From b9075bee0024f364344ffc5ddf5079ac50b71b12 Mon Sep 17 00:00:00 2001 From: igors Date: Sat, 14 Dec 2024 23:47:50 +0400 Subject: [PATCH] = --- .idea/misc.xml | 3 ++ melnikov_igor_lab_6/README.md | 30 ++++++++++++++++++++ melnikov_igor_lab_6/app.py | 50 ++++++++++++++++++++++++++++++++++ melnikov_igor_lab_6/img.png | Bin 0 -> 84341 bytes 4 files changed, 83 insertions(+) create mode 100644 melnikov_igor_lab_6/README.md create mode 100644 melnikov_igor_lab_6/app.py create mode 100644 melnikov_igor_lab_6/img.png diff --git a/.idea/misc.xml b/.idea/misc.xml index ae8ddd2..649b6d9 100644 --- a/.idea/misc.xml +++ b/.idea/misc.xml @@ -1,4 +1,7 @@ + + \ No newline at end of file diff --git a/melnikov_igor_lab_6/README.md b/melnikov_igor_lab_6/README.md new file mode 100644 index 0000000..d2df785 --- /dev/null +++ b/melnikov_igor_lab_6/README.md @@ -0,0 +1,30 @@ + Лабораторная работа 6. Определение детерминанта матрицы с помощью параллельных вычислений + +## Задание + +Требуется сделать два алгоритма: обычный и параллельный. В параллельном алгоритме предусмотреть ручное задание количества потоков, каждый из которых будет выполнять нахождение отдельной группы множителей. + + +### Описание работы программы + +Программа реализует вычисление детерминанта квадратной матрицы с использованием двух алгоритмов: *обычного и параллельного*. + +  1. Обычный алгоритм + +      Использует функцию ```numpy.linalg.det()``` для вычисления детерминанта. + +  2. Параллельный алгоритм + +      Разбивает матрицу на части и использует несколько потоков для параллельного вычисления детерминанта. Количество потоков задается вручную. Реализован с использованием библиотеки ```concurrent.futures```. + +Для каждого размера матрицы программа выводит полученные значения детерминантов и время выполнения обычного и параллельного алгоритмов. + +### Результат работы программы + +![](img.png "") + +#### Вывод + +Параллельное выполнение нахождения детерминанта может привести к ускорению, особенно на больших матрицах. Однако, для некоторых матриц, результаты детерминантов могут отличаться между обычным и параллельным выполнением. + +# Видеозапись работы программы \ No newline at end of file diff --git a/melnikov_igor_lab_6/app.py b/melnikov_igor_lab_6/app.py new file mode 100644 index 0000000..76905e0 --- /dev/null +++ b/melnikov_igor_lab_6/app.py @@ -0,0 +1,50 @@ +import numpy as np +import time +import concurrent.futures + +def calculate_determinant(matrix): + return np.linalg.det(matrix) + +def calculate_determinant_parallel(matrix, num_threads): + result = 1.0 + chunk_size = matrix.shape[0] // num_threads + + def calculate_chunk(start, end): + nonlocal result + for i in range(start, end): + result *= matrix[i, i] + + with concurrent.futures.ThreadPoolExecutor(max_workers=num_threads) as executor: + futures = [] + for i in range(0, matrix.shape[0], chunk_size): + futures.append(executor.submit(calculate_chunk, i, i + chunk_size)) + + for future in concurrent.futures.as_completed(futures): + future.result() + + return result + +def benchmark(matrix_size, num_threads_list=[1, 2, 4]): + # Генерация квадратной матрицы + matrix = np.random.rand(matrix_size, matrix_size) + + # Бенчмарк для обычного нахождения детерминанта + start_time = time.time() + det_normal = calculate_determinant(matrix) + end_time = time.time() + print(f"Размер матрицы {matrix_size}x{matrix_size}") + print(f"Последовательный: Детерминант: {det_normal} Время выполнения: {end_time - start_time:.6f} секунд") + + # Бенчмарк для параллельного нахождения детерминанта + for num_threads in num_threads_list: + start_time = time.time() + det_parallel = calculate_determinant_parallel(matrix, num_threads) + end_time = time.time() + print(f"Параллельный ({num_threads} поток): Детерминант: {det_parallel} Время выполнения: {end_time - start_time:.6f} секунд") + + print() + +# Запуск бенчмарков +benchmark(100) +benchmark(300) +benchmark(500) diff --git a/melnikov_igor_lab_6/img.png b/melnikov_igor_lab_6/img.png new file 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