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z?lol+w`^wa?_?6U17=&$W)6w=;!;-(c*=^14ZHiBh8m&+tNZbrYM6yjFz zj50Vj;yV8)E!)M+#*XE}!zCy8_fOsE|IdHl#`)bH@mv5G_V=G*5I1<3Oq_>n<3?32 vH6E_Nf15$!;rjnlJLx?xEO+8TA)HD{bAAJ;%eE&DIqf#H;#3;#pNjt%VMY Date: Sun, 18 May 2025 15:34:14 +0300 Subject: [PATCH 2/7] Add files via upload --- .../molodichenko_409163/lab5/main-5.py" | 180 ++++++++++++++++++ .../lab5/\320\273\320\260\320\2615.pdf" | Bin 0 -> 636065 bytes 2 files changed, 180 insertions(+) create mode 100644 "\320\2403213/molodichenko_409163/lab5/main-5.py" create mode 100644 "\320\2403213/molodichenko_409163/lab5/\320\273\320\260\320\2615.pdf" diff --git "a/\320\2403213/molodichenko_409163/lab5/main-5.py" "b/\320\2403213/molodichenko_409163/lab5/main-5.py" new file mode 100644 index 0000000..a72b5ac --- /dev/null +++ "b/\320\2403213/molodichenko_409163/lab5/main-5.py" @@ -0,0 +1,180 @@ +#!/usr/bin/env python3 +""" +ЛР-5 (Интерполяция функции) +Вариант 6 — универсальная программа: + • ввод данных тремя способами + • таблица конечных разностей + • методы: Лагранж, Ньютон (разд. и конечные Δ), Гаусс + • графики и элементарная валидация +""" + +import math, sys, json, pathlib +from typing import Callable, List, Tuple +import numpy as np +import matplotlib.pyplot as plt +def is_uniform(xs, rtol=1e-12, atol=1e-14): + diffs = np.diff(xs) + return np.allclose(diffs, diffs[0], rtol=rtol, atol=atol) +# ──────────────────────────────────── служебные функции ────────────── +def forward_differences(y: List[float]) -> List[List[float]]: + """Полный треугольник конечных разностей Δᵏyᵢ""" + table = [y] + while len(table[-1]) > 1: + prev = table[-1] + table.append([prev[i + 1] - prev[i] for i in range(len(prev) - 1)]) + return table + +def print_table(table: List[List[float]]) -> None: + w = max(len(table[0]), 7) + for k, row in enumerate(table): + print(f'Δ{k:>1} ', end='') + print(' '.join(f'{v:>10.6f}' for v in row).ljust(w * 12)) + print() + +# ─────────────────────────────── интерполяционные методы ───────────── +def lagrange(x: List[float], y: List[float], xp: float) -> float: + s = 0.0 + for i in range(len(x)): + li = 1.0 + for j in range(len(x)): + if i != j: + li *= (xp - x[j]) / (x[i] - x[j]) + s += y[i] * li + return s + +def newton_backward(x: List[float], y: List[float], xp: float) -> float: + h = x[1] - x[0] + u = (xp - x[-1]) / h + Δ = forward_differences(y) + res = y[-1] + term, fact = 1.0, 1 + for k in range(1, len(x)): + term *= (u + k - 1) + fact *= k + res += term * Δ[k][-1] / fact + return res + +def newton_forward(x: List[float], y: List[float], xp: float) -> float: + h = x[1] - x[0] + u = (xp - x[0]) / h + Δ = forward_differences(y) + res = y[0] + term, fact = 1.0, 1 + for k in range(1, len(x)): + term *= (u - (k - 1)) + fact *= k + res += term * Δ[k][0] / fact + return res + +def gauss_second_backward(x: List[float], y: List[float], xp: float) -> float: + """Формула Гаусса 2-я, 'назад' (центр — средняя точка)""" + n = len(x) + m = n // 2 # индекс центра + h = x[1] - x[0] + t = (xp - x[m]) / h + Δ = forward_differences(y) + + # удобные ссылки на нужные ∇-разности + def nabla(k: int, j: int) -> float: + """∇ᵏ y_{j} (j отсчитывается от x₀)""" + return Δ[k][j] + + res = y[m] + + res += t * nabla(1, m - 1) + res += t*(t + 1)/2 * nabla(2, m - 1) + res += t*(t + 1)*(t - 1)/6* nabla(3, m - 2) + res += t*(t + 1)*(t - 1)*(t - 2)/24 * nabla(4, m - 2) + res += t*(t + 1)*(t - 1)*(t - 2)*(t + 2)/120 * nabla(5, m - 3) + res += t*(t + 1)*(t - 1)*(t - 2)*(t + 2)*(t + 3)/720 * nabla(6, m - 3) + + return res + +# ──────────────────────────────── источник данных ──────────────────── +def source_keyboard() -> Tuple[List[float], List[float]]: + n = int(input("Сколько узлов? > ")) + 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 source_file(path: str) -> Tuple[List[float], List[float]]: + arr = np.loadtxt(path, delimiter=',') + return arr[:, 0].tolist(), arr[:, 1].tolist() + +def source_function(func: Callable[[float], float]) -> Tuple[List[float], List[float]]: + a = float(input("a = ")) + b = float(input("b = ")) + n = int(input("точек (≥2) = ")) + x = np.linspace(a, b, n) + y = [func(t) for t in x] + return x.tolist(), y + +# ────────────────────────────────── графика ────────────────────────── +def draw(x: List[float], y: List[float], + poly: Callable[[float], float], title: str = "") -> None: + xs = np.linspace(min(x), max(x), 400) + plt.figure() + plt.plot(xs, [poly(t) for t in xs], label='Полином', linewidth=1.2) + plt.scatter(x, y, marker='o', zorder=3, label='Узлы') + plt.title(title) + plt.grid() + plt.legend() + plt.show() + +# ─────────────────────────────── основная логика ───────────────────── +METHODS = { + 1: ("Лагранж", lagrange), + 2: ("Ньютон (разд.)", newton_forward), # для разн. h программа сама решит F/B + 3: ("Ньютон (Δ, назад)", newton_backward), +} + +def run() -> None: + print("===== Лабораторная работа 5. Выбор источника данных =====") + print("1 — Ввод с клавиатуры") + print("2 — Чтение CSV-файла (x,y)") + print("3 — Таблица сгенерирована по функции") + choice = input("> ") + + if choice == "1": + x, y = source_keyboard() + elif choice == "2": + fname = input("Имя файла > ") + x, y = source_file(fname) + elif choice == "3": + funcs = {"sin": math.sin, + "cos": math.cos, + "exp": math.exp} + print("Доступные функции:", *funcs) + fkey = input("> ") + x, y = source_function(funcs[fkey]) + else: + sys.exit("неизвестный выбор") + + if not is_uniform(x): + sys.exit("Для формул с Δ требуется равномерная сетка!") + + print("\n— Таблица конечных разностей —") + table = forward_differences(y) + print_table(table) + + xp = float(input("x*, где вычислять полином = ")) + + print("\nМетод значение") + for num, (name, fn) in METHODS.items(): + try: + fx = fn(x, y, xp) + print(f"{num:>2}. {name:<20} {fx:>12.6f}") + except Exception as e: + print(f"{num:>2}. {name:<20} ошибка: {e}") + + # пример 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-> 416585 bytes 2 files changed, 120 insertions(+) create mode 100644 "\320\2403213/molodichenko_409163/lab6/vichmat6.py" create mode 100644 "\320\2403213/molodichenko_409163/lab6/\320\273\320\260\320\2616.pdf" diff --git "a/\320\2403213/molodichenko_409163/lab6/vichmat6.py" "b/\320\2403213/molodichenko_409163/lab6/vichmat6.py" new file mode 100644 index 0000000..23deee8 --- /dev/null +++ "b/\320\2403213/molodichenko_409163/lab6/vichmat6.py" @@ -0,0 +1,120 @@ +import numpy as np +import matplotlib.pyplot as plt + +class ODESolver: + def __init__(self, f, exact=None): + self.f = f # function f(x,y) + self.exact = exact # exact solution y(x) + + def euler(self, x0, y0, xn, h): + n = int((xn - x0)/h) + xs = np.linspace(x0, x0 + n*h, n+1) + ys = np.zeros(n+1) + ys[0] = y0 + for i in range(n): + ys[i+1] = ys[i] + h * self.f(xs[i], ys[i]) + return