From f279209740ce21d60c1b425e04c5bd51f6646fed Mon Sep 17 00:00:00 2001 From: DmitriyAntonov Date: Mon, 4 Dec 2023 21:25:59 +0400 Subject: [PATCH 1/4] good start --- antonov_dmitry_lab_5/benchmark.py | 43 ++++++++++++++++++++++ antonov_dmitry_lab_5/simple_app.py | 43 ++++++++++++++++++++++ antonov_dmitry_lab_5/templates/index.html | 24 ++++++++++++ antonov_dmitry_lab_5/templates/result.html | 19 ++++++++++ 4 files changed, 129 insertions(+) create mode 100644 antonov_dmitry_lab_5/benchmark.py create mode 100644 antonov_dmitry_lab_5/simple_app.py create mode 100644 antonov_dmitry_lab_5/templates/index.html create mode 100644 antonov_dmitry_lab_5/templates/result.html diff --git a/antonov_dmitry_lab_5/benchmark.py b/antonov_dmitry_lab_5/benchmark.py new file mode 100644 index 0000000..bb21479 --- /dev/null +++ b/antonov_dmitry_lab_5/benchmark.py @@ -0,0 +1,43 @@ +import numpy as np +import time +import concurrent.futures + +def multiply_matrices(matrix_a, matrix_b): + return np.dot(matrix_a, matrix_b) + +def multiply_matrices_parallel(matrix_a, matrix_b): + with concurrent.futures.ThreadPoolExecutor() as executor: + result = executor.submit(np.dot, matrix_a, matrix_b) + return result.result() + +def benchmark_sequential(size): + matrix_a = np.random.rand(size, size) + matrix_b = np.random.rand(size, size) + + start_time = time.time() + multiply_matrices(matrix_a, matrix_b) + end_time = time.time() + + return end_time - start_time + +def benchmark_parallel(size): + matrix_a = np.random.rand(size, size) + matrix_b = np.random.rand(size, size) + + start_time = time.time() + multiply_matrices_parallel(matrix_a, matrix_b) + end_time = time.time() + + return end_time - start_time + +if __name__ == "__main__": + sizes = [100, 300, 500, 700, 900, 1000, 1200, 1400, 1700, 2000] + + for size in sizes: + sequential_time = benchmark_sequential(size) + parallel_time = benchmark_parallel(size) + + print(f"Размер матрицы: {size}x{size}") + print(f"Время обычное: {sequential_time} с") + print(f"Время параллельное: {parallel_time} с") + print(f"Ускорение: {sequential_time / parallel_time}\n") diff --git a/antonov_dmitry_lab_5/simple_app.py b/antonov_dmitry_lab_5/simple_app.py new file mode 100644 index 0000000..b714a15 --- /dev/null +++ b/antonov_dmitry_lab_5/simple_app.py @@ -0,0 +1,43 @@ +from flask import Flask, render_template, request +import numpy as np +import concurrent.futures + +app = Flask(__name__) + + +def multiply_matrices(matrix_a, matrix_b): + result = np.dot(matrix_a, matrix_b) + return result + + +def multiply_matrices_parallel(matrix_a, matrix_b): + with concurrent.futures.ThreadPoolExecutor() as executor: + result = executor.submit(np.dot, matrix_a, matrix_b) + return result.result() + + +@app.route('/') +def index(): + return render_template('index.html') + + +@app.route('/multiply', methods=['POST']) +def multiply(): + n = int(request.form.get('matrix_a')) + matrix_a = np.random.randint(10, size=(n, n)) + matrix_b = np.random.randint(10, size=(n, n)) + + operation_type = request.form.get('operation_type') + + if operation_type == 'sequential': + result = multiply_matrices(matrix_a, matrix_b) + elif operation_type == 'parallel': + result = multiply_matrices_parallel(matrix_a, matrix_b) + else: + return "Invalid operation type" + + return render_template('result.html', matrix_a=matrix_a, matrix_b=matrix_b, result=result) + + +if __name__ == '__main__': + app.run(debug=True) diff --git a/antonov_dmitry_lab_5/templates/index.html b/antonov_dmitry_lab_5/templates/index.html new file mode 100644 index 0000000..ddec7e9 --- /dev/null +++ b/antonov_dmitry_lab_5/templates/index.html @@ -0,0 +1,24 @@ + + + + + + + Matrix Multiplication + + +

Matrix Multiplication

+
+ +
+ + +
+ + +
+ + diff --git a/antonov_dmitry_lab_5/templates/result.html b/antonov_dmitry_lab_5/templates/result.html new file mode 100644 index 0000000..74775bd --- /dev/null +++ b/antonov_dmitry_lab_5/templates/result.html @@ -0,0 +1,19 @@ + + + + + + + Matrix Multiplication Result + + +

