gauss-zeidel.py" create mode 100644 "\320\2403213/pimenova_409342/lab1/matrix.txt" create mode 100644 "\320\2403213/pimenova_409342/lab1/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2611_\320\237\320\270\320\274\320\265\320\275\320\276\320\262\320\260\320\225\320\220_\320\2403213.pdf" diff --git "a/\320\2403213/pimenova_409342/lab1/gauss-zeidel.py" "b/\320\2403213/pimenova_409342/lab1/gauss-zeidel.py" new file mode 100644 index 0000000..109bc6e --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab1/gauss-zeidel.py" @@ -0,0 +1,205 @@ +import os + +global N, EPS + + +def print_M(M): + for i in M: + for j in i: + print(str(round(j, 4)).center(6), end=" ") + print() + print() + + +def read_from_file(): + with open("lab1/matrix.txt") as f: + n = int(f.readline()) + if n > 20: + raise ValueError + + eps = float(f.readline()) + M = [i.rstrip().split(" ") for i in f.readlines()] + return eps, n, M + + +def validate_matrix(M): + if len(M) != N: + raise ValueError + + for i in range(len(M)): + if (len(M[i])) != N + 1: + raise ValueError + M[i] = list(map(float, M[i])) + return M + + +# в матрицe N строк и N+1 столцов +def check_diagonal_dominance(M): + for i in range(N): + if not (abs(M[i][i]) >= sum([abs(M[i][j]) for j in range(N) if j != i])): + return False + return True + + +def change_to_get_diagonal_dominance(M): + X = ['x' + str(i) for i in range(N)] # чтоб сохранить коэфф при переменных + for i in range(N): + for j in range(i, N): + M[i], M[j] = M[j], M[i] + + # поменяла местами строки и теперь для каждой такой новой матрицы надо поменять местами столбцы + + for k in range(N): + for h in range(k, N): + for _ in range(N): + M[_][k], M[_][h] = M[_][h], M[_][k] + + if check_diagonal_dominance(M): + X[k], X[h] = X[h], X[k] + return X, M + return None, None + + +def count_norm(M): + res = 0 + for i in M: + res = max(res, sum([abs(j) for j in i])) + + return res + + +def get_C_D_matrix(M): + C = [] + D = [] + for i in range(N): + a_ii = M[i][i] if M[i][i] != 0 else 1 + c = [] + for j in range(N + 1): + if j == N: + D.append(M[i][j] / a_ii) + continue + if i == j: + c.append(0) + else: + c.append(-1 * M[i][j] / a_ii) + C.append(c) + if all([c1==0 for c1 in c]): + if D[-1] != 0: + print("cистема не совместна! решений НЕТ") + exit(0) + if D[-1] == 0: + print("да тут ваще бесконечно количество решений..") + exit(0) + + return C, D + + +def read_M(): + start = input("введите f, если хотите прочитать данные из файла matrix.txt и любой другой символ в ином случае:") + + if start.strip() == "f" and os.path.exists("lab1/matrix.txt"): + try: + eps, n, M = read_from_file() + + return eps, n, M + + except ValueError: + print("невалидные входные данные...\nзавершение работы программы..") + exit(1) + else: + n = int(input("введите размерность матрицы (≤20): ")) + eps = float(input("введите точность: ")) + print("введите матрицу:") + M = [input().strip().split() for _ in range(n)] + return eps, n, M + + +def get_tochnost(x_k, x_k1): + # max(abs(x_k_i-x_k1_i)) + a = [abs(x_k[i] - x_k1[i]) for i in range(len(x_k))] + return max(a) + + +def put_in_correct_order(x_k, X): + res = [0] * N + for i in range(N): + res[i] = round(x_k[X.index(f'x{i}')], 5) + return res + + +def gauss_zeidel(C, D, X): + print("\nРАСЧЁТЫ ПО МЕТОДУ ГАУССА-ЗЕЙДЕЛЯ:\n") + k = 0 + # x_k это D + # x_k+1 который мы сча будем заполнять это + + x_k = D # имеет вид d1 d2 d3 + x_k1 = [0] * N + print(f" номер итерации |{'x^(k)'.center(32)}| max(|x^(k)_i-x^(k+1)_i|) ") + print("-" * 90) + print(f" 0 |{str(put_in_correct_order(x_k, X)).center(32)}| - ") + while k == 0 or not (get_tochnost(x_k, x_k1) <= EPS): + x_k, x_k1 = x_k1, [0] * N + # print(f"x({k})", x_k) + for i in range(N): + x = 0 + # всего N шагов и на i-том мы берем i-1 слагаемых из x_k+1 + for j in range(i, N): + x += C[i][j] * x_k[j] + + for h in range(0, i): + x += C[i][h] * x_k1[h] + + x += D[i] + x_k1[i] = x + # здесь получили x_k1 + k += 1 + print( + f" {k} |{str(put_in_correct_order(x_k1, X)).center(32)}| {round(get_tochnost(x_k, x_k1), 4)} ") + + return k, x_k1 + + +def main(): + global N, EPS + try: + EPS, N, M = read_M() + M = validate_matrix(M) + print("БЫЛО") + print(''.join([('x' + str(i)).center(6) for i in range(N)])) + print_M(M) + X, diagonalized_M = change_to_get_diagonal_dominance(M) + + if not diagonalized_M: + print("невозможно добиться диагонального преобладания(..\n") + print("проверяем значение нормы матрицы", count_norm(M)) + if count_norm(M) >= 1: + print("ну вот( условие сходимости не выполнено(\nсистема не сойдется к ответу данным численным методом " + "или будет делать это ОЧЕНЬ долго(") + exit(1) + print("ура! условие сходимости выполнено! продолжаем..") + print() + if diagonalized_M: + print("СТАЛО для диагонального преобладания") + print(''.join([x.center(6) for x in X])) + print_M(diagonalized_M) + + C, D = get_C_D_matrix(diagonalized_M) + print("получаем матрицу С") + print_M(C) + print("и столбик свободных коэфф D:\n" + '\n'.join(list(map(str, D)))) + + k, x_k1 = gauss_zeidel(C, D, X) + + print("ИТОГО:") + x_k1 = put_in_correct_order(x_k1, X) + + print( + f"\t-потребовалось {k} итераций \n\t-ответ с учетом погрешности: {x_k1}\n\t-округленный ответ: {list([round(i, 3) for i in x_k1])}") + + except ValueError: + print("невалидные входные данные...\nзавершение работы программы..") + exit(1) + + +main() diff --git "a/\320\2403213/pimenova_409342/lab1/matrix.txt" "b/\320\2403213/pimenova_409342/lab1/matrix.txt" new file mode 100644 index 0000000..3c533b2 --- 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zG4Z%?2+twO2GJweIfw9^LwL?1JQwnF$i9&GgF|@EAv}ld3bHx!oI`jnoX(T&lIugri6Qln`+@Kr-mWIgB0Lvz zDv34_o^uG#IfUmN!gC?Vi);h21K~M`@Ej7!$odeT!a}MD-hwz+3c+Md_=aBfk?XLie&RBSa=kRA5i7^mzD#hah$%u%ITpv8ba~|P2 zkMLZ`mnYgqc+Mj{=MkRs$bLJI@SI0@F66}+ z9DZB`sSmLO;W?x&B4rUf5T5f0&v}IB@JBhxHV~fk2+w&WKIajh^GJNoBRuC3p7RLL zd4%UY!gC(sIgjuhlBdZrKzPn0@j3j^3t1N7IlMT5=ppMI;W>}Q=P}+oJV*ryt6{si||}{H;B|j zp1TOod4%UY!gKfu6Qm8~ejq&O5uOWq*F>KYp7Th2&LceM5uWo%e9j|0=MkO@+2rl| z2M-Nlf1`b#Ih;5EXWGlaTZ6eFlF5bhD6ve~V-(ATc&5D!GS6Y2iezxSDk>`%UX>wb zN|?Lt%EC(>@Wu-vqao&OugAbvxX2DUoGbzd+v|bHAbz(+4xRwa`}TSYSeByq4de>B z44&=n^b~Mn4L*%X25C^DTzdrr?*|YvIPw?E;0X)!pnZMtl!Un^l0kSb8W(thjRT*x zy`CJFzUUq)o%M>yh#M6JuBEmca0@Y#KTJRG7`?je{67Faexr2& literal 0 HcmV?d00001 From d2a95aab3026c1c0072100ff8701cdccd81a17b1 Mon Sep 17 00:00:00 2001 From: p11menova Date: Thu, 13 Mar 2025 16:09:20 +0300 Subject: [PATCH 02/10] lab1 is passed --- "\320\2403213/pimenova_409342/lab1/README.md" | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git "a/\320\2403213/pimenova_409342/lab1/README.md" "b/\320\2403213/pimenova_409342/lab1/README.md" index 5dd8dcc..a408f8a 100644 --- "a/\320\2403213/pimenova_409342/lab1/README.md" +++ "b/\320\2403213/pimenova_409342/lab1/README.md" @@ -1 +1,5 @@ -Лабораторная работа 1 +### лабораторная работа 1 + +#### «решение системы линейных алгебраических уравнений СЛАУ» + +вариант **10** – *метод Гаусса-Зейделя* From 11eb83693422189ced029c14c4e6da5a5a8f0800 Mon Sep 17 00:00:00 2001 From: p11menova Date: Sun, 23 Mar 2025 23:44:25 +0300 Subject: [PATCH 03/10] lab2 done --- "\320\2403213/pimenova_409342/lab2/README.md" | 5 +- "\320\2403213/pimenova_409342/lab2/main.py" | 211 ++++++++++++++++++ .../lab2/nonlinear_equation.py" | 96 ++++++++ .../pimenova_409342/lab2/nonlinear_system.py" | 150 +++++++++++++ 4 files changed, 461 insertions(+), 1 deletion(-) create mode 100644 "\320\2403213/pimenova_409342/lab2/main.py" create mode 100644 "\320\2403213/pimenova_409342/lab2/nonlinear_equation.py" create mode 100644 "\320\2403213/pimenova_409342/lab2/nonlinear_system.py" diff --git "a/\320\2403213/pimenova_409342/lab2/README.md" "b/\320\2403213/pimenova_409342/lab2/README.md" index 2999024..a04764a 100644 --- "a/\320\2403213/pimenova_409342/lab2/README.md" +++ "b/\320\2403213/pimenova_409342/lab2/README.md" @@ -1 +1,4 @@ -Лабораторная работа 2 +### лабораторная работа 2 + +#### «численное решение нелинейных уравнений и систем» +вариант **9** \ No newline at end of file diff --git "a/\320\2403213/pimenova_409342/lab2/main.py" "b/\320\2403213/pimenova_409342/lab2/main.py" new file mode 100644 index 0000000..3f43760 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab2/main.py" @@ -0,0 +1,211 @@ +from nonlinear_system import solve_nonlinear_system, draw_system_graphics +from nonlinear_equation import simple_iteration, chord_method, newton_method +import numpy as np +import matplotlib.pyplot as plt + + +def f1(x): + return -1.8 * x ** 3 - 2.94 * x ** 2 + 10.37 * x + 5.38 + + +def phi1(x): + return 0.174 * x ** 3 + 0.284 * x ** 2 - 0.519 + + +def dphi1_dx(x): + return 0.174 * 3 * x + 0.284 * 2 * x + + +def df1_dx(x): + return -1.8 * 3 * x ** 2 - 2.94 * 2 * x + 10.37 + + +def df1_dx2(x): + return -1.8 * 6 * x - 2.94 * 2 + + +def f2(x): + return 2 * x ** 3 + 3.41 * x ** 2 - 23.74 * x + 2.95 + + +def phi2(x): + return -2 * x ** 3 / 23.74 - 3.41 * x ** 2 / 23.74 - 2.95 / 23.74 + + +def dphi2_dx(x): + return -2 * 3 / 23.74 * x ** 2 - 3.41 * 2 / 23.74 * x + + +def df2_dx(x): + return 6 * x ** 2 + 3.41 * 2 * x - 23.74 + + +def df2_dx2(x): + return 12 * x + 3.41 * 2 + + +def f3(x): + return x ** 3 - 3.78 * x ** 2 + 1.25 * x + 3.49 + + +def df3_dx(x): + return 3 * x ** 2 - 3.78 * 2 * x + 1.25 + + +def df3_dx2(x): + return 8 * x - 3.78 * 2 + + +def phi3(x): + return (-x ** 3 + 3.78 * x ** 2 - 3.49) / 1.25 + + +def dphi3_dx(x): + return -3 / 1.25 * x ** 2 + 3.78 / 1.25 * x + + +def draw_graphics(num, root_x=None): + X = np.linspace(-5, 5, 400) + + if num == 1: + Y = f1(X) + if root_x: root_y = f1(root_x) + elif num == 2: + Y = f2(X) + if root_x: root_y = f2(root_x) + + else: + Y = f3(X) + if root_x: root_y = f3(root_x) + + plt.figure(figsize=(8, 8)) + + plt.plot(X, Y, color='cyan') + if root_x: + plt.scatter(root_x, root_y, color='hotpink') + plt.text(root_x + 0.1, root_y + 0.1, f'({round(root_x, 3)}, {round(root_y, 3)})', color='hotpink') + + plt.title('график функции') + plt.xlabel('x') + plt.ylabel('y') + + plt.axhline(0, color='black', linewidth=0.5) + plt.axvline(0, color='black', linewidth=0.5) + + plt.legend(['f(x)', 'root'] if root else ['f(x)']) + + plt.grid(True) + plt.show() + + +def solve_with_simple_iteration_method(eq_num): + correct = False + while not correct: + try: + a0, b0 = map(float, input("введите через пробел границы интервала начального приближения корня:").split()) + correct = a0 < b0 + + except Exception: + print("неет еще раз") + continue + + if eq_num == 1: + return simple_iteration(a0, b0, f1, phi1, dphi1_dx) + elif eq_num == 2: + return simple_iteration(a0, b0, f2, phi2, dphi2_dx) + elif eq_num == 3: + return simple_iteration(a0, b0, f3, phi3, dphi3_dx) + + +def solve_with_chord_method(eq_num): + correct = False + while not correct: + try: + a0, b0 = map(float, input("введите через пробел границы интервала начального приближения корня:").split()) + correct = a0 < b0 + + except Exception: + print("неет еще раз") + continue + + if eq_num == 1: + return chord_method(a0, b0, f1, df1_dx2) + elif eq_num == 2: + return chord_method(a0, b0, f2, df2_dx2) + elif eq_num == 3: + return chord_method(a0, b0, f3, df3_dx2) + + +def solve_with_newton_method(eq_num): + correct = False + while not correct: + try: + x0 = float(input("введите x0 - начальное приближение:")) + correct = True + + except Exception: + print("неет еще раз") + continue + if eq_num == 1: + return newton_method(x0, f1, df1_dx) + elif eq_num == 2: + return newton_method(x0, f2, df2_dx) + elif eq_num == 3: + return newton_method(x0, f3, df3_dx) + + +if __name__ == "__main__": + eq_or_system = input( + "приви! введите 1, если хотите решить нелинейное уравнение и любой другой символ, если систему:") + if eq_or_system == '1': + print("1)\t-1.8x^3 - 2.94x^2 + 10.37x + 5.38 = 0\n") + print("2)\t2x^3 + 3.41x^2 - 23.74x + 2.95 = 0\n") + print("3)\tx^3 - 3.78x^2 + 1.25x + 3.49") + + eq_num = int(input("введите номер уравнения, которое хотите решить:")) + print('1) метод хорд\n2) метод Ньютона\n3) метод простой итерации') + method_number = int(input("введите номер метода, которым хотите решить уравнение:")) + + root, msg = -1, '' + if method_number == 1: + pass + root, msg = solve_with_chord_method(eq_num) + elif method_number == 2: + root, msg = solve_with_newton_method(eq_num) + else: + root, msg = solve_with_simple_iteration_method(eq_num) + + if not root: + print("ERROR:", msg) + draw_graphics(eq_num) + else: + print(msg) + print(f"SUCCESS: найденный корень уравнения = {round(root, 3)}") + + draw_graphics(eq_num, root) + + else: + print("1){sin(x+y) = 1.5x - 0.1") + print(" {x^2+2y^2 =1\n") + print("2){tg(x+y+0.3) = x^2") + print(" {0.9x^2+2y^2 = 1\n") + + syst_num = int(input("введите номер системы:")) + + correct = False + while not correct: + try: + a0, b0 = map(float, input("введите начальные приближения a0 b0 через пробел:").split()) + correct = True + + except Exception: + print("неет еще раз") + continue + + x_root, y_root, msg = solve_nonlinear_system(a0, b0, syst_num) + if x_root is None or y_root is None: + print(msg) + else: + print(msg) + print(f"SUCCESS: найденный корень уравнения = ({round(x_root, 3)}, {round(y_root, 3)})") + draw_system_graphics(x_root, y_root, syst_num) diff --git "a/\320\2403213/pimenova_409342/lab2/nonlinear_equation.py" "b/\320\2403213/pimenova_409342/lab2/nonlinear_equation.py" new file mode 100644 index 0000000..b80a98d --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab2/nonlinear_equation.py" @@ -0,0 +1,96 @@ +EPS = 0.001 +MAX_ITER = 1000 + + +def simple_iteration(a0, b0, f, phi, dphi_dx): + if dphi_dx(a0) >= 1 or dphi_dx(b0) >= 1: + return None, "условие сходимости метода простой итерации не выполняется" + + x0 = a0 + x1 = phi(x0) + result_text = '' + iter_count = 0 + try: + while abs(x0 - x1) >= EPS: + if iter_count == MAX_ITER: + return None, "уравнение не имеет корней на данном промежутке" + + result_text += ''.join([i.center(20) for i in + f"№={iter_count} x_k={round(x0, 3)} x_k1={round(x1, 3)} f(x_k1)={round(f(x1), 3)} |x0-x1|={round(abs(x0 - x1), 3)}".split()]) + '\n' + x0 = x1 + x1 = phi(x0) + iter_count += 1 + + result_text += ''.join([i.center(20) for i in + f"№={iter_count} x_k={round(x0, 3)} x_k1={round(x1, 3)} f(x_k1)={round(f(x1), 3)} |x0-x1|={round(abs(x0 - x1), 3)}".split()]) + + return x1, result_text + + except Exception: + return None, "уравнение не решится данным методом(" + + +def newton_method(x0, f, df): + x1 = None + result_msg = '' + iter_count = 0 + while x1 is None or abs(x0 - x1) >= EPS and abs(f(x1)) >= EPS: + if iter_count == MAX_ITER: + return None, "превышено максимальное количество итераций" + + x0 = x1 if x1 is not None else x0 + x1 = x0 - f(x0) / df(x0) + result_msg += ''.join([i.center(16) for i in + f"№={iter_count} x_i={round(x0, 3)} x_i+1={round(x1, 3)} f(x_i+1)={round(f(x1), 3)} f'(x_i)={round(df(x0), 3)} |x0-x1|={round(abs(x0 - x1), 3)}".split()]) + '\n' + iter_count += 1 + + return x1, result_msg + + +def chord_method(a, b, f, df_dx2): + if f(a) * f(b) > 0: + return None, "уравнение не имеет корней на данном промежутке" + + x0 = None + x = None + iter_count = 0 + result_msg = '' + if not (f(a) * df_dx2(a) > 0 or f(b) * df_dx2(b) > 0): + return None, f"уравнение не сойдется данным методом, " \ + f"поскольку не выполняется условие совпадения знака функции на конце отрезка и знака второй производной\n" \ + f"f(a)={round(f(a), 3)} df_dx2(a)={round(df_dx2(a), 3)} f(b)={round(f(b), 3)} df_dx2(b)={round(df_dx2(b), 3)}" + if f(a) * df_dx2(a) > 0: # b - fixed_end + + while iter_count == 0 or abs(x0 - x) >= EPS: + + if iter_count == MAX_ITER: + return None, "превышено максимальное количество итераций" + + x0 = x if x != None else a + x = (a * f(b) - b * f(a)) / (f(b) - f(a)) + + result_msg += ''.join( + [i.center(14) for i in f"№={iter_count} a={round(a, 3)} b={round(b, 3)} x={round(x, 3)} " + f"f(a)={round(f(a), 3)} f(b)={round(f(b), 3)} f(x)={round(f(x), 3)} " + f"|x_i+1-x_i|={round(abs(x - x0), 3)}".split()]) + '\n' + b = x + iter_count += 1 + + if f(b) * df_dx2(b) > 0: + while iter_count == 0 or abs(x0 - x) >= EPS: + + if iter_count == MAX_ITER: + return None, "превышено максимальное количество итераций" + x0 = x if x is not None else b + x = (a * f(b) - b * f(a)) / (f(b) - f(a)) + result_msg += ''.join( + [i.center(14) for i in f"№={iter_count} a={round(a, 3)} b={round(b, 3)} x={round(x, 3)} " + f"f(a)={round(f(a), 3)} f(b)={round(f(b), 3)} f(x)={round(f(x), 3)} " + f"|x_i+1-x_i|={round(abs(x - x0), 3)}".split()]) + '\n' + a = x + iter_count += 1 + + result_msg += ''.join([i.center(14) for i in f"№={iter_count} a={round(a, 3)} b={round(b, 3)} x={round(x, 3)} " + f"f(a)={round(f(a), 3)} f(b)={round(f(b), 3)} f(x)={round(f(x), 3)} " + f"|x_i+1-x_i|={round(abs(x - x0), 3)}".split()]) + return x, result_msg diff --git "a/\320\2403213/pimenova_409342/lab2/nonlinear_system.py" "b/\320\2403213/pimenova_409342/lab2/nonlinear_system.py" new file mode 100644 index 0000000..980257b --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab2/nonlinear_system.py" @@ -0,0 +1,150 @@ +from math import sin, cos, tan +import numpy as np +import matplotlib.pyplot as plt + +MAX_ITER = 1000 + + +def system1_f(x, y): + return sin(x + y) - 1.5 * x + 0.1 + + +def system1_g(x, y): + return x ** 2 + 2 * y ** 2 - 1 + + +def dfdx1(x, y): + return cos(x + y) - 1.5 + + +def dfdy1(x, y): + return cos(x + y) + + +def