xs, ys + + def rk4(self, x0, y0, xn, h): + n = int((xn - x0)/h) + xs = np.linspace(x0, x0 + n*h, n+1) + ys = np.zeros(n+1) + ys[0] = y0 + for i in range(n): + x, y = xs[i], ys[i] + k1 = self.f(x, y) + k2 = self.f(x + h/2, y + h*k1/2) + k3 = self.f(x + h/2, y + h*k2/2) + k4 = self.f(x + h, y + h*k3) + ys[i+1] = y + h*(k1 + 2*k2 + 2*k3 + k4)/6 + return xs, ys + + def adams_pc(self, x0, y0, xn, h): + # 4-step Adams-Bashforth predictor, Adams-Moulton corrector + xs_rk, ys_rk = self.rk4(x0, y0, x0 + 3*h, h) + xs = list(xs_rk) + ys = list(ys_rk) + n = int((xn - x0)/h) + for i in range(3, n): + x_vals = xs[i-3:i+1] + y_vals = ys[i-3:i+1] + f_vals = [self.f(x_vals[j], y_vals[j]) for j in range(4)] + # predictor (Adams-Bashforth) + y_pred = ys[i] + h*(55*f_vals[3] - 59*f_vals[2] + 37*f_vals[1] - 9*f_vals[0])/24 + x_next = xs[i] + h + # corrector (Adams-Moulton) + f_pred = self.f(x_next, y_pred) + y_corr = ys[i] + h*(9*f_pred + 19*f_vals[3] - 5*f_vals[2] + f_vals[1])/24 + xs.append(x_next) + ys.append(y_corr) + return np.array(xs), np.array(ys) + + def runge_error(self, method, p, *args): + # compute error estimate via Runge rule + xs1, ys1 = method(*args) + h = args[3] + args_half = (args[0], args[1], args[2], h/2) + xs2, ys2 = method(*args_half) + # align: ys2 at every 2nd step + ys2_sub = ys2[::2] + err = np.max(np.abs((ys2_sub - ys1)/(2**p - 1))) + return err + + +def select_problem(): + print("Выберите ОДУ из списка:") + print("1) y' = y, y(0) = 1, точное: y = exp(x)") + print("2) y' = x, y(0) = 0, точное: y = x^2/2") + print("3) y' = x*y, y(0) = 1, точное: y = exp(x^2/2)") + choice = int(input("Номер задачи: ")) + if choice == 1: + return lambda x,y: y, lambda x: np.exp(x), 0, 1 + if choice == 2: + return lambda x,y: x, lambda x: x**2/2, 0, 0 + if choice == 3: + return lambda x,y: x*y, lambda x: np.exp(x**2/2), 0, 1 + raise ValueError("Неправильный выбор") + +if __name__ == '__main__': + f, exact, x0, y0 = select_problem() + xn = float(input("Введите x_n (конец отрезка): ")) + h = float(input("Введите шаг h: ")) + eps = float(input("Введите точность ε для оценки (например, 1e-3): ")) + + solver = ODESolver(f, exact) + + # вычисления + xe, ye = solver.euler(x0, y0, xn, h) + xr, yr = solver.rk4(x0, y0, xn, h) + xa, ya = solver.adams_pc(x0, y0, xn, h) + + # оценки погрешности + err_euler = solver.runge_error(solver.euler, 1, x0, y0, xn, h) + err_rk4 = solver.runge_error(solver.rk4, 4, x0, y0, xn, h) + true_vals = exact(xr) + err_adams = np.max(np.abs(true_vals - ya)) + + # вывод таблиц + print("\nТаблица решений:") + print("i\tx\tEuler\tRK4\tAdams\tExact") + for i, x in enumerate(xe): + print(f"{i}\t{x:.4f}\t{ye[i]:.6f}\t{yr[i]:.6f}\t{ya[i]:.6f}\t{exact(x):.6f}") + + print(f"\nОценка погрешности Эйлера (Рунге): {err_euler:.2e}") + print(f"Оценка погрешности RK4 (Рунге): {err_rk4:.2e}") + print(f"Максимальная погрешность Адамса: {err_adams:.2e}") + + # график + xs = np.linspace(x0, xn, 200) + plt.plot(xs, exact(xs), label='Exact') + plt.plot(xe, ye, 'o-', label='Euler') + plt.plot(xr, yr, 's-', label='RK4') + plt.plot(xa, ya, 'd-', label='Adams') + plt.legend() + plt.xlabel('x') + plt.ylabel('y') + plt.title("Сравнение методов") + plt.grid(True) + plt.show() + + print("\nГотово. 