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/dev/null +++ b/agliullov_daniyar_lab_6/main.py @@ -0,0 +1,86 @@ +import numpy as np +import time +from multiprocessing import Pool + +np.seterr(over='ignore') + +# Ѐункция для вычислСния Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ Гаусса +def compute_determinant_gauss(mat): + size = mat.shape[0] + matrix_copy = mat.astype(float) # ΠšΠΎΠΏΠΈΡ€ΡƒΠ΅ΠΌ ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρƒ, Ρ‡Ρ‚ΠΎΠ±Ρ‹ Π½Π΅ ΠΈΠ·ΠΌΠ΅Π½ΡΡ‚ΡŒ ΠΈΡΡ…ΠΎΠ΄Π½ΡƒΡŽ + determinant = 1.0 # ΠΠ°Ρ‡Π°Π»ΡŒΠ½ΠΎΠ΅ Π·Π½Π°Ρ‡Π΅Π½ΠΈΠ΅ Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° + + for k in range(size): + # Находим ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹ΠΉ элСмСнт Π² Ρ‚Π΅ΠΊΡƒΡ‰Π΅ΠΌ столбцС для ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΡ ошибок округлСния + max_index = np.argmax(np.abs(matrix_copy[k:size, k])) + k + if matrix_copy[max_index, k] == 0: + return 0 # Если Π½Π° Π³Π»Π°Π²Π½ΠΎΠΉ Π΄ΠΈΠ°Π³ΠΎΠ½Π°Π»ΠΈ ноль, Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚ Ρ€Π°Π²Π΅Π½ Π½ΡƒΠ»ΡŽ + # МСняСм мСстами строки + if max_index != k: + matrix_copy[[k, max_index]] = matrix_copy[[max_index, k]] + determinant *= -1 # КаТдая пСрСстановка мСняСт Π·Π½Π°ΠΊ Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° + # ΠžΠ±Π½ΡƒΠ»ΡΠ΅ΠΌ элСмСнты Π½ΠΈΠΆΠ΅ Π³Π»Π°Π²Π½ΠΎΠΉ Π΄ΠΈΠ°Π³ΠΎΠ½Π°Π»ΠΈ + for m in range(k + 1, size): + multiplier = matrix_copy[m, k] / matrix_copy[k, k] + matrix_copy[m, k:] -= multiplier * matrix_copy[k, k:] + + # ΠŸΡ€ΠΎΠΈΠ·Π²Π΅Π΄Π΅Π½ΠΈΠ΅ элСмСнтов Π½Π° Π³Π»Π°Π²Π½ΠΎΠΉ Π΄ΠΈΠ°Π³ΠΎΠ½Π°Π»ΠΈ + for j in range(size): + determinant *= matrix_copy[j, j] + return determinant + +# Ѐункция для ΠΏΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½ΠΎΠ³ΠΎ вычислСния Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° +def parallel_worker(index_range, mat): + size = mat.shape[0] + matrix_copy = mat.astype(float) + det = 1.0 + + for k in range(index_range[0], index_range[1]): + max_index = np.argmax(np.abs(matrix_copy[k:size, k])) + k + if matrix_copy[max_index, k] == 0: + return 0 + if max_index != k: + matrix_copy[[k, max_index]] = matrix_copy[[max_index, k]] + det *= -1 + for m in range(k + 1, size): + multiplier = matrix_copy[m, k] / matrix_copy[k, k] + matrix_copy[m, k:] -= multiplier * matrix_copy[k, k:] + return det + +# Ѐункция для ΠΏΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½ΠΎΠ³ΠΎ вычислСния Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° +def compute_parallel_determinant(mat, num_workers): + size = mat.shape[0] + block_size = size // num_workers + ranges = [(i * block_size, (i + 1) * block_size) for i in range(num_workers)] + + with Pool(processes=num_workers) as pool: + results = pool.starmap(parallel_worker, [(block, mat) for block in ranges]) + + # ОбъСдиняСм Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ + total_determinant = sum(results) + return total_determinant + +# Ѐункция для запуска тСстов ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ +def execute_benchmarks(): + sizes = [100, 300, 500, 1000, 1200] # Π Π°Π·ΠΌΠ΅Ρ€Ρ‹ ΠΌΠ°Ρ‚Ρ€ΠΈΡ† + for size in sizes: + random_matrix = np.random.rand(size, size) # ГСнСрация случайной ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ + print(f"--- ВСст ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ для ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ {size}x{size} ---") + + # ΠŸΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΠ½ΠΎΠ΅ вычислСниС Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° + start_time = time.time() + sequential_det = compute_determinant_gauss(random_matrix) + seq_duration = time.time() - start_time + print(f"ВрСмя ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΠ½ΠΎΠ³ΠΎ вычислСния для {size}x{size}: {seq_duration:.4f} сСкунд") + + # ΠŸΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½ΠΎΠ΅ вычислСниС с Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹ΠΌ количСством процСссов + for workers in [1, 2, 4, 6, 8, 12, 16]: + start_time = time.time() + parallel_det = compute_parallel_determinant(random_matrix, workers) + par_duration = time.time() - start_time + speedup_ratio = seq_duration / par_duration if par_duration > 0 else 0 + print(f"ΠŸΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½ΠΎΠ΅ врСмя с {workers} процСссами: {par_duration:.4f} сСкунд, УскорСниС: {speedup_ratio:.2f}") + +# Запуск тСстов ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ +if __name__ == '__main__': + execute_benchmarks() diff --git a/agliullov_daniyar_lab_6/readme.md b/agliullov_daniyar_lab_6/readme.md new file mode 100644 index 0000000..dc8c45c --- /dev/null +++ b/agliullov_daniyar_lab_6/readme.md @@ -0,0 +1,15 @@ +# Аглиуллов Данияр ИБЭбд-41 +# Лабораторная Ρ€Π°Π±ΠΎΡ‚Π° β„–6 + + Для ΠΏΠΎΠ²Ρ‹ΡˆΠ΅Π½ΠΈΡ ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ ΠΏΡ€ΠΈ вычислСнии Π΄Π΅Ρ‚Π΅Ρ€ΠΌΠΈΠ½Π°Π½Ρ‚Π° для Π±ΠΎΠ»ΡŒΡˆΠΈΡ… ΠΌΠ°Ρ‚Ρ€ΠΈΡ† Π±Ρ‹Π»Π° Π΄ΠΎΠ±Π°Π²Π»Π΅Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡ‚ΡŒ ΠΏΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½ΠΎΠΉ ΠΎΠ±Ρ€Π°Π±ΠΎΡ‚ΠΊΠΈ с использованиСм Π±ΠΈΠ±Π»ΠΈΠΎΡ‚Π΅ΠΊΠΈ multiprocessing. Π­Ρ‚ΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΎ Π·Π½Π°Ρ‡ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ ΡƒΡΠΊΠΎΡ€ΠΈΡ‚ΡŒ вычислСния Π·Π° счСт распрСдСлСния Π½Π°Π³Ρ€ΡƒΠ·ΠΊΠΈ ΠΌΠ΅ΠΆΠ΄Ρƒ нСсколькими процСссами. + +Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ тСстов: +![ΠΈΠ·ΠΎΠ±Ρ€Π°ΠΆΠ΅Π½ΠΈΠ΅ 1](../Screenshots/1.png) + +Π‘Ρ€Π°Π²Π½Π΅Π½ΠΈΠ΅ ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ: + + β€’ Π’ тСстах Π½Π° ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Π°Ρ… Ρ€Π°Π·ΠΌΠ΅Ρ€ΠΎΠΌ 100x100, 300x300 ΠΈ 500x500 Π±Ρ‹Π»ΠΎ Π·Π°ΠΌΠ΅Ρ‡Π΅Π½ΠΎ, Ρ‡Ρ‚ΠΎ ΠΏΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½Ρ‹ΠΉ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ дСмонстрируСт Π·Π½Π°Ρ‡ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠ΅ сокращСниС Π²Ρ€Π΅ΠΌΠ΅Π½ΠΈ выполнСния ΠΏΠΎ ΡΡ€Π°Π²Π½Π΅Π½ΠΈΡŽ с ΠΎΠ±Ρ‹Ρ‡Π½Ρ‹ΠΌ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΎΠΌ, особСнно Π½Π° Π±ΠΎΠ»ΡŒΡˆΠΈΡ… ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Π°Ρ…. Π­Ρ‚ΠΎ ΠΏΠΎΠ΄Ρ‚Π²Π΅Ρ€ΠΆΠ΄Π°Π΅Ρ‚ ΡΡ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒ использования многопоточности для Π·Π°Π΄Π°Ρ‡, Ρ‚Ρ€Π΅Π±ΡƒΡŽΡ‰ΠΈΡ… Π±ΠΎΠ»ΡŒΡˆΠΈΡ… Π²Ρ‹Ρ‡ΠΈΡΠ»ΠΈΡ‚Π΅Π»ΡŒΠ½Ρ‹Ρ… рСсурсов. + + β€’ На ΠΌΠ°Π»Ρ‹Ρ… Ρ€Π°Π·ΠΌΠ΅Ρ€Π°Ρ… ΠΌΠ°Ρ‚Ρ€ΠΈΡ† (Π½Π°ΠΏΡ€ΠΈΠΌΠ΅Ρ€, 100x100) прСимущСство Π±Ρ‹Π»ΠΎ Π·Π° ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹ΠΌ ΡƒΠΌΠ½ΠΎΠΆΠ΅Π½ΠΈΠ΅ΠΌ ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ ΠΈΠ·-Π·Π° Π½Π°ΠΊΠ»Π°Π΄Π½Ρ‹Ρ… расходов Π½Π° созданиС ΠΏΡƒΠ»Π° ΠΏΠΎΡ‚ΠΎΠΊΠΎΠ². Однако ΠΏΡ€ΠΈ ΡƒΠ²Π΅Π»ΠΈΡ‡Π΅Π½ΠΈΠΈ Ρ€Π°Π·ΠΌΠ΅Ρ€Π° ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ (300x300 ΠΈ 500x500) прСимущСства ΠΏΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Π° ΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ»ΠΈΡΡŒ Π±ΠΎΠ»Π΅Π΅ ΠΎΡ‡Π΅Π²ΠΈΠ΄Π½Ρ‹ΠΌΠΈ. + β€’ ΠŸΡ€ΠΈ ΠΏΡ€Π΅Π²Ρ‹ΡˆΠ΅Π½ΠΈΠΈ количСства физичСских ΠΏΠΎΡ‚ΠΎΠΊΠΎΠ² процСссора, ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΡŒ пониТаСтся Π·Π° счСт смСны контСкста ΠΏΡ€ΠΈ ΠΏΠ΅Ρ€Π΅ΠΊΠ»ΡŽΡ‡Π΅Π½ΠΈΠΈ Π²ΠΈΡ€Ρ‚ΡƒΠ°Π»ΡŒΠ½Ρ‹Ρ… ΠΏΠΎΡ‚ΠΎΠΊΠΎΠ² Π½Π° ΠΎΠ΄Π½ΠΎΠΌ ядрС + \ No newline at end of file