dgdx1(x, y): + return 2 * x + + +def dgdy1(x, y): + return 4 * y + + +def system2_f(x, y): + return tan(x * y + 0.3) - x ** 2 + + +def system2_g(x, y): + return 0.9 * x ** 2 + 2 * y ** 2 - 1 + + +def dfdx2(x, y): + return -2 * x + y / (cos((10 * y * x + 3) / 10)) ** 2 + + +def dfdy2(x, y): + return x / (cos((10 * x * y * 3) / 10)) ** 2 + + +def dgdx2(x, y): + return 1.8 * x + + +def dgdy2(x, y): + return 4 * y + + +def solve_linear_system(M) -> (float, float): + A = np.array([[M[0][0], M[0][1]], [M[1][0], M[1][1]]]) + B = np.array([M[0][2], M[1][2]]) + + try: + solution = np.linalg.solve(A, B) + return solution + except np.linalg.LinAlgError: + return None, None + + +def print_M(M): + for i in M: + for j in i: + print(str(round(j, 4)).center(6), end=" ") + print() + + +def draw_system_graphics(root_x, root_y, num): + x = np.linspace(-2, 2, 400) + y = np.linspace(-2, 2, 400) + + X, Y = np.meshgrid(x, y) + + if num == 1: + Z1 = np.sin(X + Y) - (1.5 * X - 0.1) + Z2 = X ** 2 + 2 * Y ** 2 - 1 + + else: + Z1 = np.tan(X * Y + 0.3) - x ** 2 + Z2 = 0.9 * X ** 2 + 2 * Y ** 2 - 1 + + plt.figure(figsize=(8, 8)) + + f_label = 'sin(x+y) - 1.5x + 0.1' if num == 1 else 'tg(xy + 0.3) -x^2' + g_label = 'x^2+2y^2-1' if num == 1 else '0.9x^2 + 2y^2 - 1' + + plt.contour(X, Y, Z1, levels=[0], colors='cyan') + plt.contour(X, Y, Z2, levels=[0], colors='hotpink') + plt.scatter(root_x, root_y, color='hotpink') + plt.text(root_x + 0.1, root_y + 0.1, f'({round(root_x, 3)}, {round(root_y, 3)})', color='hotpink') + + plt.title('графики системы уравнений') + plt.xlabel('x') + plt.ylabel('y') + plt.axhline(0, color='black', linewidth=0.5) + plt.axvline(0, color='black', linewidth=0.5) + + plt.legend(['root', f_label, g_label]) + + plt.grid(True) + plt.show() + + +def solve_nonlinear_system(x0, y0, num) -> (float, float, str): + x, y = x0, y0 + result_msg = '' + iter_count = 1 + + while (x == x0 and y == y0) or (abs(x0 - x) >= 0.01 or abs(y0 - y) >= 0.01): + if iter_count == MAX_ITER: + return None, None, "превышено максимальное количество итераций" + if num == 1: + M = [ + [dfdx1(x, y), dfdy1(x, y), -1 * system1_f(x, y)], + [dgdx1(x, y), dgdy1(x, y), -1 * system1_g(x, y)] + ] # якобиан системы + else: + M = [ + [dfdx2(x, y), dfdy2(x, y), -1 * system2_f(x, y)], + [dgdx2(x, y), dgdy2(x, y), -1 * system2_g(x, y)] + ] # якобиан системы + + delta_x, delta_y = solve_linear_system(M) + if not delta_x or not delta_x: + return None, None, "система не имеет решений(" + + x0, y0 = x, y + x = x0 + delta_x + y = y0 + delta_y + + result_msg += ''.join( + [i.center(15) for i in f"№={iter_count} delta_x={round(delta_x, 3)} delta_y={round(delta_y, 3)} " + f"x={round(x, 3)} y={round(y, 3)}".split()]) + "\n" + iter_count += 1 + return x, y, result_msg + +# solve_nonlinear_system(1, 0.5, 1) +# solve_nonlinear_system(-1,-1,1) +# solve_nonlinear_system(-1, -1, 2) + +# polovina(-3.66, -2.66) +# iteracia(-0.96) + +# secant(1.49, 2.49) From 5a3309a8968f5496a5f2ffd76a1ac4cb4b407166 Mon Sep 17 00:00:00 2001 From: p11menova Date: Sun, 23 Mar 2025 23:52:43 +0300 Subject: [PATCH 04/10] added report --- ...0\276\320\262\320\260\320\225\320\220.pdf" | Bin 0 -> 2028223 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"\320\2403213/pimenova_409342/lab3/README.md" | 5 +- .../pimenova_409342/lab3/integral_methods.py" | 130 ++++++++++++++++++ "\320\2403213/pimenova_409342/lab3/main.py" | 79 +++++++++++ .../pimenova_409342/lab3/storage.py" | 22 +++ 4 files changed, 235 insertions(+), 1 deletion(-) create mode 100644 "\320\2403213/pimenova_409342/lab3/integral_methods.py" create mode 100644 "\320\2403213/pimenova_409342/lab3/main.py" create mode 100644 "\320\2403213/pimenova_409342/lab3/storage.py" diff --git "a/\320\2403213/pimenova_409342/lab3/README.md" "b/\320\2403213/pimenova_409342/lab3/README.md" index facfbc9..0448052 100644 --- "a/\320\2403213/pimenova_409342/lab3/README.md" +++ "b/\320\2403213/pimenova_409342/lab3/README.md" @@ -1 +1,4 @@ -Лабораторная работа 3 +### лабораторная работа 3 + +#### «численное интегрирование» +вариант **9** \ No newline at end of file diff --git "a/\320\2403213/pimenova_409342/lab3/integral_methods.py" "b/\320\2403213/pimenova_409342/lab3/integral_methods.py" new file mode 100644 index 0000000..357289e --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab3/integral_methods.py" @@ -0,0 +1,130 @@ +def runge_rule(I_0, I_1, eps, name): + divi = 4 if "simpson" in name else 2 + return abs(I_1 - I_0) / (2 ** divi - 1) <= eps + + +def left_rectangles(a, b, n, f, eps) -> (float, str): + I_0, I_1 = 0, 0 + iter_count = 0 + result_msg = "" + + while (I_0 == 0 and I_1 == 0) or not runge_rule(I_0, I_1, eps, left_rectangles.__name__): + I_0, I_1 = 0, 0 + iter_count += 1 + delta_x = (b - a) / (2 * n) + for i in range(2 * n): + x_i = a + delta_x * i + I_1 += f(x_i) * delta_x + + if i % 2 == 0: + I_0 += f(x_i) * delta_x * 2 + + result_msg += '|'.join([i.center(16) for i in + f"{iter_count} {n} {round(I_0, 4)} {round(I_1, 4)} {round(abs(I_0 - I_1) / 3, 4)}".split()]) + '\n' + + n *= 2 + return I_1, result_msg + + +def right_rectangles(a, b, n, f, eps) -> (float, str): + I_0, I_1 = 0, 0 + iter_count = 0 + result_msg = "" + + while (I_0 == 0 and I_1 == 0) or not runge_rule(I_0, I_1, eps, right_rectangles.__name__): + I_0, I_1 = 0, 0 + iter_count += 1 + delta_x = (b - a) / (2 * n) + for i in range(2 * n): + x_i = a + delta_x * (i + 1) + I_1 += f(x_i) * delta_x + + if i % 2 == 0: + I_0 += f(x_i) * delta_x * 2 + + result_msg += '|'.join([i.center(16) for i in + f"{iter_count} {n} {round(I_0, 4)} {round(I_1, 4)} {round(abs(I_0 - I_1) / 3, 4)}".split()]) + '\n' + + n *= 2 + return I_1, result_msg + + +def middle_rectangles(a, b, n, f, eps) -> (float, str): + I_0, I_1 = 0, 0 + iter_count = 0 + result_msg = '' + while (I_0 == 0 and I_1 == 0) or not runge_rule(I_0, I_1, eps, middle_rectangles.__name__): + I_0, I_1 = 0, 0 + iter_count += 1 + delta_x = (b - a) / (2 * n) + for i in range(2 * n): + left, right = a + delta_x * i, a + delta_x * (i + 1) + x_i = (left + right) / 2 + I_1 += f(x_i) * delta_x + + if i % 2 == 0: + I_0 += f(x_i) * delta_x * 2 + + result_msg += '|'.join([i.center(16) for i in + f"{iter_count} {n} {round(I_0, 4)} {round(I_1, 4)} {round(abs(I_0 - I_1) / 3, 4)}".split()]) + '\n' + + n *= 2 + return I_1, result_msg + + +def trapezoid(a, b, n, f, eps) -> (float, str): + I_0, I_1 = 0, 0 + iter_count = 0 + result_msg = "" + + while iter_count == 0 or not runge_rule(I_0, I_1, eps, trapezoid.__name__): + iter_count += 1 + I_0 = trapezoid_count(a, b, n, f) + I_1 = trapezoid_count(a, b, n * 2, f) + + result_msg += '|'.join([i.center(16) for i in + f"{iter_count} {n} {round(I_0, 4)} {round(I_1, 4)} {round(abs(I_0 - I_1) / 3, 4)}".split()]) + '\n' + + n *= 2 + return I_1, result_msg + + +def trapezoid_count(a, b, n, f): + res = 0 + delta_x = (b - a) / n + for i in range(n): + x_i_1 = a + delta_x * i + x_i = a + delta_x * (i + 1) + s_i = (f(x_i_1) + f(x_i)) * delta_x / 2 + res += s_i + return res + + +def simpson(a, b, n, f, eps) -> (float, str): + I_0, I_1 = 0, 0 + iter_count = 0 + result_msg = "" + + while iter_count == 0 or not runge_rule(I_0, I_1, eps, simpson.__name__): + iter_count += 1 + I_0 = simpson_count(a, b, n, f) + I_1 = simpson_count(a, b, n * 2, f) + + result_msg += '|'.join([i.center(16) for i in + f"{iter_count} {n} {round(I_0, 4)} {round(I_1, 4)} {round(abs(I_0 - I_1) / 3, 4)}".split()]) + '\n' + + n *= 2 + + return I_1, result_msg + + +def simpson_count(a, b, n, f): + res = 0 + delta_x = (b - a) / n + for i in range(n): + x_i_1 = a + delta_x * i + x_i = a + delta_x * (i + 1) + s_i = (f(x_i_1) + 4 * f((x_i_1 + x_i) / 2) + f(x_i)) * delta_x / 6 + res += s_i + + return res diff --git "a/\320\2403213/pimenova_409342/lab3/main.py" "b/\320\2403213/pimenova_409342/lab3/main.py" new file mode 100644 index 0000000..8159aa8 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab3/main.py" @@ -0,0 +1,79 @@ +from integral_methods import * +from storage import * + +functions_dict = { + "1": (f1, integral1), + "2": (f2, integral2), + "3": (f3, integral3) +} + +methods_dict = { + "1": left_rectangles, + "2": right_rectangles, + "3": middle_rectangles, + "4": trapezoid, + "5": simpson +} + + +def solve(f, integral, solving_method, A, B, eps): + print("|".join(i.center(16) for i in '№ n I_0 I_1 |I_1-I_0|/2^k'.split()) + "\n" + "-" * 90) + + ans, msg = solving_method(A, B, 4, f, eps) + print(msg) + print(f"\033[1msolved with {solving_method.