Результат

+

Matrix A:

+
{{ matrix_a }}
+

Matrix B:

+
{{ matrix_b }}
+

Result:

+
{{ result }}
+ Назад + + -- 2.25.1 From 266432cfda1fee7d821bde14cdcdf2164c83ab65 Mon Sep 17 00:00:00 2001 From: DmitriyAntonov Date: Mon, 4 Dec 2023 22:40:49 +0400 Subject: [PATCH 2/4] good start2 --- antonov_dmitry_lab_5/benchmark.py | 66 +++++++++++++++++++++++------- antonov_dmitry_lab_5/simple_app.py | 37 ++++++++++++++--- 2 files changed, 84 insertions(+), 19 deletions(-) diff --git a/antonov_dmitry_lab_5/benchmark.py b/antonov_dmitry_lab_5/benchmark.py index bb21479..8221303 100644 --- a/antonov_dmitry_lab_5/benchmark.py +++ b/antonov_dmitry_lab_5/benchmark.py @@ -2,13 +2,45 @@ import numpy as np import time import concurrent.futures -def multiply_matrices(matrix_a, matrix_b): - return np.dot(matrix_a, matrix_b) -def multiply_matrices_parallel(matrix_a, matrix_b): - with concurrent.futures.ThreadPoolExecutor() as executor: - result = executor.submit(np.dot, matrix_a, matrix_b) - return result.result() +def multiply_matrices(matrix_a, matrix_b): + if len(matrix_a[0]) != len(matrix_b): + raise ValueError("Incompatible matrix dimensions for multiplication") + + result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] + + for i in range(len(matrix_a)): + for j in range(len(matrix_b[0])): + for k in range(len(matrix_b)): + result[i][j] += matrix_a[i][k] * matrix_b[k][j] + + return result + + +def multiply_matrices_parallel(matrix_a, matrix_b, num_threads): + if len(matrix_a[0]) != len(matrix_b): + raise ValueError("Incompatible matrix dimensions for multiplication") + + result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] + + with concurrent.futures.ThreadPoolExecutor(max_workers=num_threads) as executor: + futures = [] + for i in range(len(matrix_a)): + futures.append(executor.submit(_multiply_row, matrix_a, matrix_b, i)) + + for i, future in enumerate(concurrent.futures.as_completed(futures)): + result[i] = future.result() + + return result + + +def _multiply_row(matrix_a, matrix_b, i): + row_result = [0 for _ in range(len(matrix_b[0]))] + for j in range(len(matrix_b[0])): + for k in range(len(matrix_b)): + row_result[j] += matrix_a[i][k] * matrix_b[k][j] + return row_result + def benchmark_sequential(size): matrix_a = np.random.rand(size, size) @@ -20,24 +52,30 @@ def benchmark_sequential(size): return end_time - start_time -def benchmark_parallel(size): + +def benchmark_parallel(size, num_threads): matrix_a = np.random.rand(size, size) matrix_b = np.random.rand(size, size) start_time = time.time() - multiply_matrices_parallel(matrix_a, matrix_b) + multiply_matrices_parallel(matrix_a, matrix_b, num_threads) end_time = time.time() return end_time - start_time + if __name__ == "__main__": - sizes = [100, 300, 500, 700, 900, 1000, 1200, 1400, 1700, 2000] + sizes = [300] + threads = [2, 8] for size in sizes: sequential_time = benchmark_sequential(size) - parallel_time = benchmark_parallel(size) - - print(f"Размер матрицы: {size}x{size}") print(f"Время обычное: {sequential_time} с") - print(f"Время параллельное: {parallel_time} с") - print(f"Ускорение: {sequential_time / parallel_time}\n") + print(f"Размер матрицы: {size}x{size}") + + for thread in threads: + for size in sizes: + parallel_time = benchmark_parallel(size, thread) + print(f"Размер матрицы: {size}x{size}") + print(f"Время параллельное: {parallel_time} с") + print(f"Потоков: {thread}") diff --git a/antonov_dmitry_lab_5/simple_app.py b/antonov_dmitry_lab_5/simple_app.py index b714a15..87d173e 100644 --- a/antonov_dmitry_lab_5/simple_app.py +++ b/antonov_dmitry_lab_5/simple_app.py @@ -6,14 +6,41 @@ app = Flask(__name__) def multiply_matrices(matrix_a, matrix_b): - result = np.dot(matrix_a, matrix_b) + if len(matrix_a[0]) != len(matrix_b): + raise ValueError("Incompatible matrix dimensions for multiplication") + + result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] + + for i in range(len(matrix_a)): + for j in range(len(matrix_b[0])): + for k in range(len(matrix_b)): + result[i][j] += matrix_a[i][k] * matrix_b[k][j] + return result +def multiply_matrices_parallel(matrix_a, matrix_b, num_threads): + if