From c6a514e55edbccc15931ebf4593e296c3c09905f Mon Sep 17 00:00:00 2001 From: Alexey <142442789+666Daredevil666@users.noreply.github.com> Date: Tue, 10 Jun 2025 13:28:25 +0300 Subject: [PATCH 1/6] add lab1 --- "\320\2403212/bondarev_408300/lab1/input.txt" | 8 + "\320\2403212/bondarev_408300/lab1/main.py" | 179 ++++++++++++++++++ ...1\200\320\265\320\262\320\220\320\234.pdf" | Bin 0 -> 1107592 bytes 3 files changed, 187 insertions(+) create mode 100644 "\320\2403212/bondarev_408300/lab1/input.txt" create mode 100644 "\320\2403212/bondarev_408300/lab1/main.py" create mode 100644 "\320\2403212/bondarev_408300/lab1/\320\222\321\213\321\207\320\274\320\260\321\202_\320\233\320\2401_\320\221\320\276\320\275\320\264\320\260\321\200\320\265\320\262\320\220\320\234.pdf" diff --git "a/\320\2403212/bondarev_408300/lab1/input.txt" "b/\320\2403212/bondarev_408300/lab1/input.txt" new file mode 100644 index 0000000..285ef82 --- /dev/null +++ "b/\320\2403212/bondarev_408300/lab1/input.txt" @@ -0,0 +1,8 @@ +3 +4 1 1 +1 5 1 +1 1 6 +6 7 8 + + + diff --git "a/\320\2403212/bondarev_408300/lab1/main.py" "b/\320\2403212/bondarev_408300/lab1/main.py" new file mode 100644 index 0000000..7293a83 --- /dev/null +++ "b/\320\2403212/bondarev_408300/lab1/main.py" @@ -0,0 +1,179 @@ +import numpy as np +import random + + +def read_data_from_keyboard(): + print("Введите размерность матрицы n (1-20): ") + n = int(input().strip()) + if n > 20 or n <= 0: + raise ValueError("Недопустимое значение n.") + + A = [] + print(f"Введите матрицу A ({n}x{n} построчно, числа через пробел):") + for _ in range(n): + row = list(map(float, input().split())) + if len(row) != n: + raise ValueError("Неверное количество элементов в строке.") + A.append(row) + + print(f"Введите вектор b ({n} чисел через пробел):") + b = list(map(float, input().split())) + if len(b) != n: + raise ValueError("Неверное количество элементов в векторе b.") + + return n, A, b + + +def read_data_from_file(filename="input.txt"): + with open(filename, 'r') as f: + lines = [line.strip() for line in f if line.strip()] + + idx = 0 + n = int(lines[idx]) + idx += 1 + A = [] + for _ in range(n): + A.append(list(map(float, lines[idx].split()))) + idx += 1 + + b = list(map(float, lines[idx].split())) + return n, A, b + + +def generate_random_system(n): + A = [] + for i in range(n): + row = [random.uniform(-10, 10) for _ in range(n)] + diag_temp = row[i] + row[i] = 0 + sum_other = sum(abs(x) for x in row) + sign = random.choice([-1, 1]) + row[i] = sign * (sum_other + random.uniform(1, 5)) + A.append(row) + + b = [random.uniform(-10, 10) for _ in range(n)] + return np.array(A, dtype=float), np.array(b, dtype=float) + + +def check_and_make_diagonally_dominant(A, b): + n = len(A) + for i in range(n): + max_row = i + max_val = abs(A[i][i]) + for j in range(i, n): + current = abs(A[j][i]) + if current > max_val: + max_val = current + max_row = j + + if max_val == 0: + return False + + A[i], A[max_row] = A[max_row], A[i] + b[i], b[max_row] = b[max_row], b[i] + return True + + +def simple_iterations(A, b, eps=1e-6, max_iter=1000): + n = len(A) + D = np.diag(A) + if any(d == 0 for d in D): + raise ValueError("На диагонали есть нулевые элементы после перестановки.") + + B = -np.array(A) / D[:, None] + np.fill_diagonal(B, 0) + c = np.array(b) / D + + x = np.zeros(n) + for it in range(1, max_iter + 1): + x_new = B @ x + c + if np.linalg.norm(x_new - x, np.inf) < eps: + return x_new, it, (x_new - x) + x = x_new + return x, max_iter, (x - x_new) + + +def print_results(A, b, x, iterations, diff, eps): + print("\nРезультаты:") + print(f"Количество