__name__} method: {round(ans, 4)} \033[0m") + actual = integral(B) - integral(A) + print(f"actual answer F(B) - F(A): {integral(B) - integral(A)}") + print(f"inaccuracy: {round(100*abs((actual - ans)/actual), 5)}%") + + +if __name__ == "__main__": + print("\033[1mпривееет это моя лаба 3\033[0m\nвот функции, которые можно проинтегрировать:") + print("1) 2x^3 - 3x^2 + 5x - 9".center(40)) + print("2) -3x^3 - 5x^2 + 4x + 5".center(40)) + print("3) x^3 - 2x^2 - 5x + 24".center(40)) + function_num = None + while function_num is None: + function_num = input("введите \033[1mномер функции\033[0m, которую хотите проинтегрировать:").strip() + if "1" <= function_num <= "3": + break + function_num = None + print("\033[1m error: неет такой функции нет( попробуйте еще раз \033[0m") + + function = functions_dict[function_num] + + A, B = None, None + while A is None or B is None: + try: + A, B = map(float, input("введите \033[1mграницы интегрирования\033[0m через пробел:").split()) + if A > B: + raise ValueError + break + except ValueError: + print("\033[1m error: неет это должны быть числа + идти по возрастанию \033[0m") + A, B = None, None + + print("вот такие есть методы интегрирования:") + print("\n".join(f"\t{k}) {v.__name__}_method" for k, v in methods_dict.items())) + + method_num = None + while method_num is None: + method_num = input("введите \033[1mномер метода\033[0m, которым хотите решить:").strip() + if "1" <= method_num <= "5": + break + method_num = None + print("\033[1m error: неет такого метода нет( попробуйте еще раз \033[0m") + + method = methods_dict[method_num] + eps = None + while eps is None: + try: + eps = float(input("введите \033[1mточность:\033[0m")) + if eps <= 0: + raise ValueError + + except ValueError: + print("\033[1m error: нееет точность это положительное число \033[0m") + eps = None + + solve(functions_dict[function_num][0], functions_dict[function_num][1], method, A, B, eps) diff --git "a/\320\2403213/pimenova_409342/lab3/storage.py" "b/\320\2403213/pimenova_409342/lab3/storage.py" new file mode 100644 index 0000000..f86de11 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab3/storage.py" @@ -0,0 +1,22 @@ +def f1(x): + return 2 * x ** 3 - 3 * x ** 2 + 5 * x - 9 + + +def integral1(x): + return x ** 4 / 2 - x ** 3 + 5 * x ** 2 / 2 - 9 * x + + +def f2(x): + return -3 * x ** 3 - 5 * x ** 2 + 4 * x + 5 + + +def integral2(x): + return -0.75 * x ** 4 - 5 * x / 3 + 2 * x ** 2 - 5 * x + + +def f3(x): + return x ** 3 - 2 * x ** 2 - 5 * x + 24 + + +def integral3(x): + return x ** 4 / 4 - 2 / 3 * x ** 3 - 5 / 2 * x ** 2 + 24 * x From 21dc07c13a5b8b33ff948c26f5c19f2ba86fb01d Mon Sep 17 00:00:00 2001 From: p11menova Date: Tue, 8 Apr 2025 00:23:15 +0300 Subject: [PATCH 06/10] added report --- 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"\320\2403213/pimenova_409342/lab4/graphics/quadratic_approximation.png" create mode 100644 "\320\2403213/pimenova_409342/lab4/graphics_drawer.py" create mode 100644 "\320\2403213/pimenova_409342/lab4/input.txt" create mode 100644 "\320\2403213/pimenova_409342/lab4/main.py" create mode 100644 "\320\2403213/pimenova_409342/lab4/output.txt" create mode 100644 "\320\2403213/pimenova_409342/lab4/table_printer.py" diff --git "a/\320\2403213/pimenova_409342/lab4/.DS_Store" "b/\320\2403213/pimenova_409342/lab4/.DS_Store" new file mode 100644 index 0000000000000000000000000000000000000000..b3ff5e1045c8100ebbd7e40f4aa2e08c61aedae4 GIT binary patch literal 6148 zcmeHKJ5B>J5FJB`MKmcXeE^!hfr*wAY(oe6NC{G+U4f7&eL6}mK*LdZZ^l4Y*&+=H zp&7}3W6#IlC#~%fkuZB&)gn_7snCdl%7}1!)O1puC%~XNHgYdZdEBn+b|leXoZ{Xq zS<8dWrI)?^FS}i@8$P??cOLlcx~5rdy9I6Y*W1hIx0kDNztvHG{ibfe*L+7R7iYj3 za0Z+KXW&N|z@1I0&JDeH2AlzB;EMsC4-t)+3T8t+I?!ne0OT`T1v+a9#>9fDU^avW z5-b#Gp`nx*!NM^gi(e|34J}-Pu8cfo<MkJ}dhZN4149N*Z8+uqe~n*e zw8$TZ_{bS>2L2fXVbZkC3?EhQ)`QRET^rHv&?xlFR3Oj?j{ppKj$EkG?2$VBQo(G< TES%SHpg#nZ5bvCUUtr(^p;9n) literal 0 HcmV?d00001 diff --git "a/\320\2403213/pimenova_409342/lab4/README.md" "b/\320\2403213/pimenova_409342/lab4/README.md" index 6313d17..d5c61f7 100644 --- "a/\320\2403213/pimenova_409342/lab4/README.md" +++ "b/\320\2403213/pimenova_409342/lab4/README.md" @@ -1 +1,4 @@ -Лабораторная работа 4 +### лабораторная работа 3 + +#### «методы аппроксимации» +вариант **9** \ No newline at end of file diff --git "a/\320\2403213/pimenova_409342/lab4/approximation_methods.py" "b/\320\2403213/pimenova_409342/lab4/approximation_methods.py" new file mode 100644 index 0000000..0acd821 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab4/approximation_methods.py" @@ -0,0 +1,157 @@ +import math + +import numpy as np +from math import exp, log + +def count_sums_1(n, X, Y): + S_X = sum(X) + S_Y = sum(Y) + S_XX = sum(map(lambda x: x ** 2, X)) + S_XY = sum([X[i] * Y[i] for i in range(n)]) + return S_X, S_Y, S_XX, S_XY + + +def count_sums_2(n, X, Y): + S_X3 = sum(map(lambda x: x ** 3, X)) + S_X2Y = sum([X[i] ** 2 * Y[i] for i in range(n)]) + S_X4 = sum(map(lambda x: x ** 4, X)) + return S_X3, S_X2Y, S_X4 + + +def count_sums_3(n, X, Y): + S_X5 = sum(map(lambda x: x ** 5, X)) + S_X3Y = sum([X[i] ** 3 * Y[i] for i in range(n)]) + S_X6 = sum(map(lambda x: x ** 6, X)) + return S_X5, S_X6, S_X3Y + + +def linear_approximation(n, X, Y) -> (float, float): + """ + :return: коэффиценты a b аппроксимирующей функции ax+b + """ + S_X, S_Y, S_XX, S_XY = count_sums_1(n, X, Y) + + # получим сист лин уравн и по правилу Крамера посчитаем + delta = S_XX * n - S_X ** 2 + delta_1 = S_XY * n - S_X * S_Y + delta_2 = S_XX * S_Y - S_X * S_XY + + return delta_1 / delta, delta_2 / delta + + +def solve_linear_system(A, B): + A = np.array(A) + B = np.array(B) + try: + solution = np.linalg.solve(A, B) + return solution + except np.linalg.LinAlgError: + return None, None + + +def quadratic_approximation(n, X, Y) -> (float, float, float): + """ + :return: коэффиценты a b c аппроксимирующей функции ax^2 + bx +c + """ + S_X, S_Y, S_X2, S_XY = count_sums_1(n, X, Y) + S_X3, S_X2Y, S_X4 = count_sums_2(n, X, Y) + A = [[n, S_X, S_X2], + [S_X, S_X2, S_X3], + [S_X2, S_X3, S_X4]] + B = [S_Y, S_XY, S_X2Y] + + a, b, c = solve_linear_system(A, B)[::-1] + + return a, b, c + + +def cubic_approximation(n, X, Y) -> (float, float, float, float): + """ + :return: коэффиценты a b c d аппроксимирующей функции ax^3 + bx^2 +cx = d + """ + S_X, S_Y, S_X2, S_XY = count_sums_1(n, X, Y) + S_X3, S_X2Y, S_X4 = count_sums_2(n, X, Y) + S_X5, S_X6, S_X3Y = count_sums_3(n, X, Y) + A = [ + [S_X6, S_X5, S_X4, S_X3], + [S_X5, S_X4, S_X3, S_X2], + [S_X4, S_X3, S_X2, S_X], + [S_X3, S_X2, S_X, n] + ] + + B = [S_X3Y, S_X2Y, S_XY, S_Y] + return solve_linear_system(A, B) + + +def exponential_approximation(n, X, Y): + """ + :return: коэфф a, b функции ae^bx + """ + clean_X = [] + clean_Y = [] + + for x, y in zip(X, Y): + if y is not None and y > 0: # Явная проверка + clean_X.append(x) + clean_Y.append(y) + + if len(clean_Y) < 2: # Для линейной регрессии нужно минимум 2 точки + return None, None, None, None + + try: + lnY = [math.log(y) for y in clean_Y] # Более питонический способ + B, A = linear_approximation(len(lnY), clean_X, lnY) + return math.exp(A), B, clean_X, clean_Y + except (ValueError, TypeError): + return None, None, None, None + +def logarithm_approximation(n, X, Y): + clean_X = [] + clean_Y = [] + + for x, y in zip(X, Y): + if x is not None and y is not None and x > 0: # ln(x) определен только для x > 0 + clean_X.append(x) + clean_Y.append(y) + + if len(clean_X) < 2: + return None, None, None, None + + try: + # линеаризация - заменяем x на ln(x) + lnX = [math.log(x) for x in clean_X] + + # y = a*lnX + b + a, b = linear_approximation(len(lnX), lnX, clean_Y) + + return a, b, clean_X, clean_Y + + except (ValueError, TypeError, ZeroDivisionError): + return None, None, None, None + + +def pow_approximation(n, 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z3WZu$Gxv)~7628H*Kl05vaJ$>^OrF!GUiCGGTQl6vJXGxz@7^o54<7@8{rA3g~#JH z4UwoetVLRkR=Su0`M8cjopxe=z^%-RLi=3&N?1bWmwHRMV%JFD8tI%J!ft0I&{JCQ zLy|WF{c*lEo8<6cBmNktx^p6!b>S1Od?