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"\320\2403213/molodichenko_409163/lab4/lab4metop.py" create mode 100644 "\320\2403213/molodichenko_409163/lab4/\320\273\320\260\320\2614.pdf" diff --git "a/\320\2403213/molodichenko_409163/lab4/lab4.py" "b/\320\2403213/molodichenko_409163/lab4/lab4.py" new file mode 100644 index 0000000..8cc375d --- /dev/null +++ "b/\320\2403213/molodichenko_409163/lab4/lab4.py" @@ -0,0 +1,376 @@ +import numpy as np +import math +import matplotlib.pyplot as plt + + +# --------------------------------------------------------- +# Функции для чтения данных +# --------------------------------------------------------- + +def read_data_console(): + """ + Считывание данных из консоли. + Пользователь вводит количество точек n (8..12), + затем n пар (x_i, y_i). + """ + print("Чтение данных ИЗ КОНСОЛИ.") + print("Введите количество точек (8..12):") + n = int(input().strip()) + if not (8 <= n <= 12): + raise ValueError("Число точек должно быть в диапазоне [8..12].") + + x_vals = [] + y_vals = [] + print(f"Введите {n} пар (x_i, y_i), каждая в новой строке:") + for _ in range(n): + line = input().strip().split() + if len(line) < 2: + raise ValueError("Недостаточно значений в строке.") + x, y = float(line[0]), float(line[1]) + x_vals.append(x) + y_vals.append(y) + + return np.array(x_vals), np.array(y_vals) + + +def read_data_file(): + """ + Считывание данных из файла. + Формат файла (пример): + Первая строка: n (число точек) + Далее n строк, в каждой по два числа: x_i, y_i + """ + print("Чтение данных ИЗ ФАЙЛА.") + print("Введите путь к файлу (например, data.txt):") + filename = input().strip() + + with open(filename, 'r', encoding='utf-8') as f: + lines = f.read().strip().splitlines() + + if not lines: + raise ValueError("Пустой файл.") + + n = int(lines[0].strip()) + if not (8 <= n <= 12): + raise ValueError("Число точек должно быть в диапазоне [8..12].") + + if len(lines) < n + 1: + raise ValueError(f"В файле недостаточно строк. Ожидалось {n} пар данных.") + + x_vals, y_vals = [], [] + for i in range(n): + parts = lines[i + 1].split() + if len(parts) < 2: + raise ValueError(f"Недостаточно значений в строке {i + 2} файла.") + x, y = float(parts[0]), float(parts[1]) + x_vals.append(x) + y_vals.append(y) + + return np.array(x_vals), np.array(y_vals) + + +def choose_data_input(): + """ + Предлагает пользователю выбрать способ ввода данных: + 1) из консоли, + 2) из файла. + Возвращает (x_data, y_data). + """ + print("Выберите способ ввода данных:") + print(" [1] Консоль") + print(" [2] Файл") + choice = input("Ваш выбор: ").strip() + + if choice == '1': + return read_data_console() + elif choice == '2': + return read_data_file() + else: + raise ValueError("Некорректный выбор способа ввода данных.") + + +# --------------------------------------------------------- +# Модели аппроксимации (МНК). +# --------------------------------------------------------- +def fit_linear(x, y): + """ Линейная: f(x) = a + b*x """ + # polyfit вернет [b, a] + b, a = np.polyfit(x, y, deg=1) + return (a, b) + + +def linear_func(x, coeffs): + a, b = coeffs + return a + b * x + + +def fit_poly2(x, y): + """ Полином 2-й степени: f(x)= a + b*x + c*x^2 """ + c, b, a = np.polyfit(x, y, deg=2) + return (a, b, c) + + +def poly2_func(x, coeffs): + a, b, c = coeffs + return a + b * x + c * (x ** 2) + + +def fit_poly3(x, y): + """ Полином 3-й степени: f(x)= a + b*x + c*x^2 + d*x^3 """ + d, c, b, a = np.polyfit(x, y, deg=3) + return (a, b, c, d) + + +def poly3_func(x, coeffs): + a, b, c, d = coeffs + return a + b * x + c * (x ** 