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