|6HP4AY?sl3in{?hI=GAnf6t4Qgm z=UeL*y^5l12d5{;jj-u-QvzlZC_5Kip4O6@`11XOQ#w1kt+G${`IdA~1kdnz@|Dhd z%UgZR`*TJLe%NW0Mn0yQ%uE-@JX#fg#5jlMFCAQ1q8%WSa;2)74B6|oA)%qs@NkhI ziLFzI&y_h^KDLkh{-Jzcr;b}FT96MHnxCWp3+J(L!vFvP literal 0 HcmV?d00001 diff --git "a/\320\2403213/pimenova_409342/lab4/graphics_drawer.py" "b/\320\2403213/pimenova_409342/lab4/graphics_drawer.py" new file mode 100644 index 0000000..34e2f8a --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab4/graphics_drawer.py" @@ -0,0 +1,190 @@ +import numpy as np +import matplotlib.pyplot as plt +from math import exp + +def draw_linear_graph(X, Y, a, b): + plt.figure(figsize=(10, 6)) + + # Рисуем точки + plt.scatter(X, Y, color='pink', label='исходные точки (X, Y)', zorder=5) + + # Рисуем линейную функцию + x_line = np.linspace(min(X) - 0.1, max(X) + 0.1, 100) + y_line = a * x_line + b + plt.plot(x_line, y_line, label=f'аппроксимирующая функция: y = {round(a,3)}x + {round(b,3)}', color='darkcyan') + + plt.title('') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.7) + plt.legend() + plt.tight_layout() + + plt.savefig('graphics/linear_approximation.png') + plt.close() + + + +def draw_quadratic_graph(X, Y, a, b, c): + plt.figure(figsize=(10, 6)) + + # Рисуем точки + plt.scatter(X, Y, color='pink', label='исходные точки (X, Y)', zorder=5) + x_line = np.linspace(min(X) - 0.1, max(X) + 0.1, 100) + y_line = a * x_line**2 + b*x_line + c + plt.plot(x_line, y_line, label=f'аппроксимирующая функция: y = {round(a,3)}x^2 + {round(b,3)}x + {round(c, 3)}', color='lightseagreen') + + plt.title('') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.7) + plt.legend() + plt.tight_layout() + plt.savefig('graphics/quadratic_approximation.png') + plt.close() + + +def draw_cubic_approximation(X, Y, a, b, c, d): + plt.figure(figsize=(10, 6)) + + # Рисуем точки + plt.scatter(X, Y, color='pink', label='исходные точки (X, Y)', zorder=5) + x_line = np.linspace(min(X) - 0.1, max(X) + 0.1, 100) + y_line = a * x_line ** 3 + + b * x_line**2 + c*x_line + d + plt.plot(x_line, y_line, label=f'аппроксимирующая функция: y = {round(a, 3)}x^3 + {round(b, 3)}x^2 + {round(c, 3)}x + {round(d, 3)}', + color='lightseagreen') + + plt.title('') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.7) + plt.legend() + plt.tight_layout() + plt.savefig('graphics/cubic_approximation.png') + plt.close() + +def draw_exp_approximation(X, Y, acc_X, a, b): + plt.figure(figsize=(10, 6)) + + plt.scatter(X, Y, color='pink', label='исходные точки (X, Y)', zorder=5) + x_line = np.linspace(min(acc_X) - 0.1, max(acc_X) + 0.1, 100) + y_line = a * np.exp(b*x_line) + plt.plot(x_line, y_line, + label=f'аппроксимирующая функция: y = {round(a, 3)}* e^{round(b, 3)}x', + color='lightseagreen') + + plt.title('') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.7) + plt.legend() + plt.tight_layout() + plt.savefig('graphics/exp_approximation.png') + plt.close() + + + +def draw_log_approximation(X, Y, acc_x, a, b): + plt.figure(figsize=(10, 6)) + + plt.scatter(X, Y, color='pink', label='исходные точки (X, Y)', zorder=5) + x_line = np.linspace(min(acc_x) - 0.1, max(acc_x) + 0.1, 100) + y_line = a * np.log(x_line)+ b + plt.plot(x_line, y_line, + label=f'аппроксимирующая функция: y = {round(a, 3)}*ln(x) + {round(b, 3)}', + color='lightseagreen') + + plt.title('') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.7) + plt.legend() + plt.tight_layout() + plt.savefig('graphics/log_approximation.png') + plt.close() + + +def draw_pow_approximation(X, Y, acc_x, a, b): + plt.figure(figsize=(10, 6)) + + plt.scatter(X, Y, color='pink', label='исходные точки (X, Y)', zorder=5) + x_line = np.linspace(min(acc_x) - 0.1, max(acc_x) + 0.1, 100) + y_line = a * x_line**b + plt.plot(x_line, y_line, + label=f'аппроксимирующая функция: y = {round(a, 3)}x^{round(b, 3)}', + color='lightseagreen') + + plt.title('') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.7) + plt.legend() + plt.tight_layout() + plt.savefig('graphics/pow_approximation.png') + plt.close() + + +def draw_all_approximations(X, Y,results): + linear_coeffs = results["linear"] + quadratic_coeffs = results["quadratic"] + cubic_coeffs = results["cubic"] + exp_coeffs = results["exp"][0:2] + log_coeffs = results["log"][0:2] + pow_coeffs = results["pow"][0:2] + acc_X = results["exp"][2] + plt.figure(figsize=(12, 8)) + + plt.scatter(X, Y, color='cyan', label='исходные точки (X, Y)', zorder=10) + + x_min = min(X) - 0.5 + x_max = max(X) + 0.5 + x_line = np.linspace(x_min, x_max, 500) + + if linear_coeffs and linear_coeffs[0] is not None: + a, b = linear_coeffs + y_linear = a * x_line + b + plt.plot(x_line, y_linear, label=f'линейн: y = {round(a, 3)}x + {round(b, 3)}', + color='pink', linestyle='-') + + if quadratic_coeffs and all(c is not None for c in quadratic_coeffs): + a, b, c = quadratic_coeffs + y_quad = a * x_line ** 2 + b * x_line + c + plt.plot(x_line, y_quad, label=f'квадр: y = {round(a, 3)}x² + {round(b, 3)}x + {round(c, 3)}', + color='hotpink', linestyle='-') + + if cubic_coeffs and all(c is not None for c in cubic_coeffs): + a, b, c, d = cubic_coeffs + y_cubic = a * x_line ** 3 + b * x_line ** 2 + c * x_line + d + plt.plot(x_line, y_cubic, + label=f'кубич: y = {round(a, 3)}x³ + {round(b, 3)}x² + {round(c, 3)}x + {round(d, 3)}', + color='Violet', linestyle='-') + + if exp_coeffs and all(c is not None for c in exp_coeffs[:2]): + a, b = exp_coeffs[:2] + y_exp = a * np.exp(b * x_line) + plt.plot(x_line, y_exp, label=f'экспонец: y = {round(a, 3)}e^{round(b, 3)}x', + color='grey', linestyle='--') + + if log_coeffs and all(c is not None for c in log_coeffs[:2]): + a, b = log_coeffs[:2] + x_log = x_line[x_line > 0.01] # Избегаем log(0) + y_log = a * np.log(x_log) + b + plt.plot(x_log, y_log, label=f'лог: y = {round(a, 3)}ln(x) + {round(b, 3)}', + color='lightgrey', linestyle='--') + + if pow_coeffs and all(c is not None for c in pow_coeffs[:2]): + a, b = pow_coeffs[:2] + x_pow = x_line[x_line > 0.01] # Избегаем 0^b + y_pow = a * x_pow ** b + plt.plot(x_pow, y_pow, label=f'степен: y = {round(a, 3)}x^{round(b, 3)}', + color='DarkSlateGrey', linestyle='--') + + plt.title('сравнение методов аппроксимации') + plt.xlabel('Ox') + plt.ylabel('Oy') + plt.grid(True, linestyle='--', alpha=0.5) + plt.legend(bbox_to_anchor=(1.05, 1), loc='upper right') + plt.tight_layout() + + plt.savefig('graphics/all_approximations.png', bbox_inches='tight', dpi=300) + plt.show() diff --git "a/\320\2403213/pimenova_409342/lab4/input.txt" "b/\320\2403213/pimenova_409342/lab4/input.txt" new file mode 100644 index 0000000..13d40a9 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab4/input.txt" @@ -0,0 +1,3 @@ +11 +0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 +0 0.088873089 0.177273533 0.262881178 0.340078218 0.4 0.433463372 0.436082731 0.4114803 0.369276219 0.32 \ No newline at end of file diff --git "a/\320\2403213/pimenova_409342/lab4/main.py" "b/\320\2403213/pimenova_409342/lab4/main.py" new file mode 100644 index 0000000..e2083b9 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab4/main.py" @@ -0,0 +1,152 @@ +from approximation_methods import * +from graphics_drawer import * +from table_printer import * + +# мапа полученных значений коэфф +results = {"linear": [None, None], + "quadratic": [None] * 3, + "cubic": [None] * 4, + "exp": [None] * 4, + "log": [None] * 4, + "pow": [None] * 4 + } + + +def validate_data(n, x_line, y_line): + if n < 8 or n > 12: + raise ValueError + X = [float(x) for x in x_line.split()] + if len(X) != n: + raise ValueError + Y = [float(y) for y in y_line.split()] + if len(Y) != n: + raise ValueError + return n, X, Y + + +def read_data(): + while True: + try: + key = input("введите f если хотите прочитать из файла и любой другой символ в ином случае:") + if key.strip() == "f": + with open(input("введите название файла:")) as f: + n = int(f.readline()) + x_line = f.readline().replace(",", ".") + y_line = f.readline().replace(",", ".") + else: + n = int(input("введите количество узлов функции:")) + x_line = input("введите через пробел значения x_i:") + y_line = input("введите через пробел значения y_i:") + n, X, Y = validate_data(n, x_line, y_line) + return n, X, Y + + except ValueError: + print("error: некорректный ввод :( попробуйте еще раз!") + continue + + +def print_data(): + key = input("введите f, если хотите записать результаты в файл и любой другой символ, если в консоль):") + if key.strip() == "f": + with open("output.txt", mode="w") as f: + print("МЕТОД ЛИНЕЙНОЙ АППРОКСИМАЦИИ:".center(90), file=f) + print_table(n, X, Y, lambda x: results["linear"][0] * x + results["linear"][1], f) + + print("МЕТОД КВАДРАТИЧНОЙ АППРОКСИМАЦИИ:".center(90), file=f) + print_table(n, X, Y, + lambda x: results["quadratic"][0] * x ** 2 + results["quadratic"][1] * x + results["quadratic"][ + 2], f) + + print("МЕТОД КУБИЧЕСКОЙ АППРОКСИМАЦИИ:".center(90), file=f) + print_table(n, X, Y, lambda x: + results["cubic"][0] * x ** 3 + results["cubic"][1] * x ** 2 + results["cubic"][2] * x + results["cubic"][3], + f) + + if all(x is not None for x in results["exp"]): + print("МЕТОД ЭКСПОНЕНЦИАЛЬНОЙ АППРОКСИМАЦИИ".center(90), file=f) + print_table(len(results["exp"][2]), results["exp"][2], results["exp"][3], + lambda x: results["exp"][0] * math.exp(results["exp"][1] * x), f) + + if all(x is not None for x in results["log"]): + print("МЕТОД ЛОГАРИФМИЧЕСКОЙ АППРОКСИМАЦИИ".center(90), file=f) + print_table(len(results["log"][2]), results["log"][2], results["log"][3], + lambda x: results["log"][0] * math.log(x) + results["log"][1], f) + + if all(x is not