итераций: {iterations}") + print("Вектор решения:") + print(np.array2string(x, precision=9, suppress_small=True)) + + print("\nВектор погрешностей (последняя итерация):") + print(np.array2string(diff, precision=2, suppress_small=True)) + + residual = A @ x - b + print("\nВектор невязки (A*x - b):") + print(np.array2string(residual, precision=2, suppress_small=True)) + + print(f"\nПроверка точности (||Δx|| < {eps}): {np.linalg.norm(diff, np.inf):.2e}") + + +def compare_with_numpy(A, b): + try: + x_lib = np.linalg.solve(A, b) + print("\nРешение с использованием numpy.linalg.solve:") + print(np.array2string(x_lib, precision=9, suppress_small=True)) + return x_lib + except np.linalg.LinAlgError: + print("\nМатрица вырождена, библиотечное решение невозможно.") + return None + + +def main(): + print("Лабораторная работа: Метод простых итераций") + print("=" * 50) + + source = input("Ввод данных:\n1 - Клавиатура\n2 - Файл\n3 - Случайная генерация\nВыбор: ").strip() + + if source == '1': + n, A, b = read_data_from_keyboard() + A = np.array(A, dtype=float) + b = np.array(b, dtype=float) + elif source == '2': + n, A, b = read_data_from_file() + A = np.array(A, dtype=float) + b = np.array(b, dtype=float) + elif source == '3': + print("Введите размерность матрицы n (1-20): ") + n = int(input().strip()) + if n > 20 or n <= 0: + print("Недопустимое значение n!") + return + A, b = generate_random_system(n) + print("\nСгенерированная матрица A:") + print(np.array2string(A, precision=2, suppress_small=True)) + print("\nСгенерированный вектор b:") + print(np.array2string(b, precision=2, suppress_small=True)) + else: + print("Неверный ввод!") + return + + if not check_and_make_diagonally_dominant(A, b): + print("Невозможно достичь диагонального преобладания!") + return + + eps = float(input("Введите точность (например, 1e-6): ").strip() or 1e-6) + + try: + x, iterations, diff = simple_iterations(A, b, eps) + except ValueError as e: + print(f"Ошибка: {str(e)}") + return + + print_results(A, b, x, iterations, diff, eps) + x_lib = compare_with_numpy(A, b) + + if x_lib is not None: + diff = x - x_lib + print("\nРазница с библиотечным решением:") + print(f"Максимальная: {np.abs(diff).max():.2e}") + print(f"Средняя: {np.abs(diff).mean():.2e}") + print("\nОбъяснение: Различия вызваны:") + print("- Ограниченным числом итераций метода") + print("- Накоплением ошибок округления") + print("- Особенностями метода (диагональное преобладание)") + + +if __name__ == "__main__": + main() \ No newline at end of file diff --git "a/\320\2403212/bondarev_408300/lab1/\320\222\321\213\321\207\320\274\320\260\321\202_\320\233\320\2401_\320\221\320\276\320\275\320\264\320\260\321\200\320\265\320\262\320\220\320\234.pdf" "b/\320\2403212/bondarev_408300/lab1/\320\222\321\213\321\207\320\274\320\260\321\202_\320\233\320\2401_\320\221\320\276\320\275\320\264\320\260\321\200\320\265\320\262\320\220\320\234.pdf" new file mode 100644 index 0000000000000000000000000000000000000000..c6edfaa996e3a4975c4824e40b5649adbb6ce9f4 GIT binary patch literal 1107592 zcmeFXV{~TQ)-_tOQ>oZVg%#VjZ5vN)qvA>`wr$(2*tTukUuqxhz0do$uianww%gkI z^Q`%-HP@Q%qmR)Cv8>7*A2b6#ExxtB88jy+K8-NI!okSy z<7%PjU?gZ{U~OoGPa|n$W#V9pPsd76htJIoZSP=bq-P230#v4^7J)ZhXoE0la)tAKSdG0roQY#r|^Hj<5Cm=B!zF z!~3Pma^CHoz~_j!)~zj>!azgpm>$WFX6|eSjzWO z{Uyiuvw`!nKUB_HHeoAPHv|VZAxa9cs2vTq8B*D_xd;z$10DT@(kBR9zLw5$uG?&P z&d!@J4dN~Rsta-^kvSEa zkAZu~%2{_64YZZqK6BWI?DlQoJ4+}nD2r#cFXE+K0yhaLRh#_Eci#6D>-9>6BR1v$ zUPU`Bzf&J`bF8?E^XocjfaCb|@g`!Ho1Dd1wPH*CB-e(bCyO*i&z@X4BrQq=NvG

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