len(matrix_a[0]) != len(matrix_b): + raise ValueError("Incompatible matrix dimensions for multiplication") + + result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] + + with concurrent.futures.ThreadPoolExecutor(max_workers=num_threads) as executor: + futures = [] + for i in range(len(matrix_a)): + futures.append(executor.submit(_multiply_row, matrix_a, matrix_b, i)) + + for i, future in enumerate(concurrent.futures.as_completed(futures)): + result[i] = future.result() + + return result + +def _multiply_row(matrix_a, matrix_b, i): + row_result = [0 for _ in range(len(matrix_b[0]))] + for j in range(len(matrix_b[0])): + for k in range(len(matrix_b)): + row_result[j] += matrix_a[i][k] * matrix_b[k][j] + return row_result -def multiply_matrices_parallel(matrix_a, matrix_b): - with concurrent.futures.ThreadPoolExecutor() as executor: - result = executor.submit(np.dot, matrix_a, matrix_b) - return result.result() @app.route('/') -- 2.25.1 From a4a35b552985ed38e6db4abdca920a39ea32582e Mon Sep 17 00:00:00 2001 From: DmitriyAntonov Date: Mon, 4 Dec 2023 23:02:40 +0400 Subject: [PATCH 3/4] good start2 --- antonov_dmitry_lab_5/benchmark.py | 55 +++++++++++++++--------------- antonov_dmitry_lab_5/simple_app.py | 41 +++++++++++----------- 2 files changed, 50 insertions(+), 46 deletions(-) diff --git a/antonov_dmitry_lab_5/benchmark.py b/antonov_dmitry_lab_5/benchmark.py index 8221303..1d4db87 100644 --- a/antonov_dmitry_lab_5/benchmark.py +++ b/antonov_dmitry_lab_5/benchmark.py @@ -1,11 +1,12 @@ +import multiprocessing + import numpy as np import time -import concurrent.futures def multiply_matrices(matrix_a, matrix_b): if len(matrix_a[0]) != len(matrix_b): - raise ValueError("Incompatible matrix dimensions for multiplication") + raise ValueError("матрицы имеют разную длину") result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] @@ -17,29 +18,29 @@ def multiply_matrices(matrix_a, matrix_b): return result -def multiply_matrices_parallel(matrix_a, matrix_b, num_threads): - if len(matrix_a[0]) != len(matrix_b): - raise ValueError("Incompatible matrix dimensions for multiplication") - - result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] - - with concurrent.futures.ThreadPoolExecutor(max_workers=num_threads) as executor: - futures = [] - for i in range(len(matrix_a)): - futures.append(executor.submit(_multiply_row, matrix_a, matrix_b, i)) - - for i, future in enumerate(concurrent.futures.as_completed(futures)): - result[i] = future.result() - - return result - - -def _multiply_row(matrix_a, matrix_b, i): +def multiply_row(args): + matrix_a, matrix_b, i = args row_result = [0 for _ in range(len(matrix_b[0]))] for j in range(len(matrix_b[0])): for k in range(len(matrix_b)): row_result[j] += matrix_a[i][k] * matrix_b[k][j] - return row_result + return row_result, i + + +def multiply_matrices_parallel(matrix_a, matrix_b, threads): + if len(matrix_a[0]) != len(matrix_b): + raise ValueError("матрицы имеют разную длину") + + result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] + + with multiprocessing.Pool(processes=threads) as pool: + args_list = [(matrix_a, matrix_b, i) for i in range(len(matrix_a))] + rows_results = pool.map(multiply_row, args_list) + + for row_result, row_index in rows_results: + result[row_index] = row_result + + return result def benchmark_sequential(size): @@ -66,12 +67,12 @@ def benchmark_parallel(size, num_threads): if __name__ == "__main__": sizes = [300] - threads = [2, 8] - - for size in sizes: - sequential_time = benchmark_sequential(size) - print(f"Время обычное: {sequential_time} с") - print(f"Размер матрицы: {size}x{size}") + threads = [2, 16, 32] + # + # for size in sizes: + # sequential_time = benchmark_sequential(size) + # print(f"Время обычное: {sequential_time} с") + # print(f"Размер матрицы: {size}x{size}") for thread in threads: for size in sizes: diff --git a/antonov_dmitry_lab_5/simple_app.py b/antonov_dmitry_lab_5/simple_app.py index 87d173e..740bcda 100644 --- a/antonov_dmitry_lab_5/simple_app.py +++ b/antonov_dmitry_lab_5/simple_app.py @@ -1,3 +1,5 @@ +import multiprocessing + from flask import