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z+_TvTz3-z7ghCaPz|389tuEwXuEkyo;r9EcR7cCFo2;XXZG-z(M0;e&Zw`duq726Y zPV8jSXOQJa;9B+91;@^(3jCG$wiB1`57@LgK)4@14j~@W`c#yenj&Q6n`kxSAD699 znOpvK!}fwiKk5G8$HFfn1SQU&KL1AX|Lq4YXBUTNMBx3Q3bPkTA1!q~wF;G|!T$zX CB abs(mat[max_row][i]): + max_row = k + + if abs(mat[max_row][i]) < 1e-9: + return 0 + + mat[[i, max_row]] = mat[[max_row, i]] + + for k in range(i + 1, n): + factor = mat[k][i] / mat[i][i] + for j in range(i, n): + mat[k][j] -= factor * mat[i][j] + + det = 1 + for i in range(n): + det *= mat[i][i] + return det + +def determinant_parallel_worker(matrix_part, row_indices): + n_part = len(matrix_part) + local_matrix = np.copy(matrix_part) + local_row_indices = np.copy(row_indices) + + for i in range(n_part): + max_row = i + for k in range(i + 1, n_part): + if abs(local_matrix[k][i]) > abs(local_matrix[max_row][i]): + max_row = k + + if abs(local_matrix[max_row][i]) < 1e-9: + return 0, local_row_indices + + local_matrix[[i, max_row]] = local_matrix[[max_row, i]] + local_row_indices[[i, max_row]] = local_row_indices[[max_row, i]] + + for k in range(i + 1, n_part): + factor = local_matrix[k][i] / local_matrix[i][i] + for j in range(i, n_part): + local_matrix[k][j] -= factor * local_matrix[i][j] + + det_part = 1 + for i in range(n_part): + det_part *= local_matrix[i][i] + return det_part, local_row_indices + + +def determinant_parallel(matrix, num_threads): + n = len(matrix) + if n == 1: + return matrix[0][0] + + if num_threads > n: + num_threads = n + + chunk_size = n // num_threads + + with multiprocessing.Pool(processes=num_threads) as pool: + results = [] + row_indices = np.arange(n) + for i in range(num_threads): + start_row = i * chunk_size + end_row = (i + 1) * chunk_size if i < num_threads - 1 else n + res = pool.apply_async(determinant_parallel_worker, + (matrix[start_row:end_row, :], row_indices[start_row:end_row])) + results.append(res) + + partial_dets = [] + for res in results: + det_part, row_indices_part = res.get() + partial_dets.append(det_part) + + + final_det = 1 + for det_part in partial_dets: + final_det *= det_part + + return final_det + + + +def calculate_determinant(matrix, num_threads): + if num_threads == 1: + return determinant_sequential(matrix) + else: + return determinant_parallel(matrix, num_threads) + + +if __name__ == '__main__': + sizes = [100, 300, 500] + num_threads_list = [1, 2, 4] + + for size in sizes: + matrix = np.random.rand(size, size) + for num_threads in num_threads_list: + start_time = time.time() + if num_threads == 1: + calculation_method = "Последовательный" + else: + calculation_method = f"Параллельный ({num_threads} потоков)" + det = calculate_determinant(matrix, num_threads) + end_time = time.time() + print( + f"Размер матрицы: {size}x{size}, Метод вычисления: {calculation_method}, Время: {end_time - start_time:.4f} сек.") diff --git a/rogashova_ekaterina_lab_6/readme.md b/rogashova_ekaterina_lab_6/readme.md new file mode 100644 index 0000000..308d692 --- /dev/null +++ b/rogashova_ekaterina_lab_6/readme.md @@ -0,0 +1,17 @@ +# Лабораторная работа №6 + +## Описание +Написана программа, которая вычисляет определитель квадратной матрицы двумя способами: +последовательно и параллельно, и сравнивает время их выполнения. + +Для каждой матрицы вычисляется детерминант с использованием различных количеств потоков (1, 2 и 4) и выводится время работы. + +## Вывод работы +Для матрицы 300x300 и 500x500 результаты показывают значительное преимущество параллельных вычислений. +Параллельные вычисления с 4 потоками значительно более эффективны, чем с 2 потоками для больших матриц (300x300 и 500x500). Это может указывать на то, что алгоритм выгодно распараллеливается, и использование большего числа потоков помогает снизить время исполнения. +Однако на малых матрицах (100x100) из-за высокой нагрузки на управление потоками производительность уменьшается (или не значительная). + +![img.png](img.png) + +## Видео +Работоспособность представлена на [видео](https://vk.com/video204968285_456240930). \ No newline at end of file