2) + d * (x ** 3) + + +def fit_exponential(x, y): + """ + Экспоненциальная: f(x) = A*exp(B*x) + Нужно y>0. + """ + if any(val <= 0 for val in y): + raise ValueError("Невозможно экспоненциальное приближение: y <= 0.") + ln_y = np.log(y) + B, lnA = np.polyfit(x, ln_y, deg=1) + A = math.exp(lnA) + return (A, B) + + +def exponential_func(x, coeffs): + A, B = coeffs + return A * np.exp(B * x) + + +def fit_logarithmic(x, y): + """ + Логарифмическая: f(x)= a + b*ln(x). + Нужно x>0. + """ + if any(val <= 0 for val in x): + raise ValueError("Невозможно логарифмическое приближение: x <= 0.") + ln_x = np.log(x) + b, a = np.polyfit(ln_x, y, deg=1) + return (a, b) + + +def logarithmic_func(x, coeffs): + a, b = coeffs + return a + b * np.log(x) + + +def fit_power(x, y): + """ + Степенная: f(x)= A*x^B. + Нужно x>0, y>0. + """ + if any(val <= 0 for val in x): + raise ValueError("Невозможно степенное приближение: x <= 0.") + if any(val <= 0 for val in y): + raise ValueError("Невозможно степенное приближение: y <= 0.") + ln_x = np.log(x) + ln_y = np.log(y) + B, lnA = np.polyfit(ln_x, ln_y, deg=1) + A = math.exp(lnA) + return (A, B) + + +def power_func(x, coeffs): + A, B = coeffs + return A * (x ** B) + + +# --------------------------------------------------------- +# Оценки (СКО, R^2, Пирсон). +# --------------------------------------------------------- +def sse(x, y, func, coeffs): + return np.sum((func(x, coeffs) - y) ** 2) + + +def rmse(x, y, func, coeffs): + n = len(x) + return math.sqrt(sse(x, y, func, coeffs) / n) + + +def determination_coefficient(x, y, func, coeffs): + ss_res = sse(x, y, func, coeffs) + y_mean = np.mean(y) + ss_tot = np.sum((y - y_mean) ** 2) + if ss_tot == 0: + return 0 + return 1 - (ss_res / ss_tot) + + +def pearson_correlation(x, y): + x_mean, y_mean = np.mean(x), np.mean(y) + num = np.sum((x - x_mean) * (y - y_mean)) + den = math.sqrt(np.sum((x - x_mean) ** 2) * np.sum((y - y_mean) ** 2)) + return num / den if den != 0 else 0 + + +def interpret_r2(r2): + if r2 < 0.3: + return "Очень слабая зависимость (R^2 < 0.3)." + elif r2 < 0.5: + return "Слабая зависимость (0.3 <= R^2 < 0.5)." + elif r2 < 0.7: + return "Зависимость средней силы (0.5 <= R^2 < 0.7)." + elif r2 < 0.9: + return "Достаточно сильная зависимость (0.7 <= R^2 < 0.9)." + else: + return "Очень сильная зависимость (R^2 >= 0.9)." + + +# --------------------------------------------------------- +# Набор рассматриваемых моделей +# --------------------------------------------------------- +MODELS = [ + ("Линейная", fit_linear, linear_func), + ("Полиномиальная 2", fit_poly2, poly2_func), + ("Полиномиальная 3", fit_poly3, poly3_func), + ("Экспоненциальная", fit_exponential, exponential_func), + ("Логарифмическая", fit_logarithmic, logarithmic_func), + ("Степенная", fit_power, power_func), +] + + +# --------------------------------------------------------- +# Рисование итогового графика +# --------------------------------------------------------- +def plot_results(x, y, results): + plt.figure(figsize=(8, 6)) + plt.scatter(x, y, c='black', label='Исходные точки') + + x_min, x_max = min(x), max(x) + dx = 0.05 * (x_max - x_min) if x_max > x_min else 1.0 + x_plot = np.linspace(x_min - dx, x_max + dx, 300) + + for (name, coeffs, func_obj, this_rmse, this_r2) in results: + # Лог/степень -> x>0 + if "Логарифмическая" in name or "Степенная" in name: + x_pos = x_plot[x_plot > 0] + if