None for x in results["pow"]): + print("МЕТОД СТЕПЕННОЙ АППРОКСИМАЦИИ".center(90), file=f) + print_table(len(results["pow"][2]), results["pow"][2], results["pow"][3], + lambda x: results["log"][0] * x ** results["log"][1], f) + + return + + print("МЕТОД ЛИНЕЙНОЙ АППРОКСИМАЦИИ:".center(90)) + print_table(n, X, Y, lambda x: results["linear"][0] * x + results["linear"][1], None) + + print("МЕТОД КВАДРАТИЧНОЙ АППРОКСИМАЦИИ:".center(90)) + print_table(n, X, Y, + lambda x: results["quadratic"][0] * x ** 2 + results["quadratic"][1] * x + results["quadratic"][2], + None) + print("МЕТОД КУБИЧЕСКОЙ АППРОКСИМАЦИИ:".center(90)) + print_table(n, X, Y, lambda x: + results["cubic"][0] * x ** 3 + results["cubic"][1] * x ** 2 + results["cubic"][2] * x + results["cubic"][3], None) + + if all(x is not None for x in results["exp"]): + print("МЕТОД ЭКСПОНЕНЦИАЛЬНОЙ АППРОКСИМАЦИИ".center(90)) + print_table(len(results["exp"][2]), results["exp"][2], results["exp"][3], + lambda x: results["exp"][0] * math.exp(results["exp"][1] * x), + None) + + if all(x is not None for x in results["log"]): + print("МЕТОД ЛОГАРИФМИЧЕСКОЙ АППРОКСИМАЦИИ".center(90)) + print_table(len(results["log"][2]), results["log"][2], results["log"][3], + lambda x: results["log"][0] * math.log(x) + results["log"][1], None) + + if all(x is not None for x in results["pow"]): + print("МЕТОД СТЕПЕННОЙ АППРОКСИМАЦИИ".center(90)) + print_table(len(results["pow"][2]), results["pow"][2], results["pow"][3], + lambda x: results["log"][0] * x ** results["log"][1], None) + + +if __name__ == "__main__": + n, X, Y = read_data() + + a, b = linear_approximation(n, X, Y) + results["linear"] = a, b + draw_linear_graph(X, Y, a, b) + + a, b, c = quadratic_approximation(n, X, Y) + results["quadratic"] = float(a), float(b), float(c) + draw_quadratic_graph(X, Y, a, b, c) + + a, b, c, d = cubic_approximation(n, X, Y) + results["cubic"] = float(a), float(b), float(c), float(d) + draw_cubic_approximation(X, Y, a, b, c, d) + + try: + a, b, accepted_X, accepted_Y = exponential_approximation(n, X, Y) + results["exp"] = float(a), float(b), accepted_X, accepted_Y + draw_exp_approximation(X, Y, accepted_X, a, b) + except TypeError: + print( + "error: ОДЗ логарифма x>0 -> недостаточно точек с положительными значениями функции для аппроксимации данным методом") + + try: + a, b, accepted_X, accepted_Y = logarithm_approximation(n, X, Y) + results["log"] = float(a), float(b), accepted_X, accepted_Y + draw_log_approximation(X, Y, accepted_X, a, b) + + except TypeError: + print( + "error: ОДЗ логарифма x>0 -> недостаточно точек с положительными значениями функции для аппроксимации данным методом") + + try: + a, b, accepted_X, accepted_Y = pow_approximation(n, X, Y) + results["pow"] = float(a), float(b), accepted_X, accepted_Y + draw_pow_approximation(X, Y, accepted_X, a, b) + + except TypeError: + print( + "error: ОДЗ логарифма x>0 -> недостаточно точек с положительными значениями функции для аппроксимации данным методом") + + print_data() + draw_all_approximations(X, Y, results) diff --git "a/\320\2403213/pimenova_409342/lab4/output.txt" "b/\320\2403213/pimenova_409342/lab4/output.txt" new file mode 100644 index 0000000..f2f2dc9 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab4/output.txt" @@ -0,0 +1,66 @@ + МЕТОД ЛИНЕЙНОЙ АППРОКСИМАЦИИ: + X | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + Y | 0.0 | 0.0889 | 0.1773 | 0.2629 | 0.3401 | 0.4 | 0.4335 | 0.4361 | 0.4115 | 0.3693 | 0.32 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + phi(X) | 0.1189 | 0.154 | 0.1891 | 0.2242 | 0.2594 | 0.2945 | 0.3296 | 0.3647 | 0.3999 | 0.435 | 0.4701 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + e_i | 0.1189 | 0.0651 | 0.0118 | -0.0386 | -0.0807 | -0.1055 | -0.1038 | -0.0713 | -0.0116 | 0.0657 | 0.1501 +СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: 0.0856 + + + МЕТОД КВАДРАТИЧНОЙ АППРОКСИМАЦИИ: + X | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + Y | 0.0 | 0.0889 | 0.1773 | 0.2629 | 0.3401 | 0.4 | 0.4335 | 0.4361 | 0.4115 | 0.3693 | 0.32 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + phi(X) | -0.0244 | 0.0967 | 0.1987 | 0.2815 | 0.3453 | 0.39 | 0.4156 | 0.4221 | 0.4094 | 0.3777 | 0.3269 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + e_i | -0.0244 | 0.0078 | 0.0214 | 0.0187 | 0.0053 | -0.01 | -0.0179 | -0.014 | -0.0021 | 0.0084 | 0.0069 +СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: 0.0142 + + + МЕТОД КУБИЧЕСКОЙ АППРОКСИМАЦИИ: + X | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + Y | 0.0 | 0.0889 | 0.1773 | 0.2629 | 0.3401 | 0.4 | 0.4335 | 0.4361 | 0.4115 | 0.3693 | 0.32 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + phi(X) | -0.0068 | 0.0931 | 0.1857 | 0.268 | 0.3371 | 0.39 | 0.4238 | 0.4356 | 0.4224 | 0.3812 | 0.3092 +------------------------------------------------------------------------------------------------------------------------------------------------------------ + e_i | -0.0068 | 0.0043 | 0.0084 | 0.0051 | -0.003 | -0.01 | -0.0096 | -0.0005 | 0.0109 | 0.0119 | -0.0108 +СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: 0.0082 + + + МЕТОД ЭКСПОНЕНЦИАЛЬНОЙ АППРОКСИМАЦИИ + X | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 +----------------------------------------------------------------------------------------------------------------------------------------------- + Y | 0.0889 | 0.1773 | 0.2629 | 0.3401 | 0.4 | 0.4335 | 0.4361 | 0.4115 | 0.3693 | 0.32 +----------------------------------------------------------------------------------------------------------------------------------------------- + phi(X) | 0.1729 | 0.1948 | 0.2196 | 0.2475 | 0.2789 | 0.3143 | 0.3543 | 0.3993 | 0.45 | 0.5072 +----------------------------------------------------------------------------------------------------------------------------------------------- + e_i | 0.084 | 0.0175 | -0.0433 | -0.0926 | -0.1211 | -0.1191 | -0.0818 | -0.0122 | 0.0807 | 0.1872 +СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: 0.0975 + + + МЕТОД ЛОГАРИФМИЧЕСКОЙ АППРОКСИМАЦИИ + X | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 +----------------------------------------------------------------------------------------------------------------------------------------------- + Y | 0.0889 | 0.1773 | 0.2629 | 0.3401 | 0.4 | 0.4335 | 0.4361 | 0.4115 | 0.3693 | 0.32 +----------------------------------------------------------------------------------------------------------------------------------------------- + phi(X) | 0.1168 | 0.2119 | 0.2675 | 0.3069 | 0.3375 | 0.3625 | 0.3836 | 0.402 | 0.4181 | 0.4326 +----------------------------------------------------------------------------------------------------------------------------------------------- + e_i | 0.028 | 0.0346 | 0.0046 | -0.0332 | -0.0625 | -0.071 | -0.0524 | -0.0095 | 0.0488 | 0.1126 +СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: 0.0547 + + + МЕТОД СТЕПЕННОЙ АППРОКСИМАЦИИ + X | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 +----------------------------------------------------------------------------------------------------------------------------------------------- + Y | 0.0889 | 0.1773 | 0.2629 | 0.3401 | 0.4 | 0.4335 | 0.4361 | 0.4115 | 0.3693 | 0.32 +----------------------------------------------------------------------------------------------------------------------------------------------- + phi(X) | 0.0796 | 0.1006 | 0.1154 | 0.1272 | 0.1371 | 0.1458 | 0.1536 | 0.1607 | 0.1672 | 0.1733 +----------------------------------------------------------------------------------------------------------------------------------------------- + e_i | -0.0092 | -0.0766 | -0.1475 | -0.2129 | -0.2629 | -0.2876 | -0.2825 | -0.2508 | -0.2021 | -0.1467 +СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: 0.2074 + + diff --git "a/\320\2403213/pimenova_409342/lab4/table_printer.py" "b/\320\2403213/pimenova_409342/lab4/table_printer.py" new file mode 100644 index 0000000..2314267 --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab4/table_printer.py" @@ -0,0 +1,18 @@ +import math + + +def print_table(n, X, Y, phi, output_file): + print("X".center(10) + "|" + "|".join([str(round(x, 4)).center(12) for x in X]), file=output_file) + print("-" * (n + 1) * 13, file=output_file) + print("Y".center(10) + "|" + "|".join([str(round(y, 4)).center(12) for y in Y]), file=output_file) + print("-" * (n + 1) * 13, file=output_file) + + print("phi(X)".center(10) + "|" + "|".join([str(round(phi(x), 4)).center(12) for x in X]), file=output_file) + print("-" * (n + 1) * 13, file=output_file) + + e_i = [phi(X[i]) - Y[i] for i in range(n)] + print("e_i".center(10) + "|" + "|".join([str(round(e, 4)).center(12) for e