82 lines
2.9 KiB
Python
82 lines
2.9 KiB
Python
|
import time
|
|||
|
|
import random
|
|||
|
|
from multiprocessing import Pool
|
|||
|
|
|
|||
|
|
# Генерация квадратной матрицы со случайными элементами
|
|||
|
|
def generate_matrix(size):
|
|||
|
|
return [[random.randint(0, 10) for _ in range(size)] for _ in range(size)]
|
|||
|
|
|
|||
|
|
# Рекурсивное вычисление по определителю (по первой строке)
|
|||
|
|
def determinant_recursive(matrix):
|
|||
|
|
n = len(matrix)
|
|||
|
|
if n == 1:
|
|||
|
|
return matrix[0][0]
|
|||
|
|
elif n == 2:
|
|||
|
|
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
|
|||
|
|
else:
|
|||
|
|
det = 0
|
|||
|
|
for c in range(n):
|
|||
|
|
if n > 1:
|
|||
|
|
minor = [row[:c] + row[c+1:] for row in matrix[1:]]
|
|||
|
|
else:
|
|||
|
|
minor = []
|
|||
|
|
det += ((-1)**c) * matrix[0][c] * determinant_recursive(minor)
|
|||
|
|
return det
|
|||
|
|
|
|||
|
|
# Вычисление части определителя, выполняется каждым процессом
|
|||
|
|
def worker(chunk):
|
|||
|
|
start, end, matrix = chunk
|
|||
|
|
local_det = 0
|
|||
|
|
|
|||
|
|
if len(matrix) == 1:
|
|||
|
|
local_det = matrix[0][0]
|
|||
|
|
else:
|
|||
|
|
for c in range(start, end):
|
|||
|
|
minor = [row[:c] + row[c + 1:] for row in matrix[1:]]
|
|||
|
|
local_det += ((-1)**c) * matrix[0][c] * determinant_recursive(minor)
|
|||
|
|
|
|||
|
|
return local_det
|
|||
|
|
|
|||
|
|
# Параллельное вычисление определителя матрицы
|
|||
|
|
def parallel_determinant(matrix, num_processes):
|
|||
|
|
n = len(matrix)
|
|||
|
|
|
|||
|
|
with Pool(processes=num_processes) as pool:
|
|||
|
|
num_chunks = min(n, num_processes)
|
|||
|
|
chunk_size = n // num_chunks
|
|||
|
|
remainder = n % num_chunks
|
|||
|
|
|
|||
|
|
chunks = []
|
|||
|
|
start_col = 0
|
|||
|
|
for i in range(num_chunks):
|
|||
|
|
end_col = start_col + chunk_size + (1 if i < remainder else 0)
|
|||
|
|
chunks.append((start_col, end_col, matrix))
|
|||
|
|
start_col = end_col
|
|||
|
|
|
|||
|
|
results = pool.map(worker, chunks)
|
|||
|
|
|
|||
|
|
return sum(results)
|
|||
|
|
|
|||
|
|
if __name__ == "__main__":
|
|||
|
|
sizes = [2, 4, 6, 8, 10]
|
|||
|
|
process_counts = [2, 4, 8]
|
|||
|
|
|
|||
|
|
print("| Размер | Метод | Кол-во процессов | Время (мс) | Детерминант |")
|
|||
|
|
|
|||
|
|
for size in sizes:
|
|||
|
|
matrix = generate_matrix(size)
|
|||
|
|
|
|||
|
|
# Последовательное
|
|||
|
|
start_time = time.time()
|
|||
|
|
det_recursive = determinant_recursive(matrix)
|
|||
|
|
end_time = time.time()
|
|||
|
|
recursive_time_ms = (end_time - start_time) * 1000
|
|||
|
|
print(f"| {size}x{size} | Последовательный | - | {recursive_time_ms} | {det_recursive} |")
|
|||
|
|
|
|||
|
|
# Параллельное
|
|||
|
|
for num_processes in process_counts:
|
|||
|
|
start_time = time.time()
|
|||
|
|
det_parallel = parallel_determinant(matrix, num_processes)
|
|||
|
|
end_time = time.time()
|
|||
|
|
parallel_time_ms = (end_time - start_time) * 1000
|
|||
|
|
print(f"| {size}x{size} | Параллельный | {num_processes} | {parallel_time_ms} | {det_parallel} |")
|