len(x_pos) == 0: + continue + y_plot = func_obj(x_pos, coeffs) + plt.plot(x_pos, y_plot, label=name) + else: + y_plot = func_obj(x_plot, coeffs) + plt.plot(x_plot, y_plot, label=name) + + plt.title("Сравнение аппроксимаций") + plt.xlabel("x") + plt.ylabel("y") + plt.grid(True) + plt.legend() + plt.show() + + +# --------------------------------------------------------- +# Вспомогательная функция для вывода текста и (опционально) записи в файл +# --------------------------------------------------------- +def print_to_console_and_file(text, file_obj=None, end="\n"): + """ + Выводит строку text в консоль (print) и дублирует её в файл file_obj, + если file_obj не None. + """ + print(text, end=end) + if file_obj is not None: + file_obj.write(text + end) + + +# --------------------------------------------------------- +# Основная программа +# --------------------------------------------------------- +def main(): + # 1) Читаем данные + try: + x_data, y_data = choose_data_input() + except Exception as e: + print(f"Ошибка при вводе данных: {e}") + return + + # 2) Обрабатываем все модели + results = [] # (model_name, coeffs, func, rmse_val, r2_val) + + for model_name, fit_f, func_f in MODELS: + try: + coeffs = fit_f(x_data, y_data) + curr_rmse = rmse(x_data, y_data, func_f, coeffs) + curr_r2 = determination_coefficient(x_data, y_data, func_f, coeffs) + results.append((model_name, coeffs, func_f, curr_rmse, curr_r2)) + except Exception as exc: + # Не удалось применить модель (напр., логарифм при x<=0) + print(f"[Предупреждение] Модель «{model_name}» не подходит: {exc}") + + if not results: + print("Не удалось построить ни одной аппроксимации.") + return + + # 2б) Спросим у пользователя, хочет ли он сохранить результаты в файл. + save_to_file = False + outfile = None + print("Хотите ли сохранить результаты в файл? (y/n)") + ans = input().strip().lower() + if ans == 'y': + print("Введите имя файла для сохранения (например, output.txt):") + out_filename = input().strip() + try: + outfile = open(out_filename, 'w', encoding='utf-8') + save_to_file = True + except Exception as e: + print(f"Не удалось открыть файл на запись: {e}") + + # 3) Вывод результатов в консоль (и файл, если нужно) + best_model, best_rmse, best_coeffs, best_func = None, float('inf'), None, None + + print_to_console_and_file("\nРезультаты аппроксимации:", outfile) + + for (model_name, coeffs, func_f, curr_rmse, curr_r2) in results: + print_to_console_and_file("", outfile) # пустая строка + print_to_console_and_file(f"Модель: {model_name}", outfile) + print_to_console_and_file(f" Коэффициенты: {coeffs}", outfile) + print_to_console_and_file(f" RMSE (СКО): {curr_rmse:.6f}", outfile) + print_to_console_and_file(f" R^2 : {curr_r2:.6f}", outfile) + print_to_console_and_file(f" -> {interpret_r2(curr_r2)}", outfile) + + # Линейная — Пирсон + if model_name == "Линейная": + r_xy = pearson_correlation(x_data, y_data) + print_to_console_and_file(f" Коэффициент корреляции Пирсона: r_xy = {r_xy:.6f}", outfile) + + # Минимальный RMSE -> лучшая модель + if curr_rmse < best_rmse: + best_rmse = curr_rmse + best_model = model_name + best_coeffs = coeffs + best_func = func_f + + print_to_console_and_file("", outfile) + print_to_console_and_file(f"Лучшая модель по критерию минимума RMSE: {best_model}", outfile) + + # 4) Остатки + print_to_console_and_file("", outfile) + print_to_console_and_file(f"Остатки eps_i = f(x_i) - y_i для лучшей модели:", outfile) + fvals = best_func(x_data, best_coeffs) + for i, (xx, yy, fv) in enumerate(zip(x_data, y_data, fvals), start=1): + eps = fv - yy + line = (f" Точка {i}: x={xx}, y={yy}, " + f"f(x)={fv:.5f}, eps={eps:.5f}") + print_to_console_and_file(line, outfile) + + # Закроем файл, если нужно + if outfile is not None: + outfile.close() + print("\nРезультаты также сохранены в файл:", out_filename) + + # 5) Построение единого графика + plot_results(x_data, y_data, results) + + +# --------------------------------------------------------- +# Запуск +# --------------------------------------------------------- +if __name__ == "__main__": + main() diff --git "a/\320\2403213/molodichenko_409163/lab4/lab4metop.py" "b/\320\2403213/molodichenko_409163/lab4/lab4metop.py" new file mode 100644 index 0000000..e5c1480 --- /dev/null +++ "b/\320\2403213/molodichenko_409163/lab4/lab4metop.py" @@ -0,0 +1,81 @@ +import numpy as np +from scipy.optimize import minimize_scalar + +# Целевая функция +f = lambda x: 6*x[0]**2 + x[1]**2 - x[0]*x[1] + 4*x[0] - 8*x[1] + 1 + +# Градиент функции +def grad_f(x): + df_dx1 = 12*x[0] - x[1] + 4 + df_dx2 = 2*x[1] - x[0] - 8 + return np.array([df_dx1, df_dx2]) + +# Округление до 4 значащих цифр +def round_significant(x, digits=4): + return np.array([float(f"{xi:.{digits}g}") for xi in x]) + +# Метод покоординатного спуска +def coordinate_descent(x0, eps=1e-4): + x = np.array(x0, dtype=float) + iterations = 0 + while True: + x_prev = x.copy() + iterations += 1 + + # Минимизация по x1 + f1 = lambda x1: f([x1, x[1]]) + res1 = minimize_scalar(f1) + x[0] = res1.x + + # Минимизация по x2 + f2 = lambda x2: f([x[0], x2]) + res2 = minimize_scalar(f2) + x[1] = res2.x + + if np.linalg.norm(x - x_prev) < eps: + break + + print(f"Coordinate Descent iterations: {iterations}") + return round_significant(x) + +# Метод градиентного спуска +def gradient_descent(x0, alpha=0.05, eps=1e-4): + x = np.array(x0, dtype=float) + iterations = 0 + while True: + x_prev = x.copy() + iterations += 1 + g = grad_f(x) + x = x - alpha * g + if np.linalg.norm(x - x_prev) < eps: + break + print(f"Gradient Descent iterations: {iterations}") + return round_significant(x) + +# Метод наискорейшего спуска +def steepest_descent(x0, eps=1e-4): + x = np.array(x0, dtype=float) + iterations = 0 + while True: + x_prev = x.copy() + iterations += 1 + g = grad_f(x) + direction = -g + + # Одномерная минимизация вдоль направления + phi = lambda alpha: f(x + alpha * direction) + res = minimize_scalar(phi) + alpha = res.x + + x = x + alpha * direction + if np.linalg.norm(x - x_prev) < eps: + break + print(f"Steepest Descent iterations: {iterations}") + return round_significant(x) + +# Тестирование +x0 = [2, 2] +print("Coordinate Descent result:", coordinate_descent(x0)) +print("Gradient Descent result:", gradient_descent(x0)) +print("Steepest Descent result:", steepest_descent(x0)) + diff --git "a/\320\2403213/molodichenko_409163/lab4/\320\273\320\260\320\2614.pdf" "b/\320\2403213/molodichenko_409163/lab4/\320\273\320\260\320\2614.pdf" new file mode 100644 index 0000000000000000000000000000000000000000..832b3a03469909760550f4536dc9c05d31ed5b12 GIT binary patch literal 854619 zcmdqJby$^Kw?3?5(Ty~VSTw9fgLHSJfOISn=|#67-5mlVAtfLo2#5mGErK9Yf{Ri@ zK#=B};NJVyv)?$s@0`Dm7uUs#=XvIsbB=kBdyIPsR6|CNgNsuD8v|Mk{$XQqLEsQa 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