in e_i]), file=output_file) + + e_i2 = list(map(lambda x: x ** 2, e_i)) + print(f"СРЕДНЕКВАДРАТИЧНОЕ ОТКЛОНЕНИЕ: {round(math.sqrt(sum(e_i2) / n), 4)}", file=output_file) + print("\n", file=output_file) From b50baa0780d66e0b31b8f6edfe1851f1506032ff Mon Sep 17 00:00:00 2001 From: p11menova Date: Mon, 26 May 2025 14:22:22 +0300 Subject: [PATCH 08/10] lab4 done --- "\320\2403213/pimenova_409342/lab4/README.md" | 2 +- ...260\321\202_\320\273\320\260\320\2614.pdf" | Bin 0 -> 2503806 bytes "\320\2403213/pimenova_409342/lab5/input.txt" | 7 + .../pimenova_409342/lab5/input2.txt" | 7 + .../pimenova_409342/lab5/interpolation.png" | Bin 0 -> 29851 bytes .../lab5/interpolation_methods.py" | 90 ++++++++ "\320\2403213/pimenova_409342/lab5/main.py" | 116 +++++++++++ "\320\2403213/pimenova_409342/lab6/main.py" | 197 ++++++++++++++++++ 8 files changed, 418 insertions(+), 1 deletion(-) create mode 100644 "\320\2403213/pimenova_409342/lab4/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2614.pdf" create mode 100644 "\320\2403213/pimenova_409342/lab5/input.txt" create mode 100644 "\320\2403213/pimenova_409342/lab5/input2.txt" create mode 100644 "\320\2403213/pimenova_409342/lab5/interpolation.png" create mode 100644 "\320\2403213/pimenova_409342/lab5/interpolation_methods.py" create mode 100644 "\320\2403213/pimenova_409342/lab5/main.py" create mode 100644 "\320\2403213/pimenova_409342/lab6/main.py" diff --git "a/\320\2403213/pimenova_409342/lab4/README.md" "b/\320\2403213/pimenova_409342/lab4/README.md" index d5c61f7..5f70d4c 100644 --- "a/\320\2403213/pimenova_409342/lab4/README.md" +++ "b/\320\2403213/pimenova_409342/lab4/README.md" @@ -1,4 +1,4 @@ -### лабораторная работа 3 +### лабораторная работа 4 #### «методы аппроксимации» вариант **9** \ No newline at end of file diff --git "a/\320\2403213/pimenova_409342/lab4/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2614.pdf" "b/\320\2403213/pimenova_409342/lab4/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2614.pdf" new file mode 100644 index 0000000000000000000000000000000000000000..42949182bdad5598192cc5860d14f9d2debb893d GIT binary patch literal 2503806 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zB%ZzrNfZ+1ip+K7*c9=AV<{LBIq!&Ct_VDYXl_e#OBhCdUQ)>iAinTGalP{XiSNO} z%6hsO08AYSMa_Iq4~Od!cqpTX&|Yr556zI?ecTy%TU@*CX}_lfa;;qQXHtxymW!aw)N zz;eUC|M#(M85cn@Q6Gqb)!RN_Sl9~TioZv%NJ`Sep;)A#3hm7p)RO*lZY%ALN3qk8 z(AHufA@ov4u^$k-F1+3l#&bn^B~C-ZBn*V{lRdt5Cgz1 z*P*ayD<3BVz|R#V6-SuRgbH$`;VW67C5JTdW{6BK;(PvG!v9d*!g~tGX}r?p&q?~I zO4kmu#?~s9f4XR#FI#K|DahpD#~mp57E{pV%HYqdsHpfxX;JM<1BZ|`!?`WJ_;^Ej z{x)Rs`ADQHoDp-XRyE&};l7CPa9(-5z$TR7E)q1Yla44zl4FvRvT<*;R-dP#{g%9C zDZJLu4_T1_HOdhSbn6WSAC_n<>urDpIvNSQIe@+X5gZwH^pl(e&)0fgPv%s1c2LCm!P9G{hP*^2}c-M$Ssi41EW8}2){ z-hl-e4mD%i{_w_w{d=`dQ$!tT-Me5~efZLxaiQ_>;s_%}QJ!rM!57Qf6LKMjh^-`F zz^!hq5$GEIwi(U8aqVeMA|Fn-3(vvPcGjDN_;zjPs|69&TCmpnq1cTR)U%PfqcRYT z1V$lYE#^cSq?3?Bn5$_ubm*vL3xMMW{9kLFtOOtYzD{&ojd{6y!7iQS2+YGV`!$%} zccnkAte9L~asa-+3Bp>brKP1Kf#Yj}H%2qp`P!wuy= len(deltas) or center - (i // 2) < 0 or center + ((i - 1) // 2) >= len(deltas[i]): + break + + idx = center - (i // 2) + val = deltas[i][idx] + + t_term *= t + (k - 1) if i % 2 == 1 else t - (k - 1) + if i % 2 == 0: + k += 1 + + term = (t_term * val) / factorial(i) + result += term + + return result + + +def plot_gauss(x, y, x_plot): + return [gauss_central_even(x, y, xi) for xi in x_plot] + diff --git "a/\320\2403213/pimenova_409342/lab5/main.py" "b/\320\2403213/pimenova_409342/lab5/main.py" new file mode 100644 index 0000000..174032c --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab5/main.py" @@ -0,0 +1,116 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib + +from interpolation_methods import * +matplotlib.use('TkAgg') + + +def main(): + def input_table_manual(): + n = int(input("введите количество точек: ")) + x, y = [], [] + for i in range(n): + xi = float(input(f"x[{i}]: ")) + yi = float(input(f"y[{i}]: ")) + x.append(xi) + y.append(yi) + return x, y + + def input_table_file(path): + x, y = [], [] + try: + with open(path, 'r') as f: + for line in f: + parts = line.strip().split() + x.append(float(parts[0])) + y.append(float(parts[1])) + return x, y + except FileNotFoundError: + return None, None + + def input_table_function(): + import math + print("1 - sin(x)\n2 - cos(x)\n3 - ln(1 + x)") + f_choice = int(input("выберите функцию: ")) + func = {1: math.sin, 2: math.cos, 3: lambda x: math.log(1 + x)}[f_choice] + + while True: + a = float(input("введите начало интервала: ")) + b = float(input("введите конец интервала: ")) + if a >= b: + print("нееееет начало интервала должно быть меньше конца") + continue + if f_choice == 3 and (a <= -1 or b <= -1): + print("неееет для ln(1 + x) x должен быть > -1. Попробуйте снова.") + else: + break + + n = int(input("введите число точек: ")) + x = np.linspace(a, b, n) + y = [func(xi) for xi in x] + return list(x), y + + def menu(): + print("выберите способ ввода:\n1 - вручную\n2 - из файла\n3 - функция") + ch = int(input("таак: ")) + if ch == 1: + return input_table_manual() + elif ch == 2: + x, y = None, None + path = input("укажите путь к файлу: ") + x, y = input_table_file(path) + while x is None is y is None: + + print("неет такого файла нет") + path = input("укажите путь к файлу: ") + x, y = input_table_file(path) + return x, y + elif ch == 3: + return input_table_function() + + x, y = menu() + x_interp = float(input("введите значение X для интерполяции: ")) + if not (min(x) <= x_interp <= max(x)): + print("неееет значение X должно быть в интервале интерполяции") + return + + x_plot = np.linspace(min(x), max(x), 500) + + y_lagr = lagrange(x, y, x_interp) + f_newton = newton_divided_diff(x, y) + y_newton = newton_divided_interpolation(x, f_newton, x_interp) + deltas = finite_diff_table(y) + table = PrettyTable() + table.title = "таблица конечных разностей" + table.add_column("x", [round(i, 4) for i in x]) + table.add_column("y", [round(i, 4) for i in y]) + for i in range(1, len(x)): + table.add_column(f"∆{i} y", [round(deltas[i][j], 4) if j < len(deltas[i]) else "" for j in range(len(x))]) + print(table) + y_gauss = gauss_central_even(x, y, x_interp) + + y_l_plot = [lagrange(x, y, xi) for xi in x_plot] + y_n_plot = [newton_divided_interpolation(x, f_newton, xi) for xi in x_plot] + y_g_plot = plot_gauss(x, y, x_plot) + + print("\nИТОГО:") + print(f"интерполяция многочленом Лагранжа: {x_interp}: {y_lagr:.6f}") + print(f"интерполяция многочленом Ньютона (разделенные разности): {x_interp}: {y_newton:.6f}") + print(f"интерполяция многочленом Гаусса: {x_interp}: {y_gauss:.6f}") + + plt.plot(x, y, "ro", color="cyan", label='Узлы') + plt.plot(x_plot, y_l_plot, color="deeppink", linestyle='--', alpha=0.5, label='Лагранж') + plt.plot(x_plot, y_n_plot, color="purple", linestyle='-.', alpha=0.5, label='Ньютон, разд. разн.') + plt.plot(x_plot, y_g_plot, color="lime", linestyle=':', alpha=0.8, label='Гаусс') + + plt.axvline(x_interp, color='gray', linestyle=':') + plt.legend() + plt.title("интерполяция: Лагранж, Ньютон, Гаусс") + plt.grid(True, color="lightgray") + plt.savefig("interpolation.png") + plt.show() + + +if __name__ == '__main__': + main() diff --git "a/\320\2403213/pimenova_409342/lab6/main.py" "b/\320\2403213/pimenova_409342/lab6/main.py" new file mode 100644 index 0000000..2158bcd --- /dev/null +++ "b/\320\2403213/pimenova_409342/lab6/main.py" @@ -0,0 +1,197 @@ +import numpy as np +import matplotlib.pyplot as plt +import math + + +def euler_method(f, x0, y0, xn, h): + x_values = [x0] + y_values = [y0] + x = x0 + y = y0 + while x < xn - 1e-8: + y += h * f(x, y) + x += h + x_values.append(x) + y_values.append(y) + return x_values, y_values + + +def runge_kutta_4(f, x0, y0, xn, h): + x_values = [x0] + y_values = [y0] + x = x0 + y = y0 + while x < xn - 1e-8: + k1 = h * f(x, y) + k2 = h * f(x + h / 2, y + k1 / 2) + k3 = h * f(x + h / 2, y + k2 / 2) + k4 = h * f(x + h, y + k3) + y += (k1 + 2 * k2 + 2 * k3 + k4) / 6 + x += h + x_values.append(x) + y_values.append(y) + return x_values, y_values + + +def adams_method(f, x0, y0, xn, h): + x_rk, y_rk = runge_kutta_4(f, x0, y0, x0 + 3 * h, h) + x_values = x_rk.copy() + y_values = y_rk.copy() + x = x0 + 3 * h + while x < xn - 1e-8: + f0 = f(x_values[-4], y_values[-4]) + f1 = f(x_values[-3], y_values[-3]) + f2 = f(x_values[-2], y_values[-2]) + f3 = f(x_values[-1], y_values[-1]) + + # предиктор + y_pred = y_values[-1] + h * (55 * f3 - 59 * f2 + 37 * f1 - 9 * f0) / 24 + x_next = x + h + f_pred = f(x_next, y_pred) + + # корректор + y_corr = y_values[-1] + h * (9 * f_pred + 19 * f3 - 5 * f2 + f1) / 24 + x_values.append(x_next) + y_values.append(y_corr) + x = x_next + return x_values, y_values + + +def get_equation(equation_choice): + """Возвращает функцию правой части ОДУ по выбору пользователя""" + equations = { + '1': lambda x, y: x + y, + '2': lambda x, y: x ** 2 + y ** 2, + '3': lambda x, y: 2 * x - y + } + return equations.get(equation_choice, equations['1']) + + +def get_exact_solution(equation_choice, x0, y0): + solutions = { + '1': lambda x: -x - 1 + (y0 + x0 + 1) * math.exp(x - x0), + '3': lambda x: 2 * x - 2 + (y0 - 2 * x0 + 2) * math.exp(-(x - x0)) + } + return solutions.get(equation_choice) + + +def runge_rule_error(y_h, y_h2, p): + return abs(y_h - y_h2) / (2 ** p - 1) + + +def calculate_errors(results, exact_solution_func, h, equation_choice, x0, y0, xn): + errors = {} + for method_name, (x_values, y_values) in results.items(): + if method_name in ['euler', 'runge_kutta4']: + h_half = h / 2 + if method_name == 'euler': + _, y_values_half = euler_method(get_equation(equation_choice), x0, y0, xn, h_half) + order = 1 + elif method_name == 'runge_kutta4': + _, y_values_half = runge_kutta_4(get_equation(equation_choice), x0, y0, xn, h_half) + order = 4 + # Находим ближайшие точки для сравнения (последняя точка при шаге h и соответствующая при шаге h/2) + y_h_end = y_values[-1] + y_h2_end = y_values_half[int(len(y_values_half) * h / (xn - x0))] if y_values_half else float('nan') + errors[method_name] = runge_rule_error(y_h_end, y_h2_end, order) + elif method_name == 'adams': + if exact_solution_func: + exact_values = [exact_solution_func(x) for x in x_values] + errors[method_name] = max(abs(y - exact) for y, exact in zip(y_values, exact_values)) + else: + errors[method_name] = float('nan') + else: + errors[method_name] = float('nan') + return errors + + +def display_errors(errors): + print("\nпогрешности методов:") + for method_name, error in errors.items(): + print(f"{method_name}: {error:.6f}") + + +def print_results_table(euler_results, rk4_results, adams_results, exact_values=None): + x_euler, y_euler = euler_results + _, y_rk4 = rk4_results + _, y_adams = adams_results + + print("\n{:<10} {:<15} {:<15} {:<15} {:<15}".format("X", "euler", "Runge-Kutta4", "adams", "Exact")) + print("-" * 70) + for i, x in enumerate(x_euler): + exact = f"{exact_values[i]:.6f}" if exact_values else "N/A" + print("{:<10.4f} {:<15.6f} {:<15.6f} {:<15.6f} {:<15}".format(x, y_euler[i], y_rk4[i], y_adams[i], exact)) + + +def plot_results(euler_results, rk4_results, adams_results, exact_solution_func=None): + x_euler, y_euler = euler_results + x_rk4, y_rk4 = rk4_results + x_adams, y_adams = adams_results + + plt.figure(figsize=(10, 6)) + plt.plot(x_euler, y_euler, label='euler', linestyle='--', color="cyan") + plt.plot(x_rk4, y_rk4, label='runge-kutta 4', linestyle='-.', color="deeppink") + plt.plot(x_adams, y_adams, label='adams', linestyle=':') + if exact_solution_func: + x_exact = np.linspace(min(x_euler), max(x_euler), 500) + y_exact = [exact_solution_func(x) for x in x_exact] + plt.plot(x_exact, y_exact, label='Exact', color='black') + + plt.xlabel('x') + plt.ylabel('y') + plt.title('сравнение численных методов решения дифф уравнений') + plt.legend() + plt.grid(True) + plt.show() + + +def get_input(): + """Получает входные данные от пользователя""" + print("выберите уравнение для решения:") + print("1: dy/dx = x + y") + print("2: dy/dx = x^2 + y^2") + print("3: dy/dx = 2x - y") + equation_choice = input("введите номер уравнения (1, 2 или 3): ") + + try: + x0 = float(input("введите начальное значение x (x0): ")) + y0 = float(input("введите начальное значение y (y0): ")) + xn = float(input("введите конечное значение x (xn): ")) + h = float(input("введите шаг интегрирования (h): ")) + epsilon = float(input("введите желаемую точность (epsilon) ")) + except ValueError: + print("нееееет это все числа") + return None, None, None, None, None, None, None + + exact_solution_func = get_exact_solution(equation_choice, x0, y0) + return equation_choice, x0, y0, xn, h, epsilon, exact_solution_func + + +def solve_and_evaluate(equation_choice, x0, y0, xn, h, epsilon, exact_solution_func=None): + """Решает ОДУ различными методами, выводит результаты и строит графики""" + f = get_equation(equation_choice) + results = { + 'euler': euler_method(f, x0, y0, xn, h), + 'runge_kutta4': runge_kutta_4(f, x0, y0, xn, h), + 'adams': adams_method(f, x0, y0, xn, h) + } + + errors = calculate_errors(results, exact_solution_func, h, equation_choice, x0, y0, xn) + display_errors(errors) + + exact_values = [exact_solution_func(x) for x in results['euler'][0]] if exact_solution_func else None + print_results_table(results['euler'], results['runge_kutta4'], results['adams'], exact_values) + + plot_results(results['euler'], results['runge_kutta4'], results['adams'], exact_solution_func) + + +def main(): + """Главная функция, запускающая процесс решения и сравнения методов""" + inputs = get_input() + if inputs: + equation_choice, x0, y0, xn, h, epsilon, exact_solution_func = inputs + solve_and_evaluate(equation_choice, x0, y0, xn, h, epsilon, exact_solution_func) + + +if __name__ == "__main__": + main() \ No newline at end of file From be37fe5e36f831a108ceb2fddd0426876e4c3fb7 Mon Sep 17 00:00:00 2001 From: p11menova Date: Mon, 26 May 2025 14:23:09 +0300 Subject: [PATCH 09/10] lab6 done --- "\320\2403213/pimenova_409342/lab6/README.md" | 5 ++++- "\320\2403213/pimenova_409342/lab6/main.py" | 6 +----- ...260\321\202_\320\273\320\260\320\2616.pdf" | Bin 0 -> 1229705 bytes 3 files changed, 5 insertions(+), 6 deletions(-) create mode 100644 "\320\2403213/pimenova_409342/lab6/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2616.pdf" diff --git "a/\320\2403213/pimenova_409342/lab6/README.md" "b/\320\2403213/pimenova_409342/lab6/README.md" index 5039391..32b5a6f 100644 --- "a/\320\2403213/pimenova_409342/lab6/README.md" +++ "b/\320\2403213/pimenova_409342/lab6/README.md" @@ -1 +1,4 @@ -Лабораторная работа 6 +### лабораторная работа 4 + +#### «методы решения дифференциальных уравнений» +вариант **9** \ No newline at end of file diff --git "a/\320\2403213/pimenova_409342/lab6/main.py" "b/\320\2403213/pimenova_409342/lab6/main.py" index 2158bcd..6007362 100644 --- "a/\320\2403213/pimenova_409342/lab6/main.py" +++ "b/\320\2403213/pimenova_409342/lab6/main.py" @@ -58,7 +58,6 @@ def adams_method(f, x0, y0, xn, h): def get_equation(equation_choice): - """Возвращает функцию правой части ОДУ по выбору пользователя""" equations = { '1': lambda x, y: x + y, '2': lambda x, y: x ** 2 + y ** 2, @@ -90,7 +89,7 @@ def calculate_errors(results, exact_solution_func, h, equation_choice, x0, y0, x elif method_name == 'runge_kutta4': _, y_values_half = runge_kutta_4(get_equation(equation_choice), x0, y0, xn, h_half) order = 4 - # Находим ближайшие точки для сравнения (последняя точка при шаге h и соответствующая при шаге h/2) + # находим ближайшие точки для сравнения (последняя точка при шаге h и соответствующая при шаге h/2) y_h_end = y_values[-1] y_h2_end = y_values_half[int(len(y_values_half) * h / (xn - x0))] if y_values_half else float('nan') errors[method_name] = runge_rule_error(y_h_end, y_h2_end, order) @@ -146,7 +145,6 @@ def plot_results(euler_results, rk4_results, adams_results, exact_solution_func= def get_input(): - """Получает входные данные от пользователя""" print("выберите уравнение для решения:") print("1: dy/dx = x + y") print("2: dy/dx = x^2 + y^2") @@ -168,7 +166,6 @@ def get_input(): def solve_and_evaluate(equation_choice, x0, y0, xn, h, epsilon, exact_solution_func=None): - """Решает ОДУ различными методами, выводит результаты и строит графики""" f = get_equation(equation_choice) results = { 'euler': euler_method(f, x0, y0, xn, h), @@ -186,7 +183,6 @@ def solve_and_evaluate(equation_choice, x0, y0, xn, h, epsilon, exact_solution_f def main(): - """Главная функция, запускающая процесс решения и сравнения методов""" inputs = get_input() if inputs: equation_choice, x0, y0, xn, h, epsilon, exact_solution_func = inputs diff --git "a/\320\2403213/pimenova_409342/lab6/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2616.pdf" "b/\320\2403213/pimenova_409342/lab6/\320\262\321\213\321\207\320\274\320\260\321\202_\320\273\320\260\320\2616.pdf" new file mode 100644 index 0000000000000000000000000000000000000000..f1fc5492d66cd21ca1b999fa1760c4609dcab9db GIT binary patch literal 1229705 zcmeFa1z42n_djePB}k|!s4z&QbPPj?v>+wjNDSQ!T_Q+H3rb0YgrE{4ttcfeDM*K; zDBZmG46?$iyZifo_y2$2-*vrvUAw@{6X(89ea`2c=UFOQVNnJaMkp>eRU!BX7n=pb z46)QT!Num~Wm0gmf-?!}Aau+u4Vh$h4B@sAR`9hPlcbJ?AuZg34#Fglu(8uaDA>T^ za+a0|2n#C|b%2Z=!pztL9M8hSf%-s7$Hr9L!oU(-75OV%9|BH0a09pv+(HjrgNv0N`OUR!xY%$DeUxxWF%C(Il8#Bp(#`@1!OnEk zSl?D1g1R7t6(s?Ll?!

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