84 lines
2.8 KiB
Python
84 lines
2.8 KiB
Python
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import random
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import time
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import multiprocessing
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import numpy as np
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# Генерация матрицы
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def generate_matrix(size):
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return [[random.randint(0, 10) for _ in range(size)] for _ in range(size)]
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# Вычисление детерминанта матрицы (рекурсивно)
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def determinant(matrix):
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size = len(matrix)
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if size == 2:
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return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
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det = 0
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for col in range(size):
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submatrix = [row[:col] + row[col+1:] for row in matrix[1:]]
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det += ((-1) ** col) * matrix[0][col] * determinant(submatrix)
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return det
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# Вычисление детерминанта параллельно
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def parallel_determinant(matrix, num_processes):
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size = len(matrix)
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if size <= 2:
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return determinant(matrix)
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# Разбиение задачи по строкам на несколько потоков
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chunk_size = size // num_processes
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chunks = []
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# Создание задач для потоков
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for i in range(num_processes):
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start_row = i * chunk_size
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end_row = (i + 1) * chunk_size if i < num_processes - 1 else size
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chunks.append((matrix[start_row:end_row], i))
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with multiprocessing.Pool(processes=num_processes) as pool:
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results = pool.starmap(calculate_determinant_chunk, [(matrix, chunk[0], chunk[1]) for chunk in chunks])
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det = sum(results)
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return det
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# Вычисление детерминанта для части матрицы в одном процессе
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def calculate_determinant_chunk(matrix, chunk, chunk_index):
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size = len(matrix)
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det = 0
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for row in chunk:
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for col in range(size):
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submatrix = [r[:col] + r[col+1:] for r in matrix[1:]]
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det += ((-1) ** (chunk_index + col)) * matrix[0][col] * determinant(submatrix)
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return det
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# Замер времени для параллельного вычисления детерминанта
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def benchmark(size, num_processes=1):
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matrix = generate_matrix(size)
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start_time = time.time()
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parallel_determinant(matrix, num_processes)
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par_time = time.time() - start_time
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return par_time
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def main():
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# Размеры матриц
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matrix_sizes = [9, 10, 11]
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# Количество потоков
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num_processes_list = [1, 2, 4, 6, 8]
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# Таблица с бенчмарками
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print("-*" * 40)
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print(f"{'Количество потоков':<20}{'|9x9 (сек.)':<20}{'|10x10 (сек.)':<20}{'|11x11 (сек.)'}")
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print("-*" * 40)
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for num_processes in num_processes_list:
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row = f"{num_processes:<20}"
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for size in matrix_sizes:
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par_time = benchmark(size, num_processes)
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row += f"|{par_time:.4f}".ljust(20)
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print(row)
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print("-*" * 40)
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if __name__ == "__main__":
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main()
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