Flask, render_template, request import numpy as np import concurrent.futures @@ -7,7 +9,7 @@ app = Flask(__name__) def multiply_matrices(matrix_a, matrix_b): if len(matrix_a[0]) != len(matrix_b): - raise ValueError("Incompatible matrix dimensions for multiplication") + raise ValueError("матрицы имеют разную длину") result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] @@ -18,30 +20,31 @@ def multiply_matrices(matrix_a, matrix_b): return result -def multiply_matrices_parallel(matrix_a, matrix_b, num_threads): - if len(matrix_a[0]) != len(matrix_b): - raise ValueError("Incompatible matrix dimensions for multiplication") - result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] - - with concurrent.futures.ThreadPoolExecutor(max_workers=num_threads) as executor: - futures = [] - for i in range(len(matrix_a)): - futures.append(executor.submit(_multiply_row, matrix_a, matrix_b, i)) - - for i, future in enumerate(concurrent.futures.as_completed(futures)): - result[i] = future.result() - - return result - -def _multiply_row(matrix_a, matrix_b, i): +def multiply_row(args): + matrix_a, matrix_b, i = args row_result = [0 for _ in range(len(matrix_b[0]))] for j in range(len(matrix_b[0])): for k in range(len(matrix_b)): row_result[j] += matrix_a[i][k] * matrix_b[k][j] - return row_result + return row_result, i +def multiply_matrices_parallel(matrix_a, matrix_b, threads): + if len(matrix_a[0]) != len(matrix_b): + raise ValueError("матрицы имеют разную длину") + + result = [[0 for _ in range(len(matrix_b[0]))] for _ in range(len(matrix_a))] + + with multiprocessing.Pool(processes=threads) as pool: + args_list = [(matrix_a, matrix_b, i) for i in range(len(matrix_a))] + rows_results = pool.map(multiply_row, args_list) + + for row_result, row_index in rows_results: + result[row_index] = row_result + + return result + @app.route('/') def index(): @@ -59,7 +62,7 @@ def multiply(): if operation_type == 'sequential': result = multiply_matrices(matrix_a, matrix_b) elif operation_type == 'parallel': - result = multiply_matrices_parallel(matrix_a, matrix_b) + result = multiply_matrices_parallel(matrix_a, matrix_b, 16) else: return "Invalid operation type" -- 2.25.1 From d3c914ad38348be81d2d96f2c6ea769e37aa92f6 Mon Sep 17 00:00:00 2001 From: DmitriyAntonov Date: Tue, 5 Dec 2023 13:01:36 +0400 Subject: [PATCH 4/4] antonov_dmitry_lab_5_ready --- antonov_dmitry_lab_5/README.md | 91 +++++++++++++++++++++ antonov_dmitry_lab_5/benchmark.py | 12 +-- antonov_dmitry_lab_5/screens/img.png | Bin 0 -> 25713 bytes antonov_dmitry_lab_5/screens/img_1.png | Bin 0 -> 69395 bytes antonov_dmitry_lab_5/screens/img_2.png | Bin 0 -> 57105 bytes antonov_dmitry_lab_5/screens/img_3.png | Bin 0 -> 64675 bytes antonov_dmitry_lab_5/templates/index.html | 6 +- antonov_dmitry_lab_5/templates/result.html | 8 +- 8 files changed, 104 insertions(+), 13 deletions(-) create mode 100644 antonov_dmitry_lab_5/README.md create mode 100644 antonov_dmitry_lab_5/screens/img.png create mode 100644 antonov_dmitry_lab_5/screens/img_1.png create mode 100644 antonov_dmitry_lab_5/screens/img_2.png create mode 100644 antonov_dmitry_lab_5/screens/img_3.png diff --git a/antonov_dmitry_lab_5/README.md b/antonov_dmitry_lab_5/README.md new file mode 100644 index 0000000..dc87597 --- /dev/null +++ b/antonov_dmitry_lab_5/README.md @@ -0,0 +1,91 @@ +# Лабораторная работа №5 - Вспоминаем математику или параллельное перемножение матриц + +Изучение параллельного умножения матриц + +# Задачи + +Кратко: реализовать умножение двух больших квадратных матриц. + +Подробно: в лабораторной работе требуется сделать два алгоритма: обычный и параллельный +(задание со * - реализовать это в рамках одного алгоритма). В параллельном алгоритме предусмотреть +ручное задание количества потоков (число потоков = 1 как раз и реализует задание со *), каждый из +которых будет выполнять умножение элементов матрицы в рамках своей зоны ответственности. + +Сделать несколько бенчмарков последовательного и параллельного алгоритма на умножение двух матриц +размером 100x100, 300x300, 500x500 элементов. +# Запуск + +Проект запускается в ide просто по нажатию у питон файла на функцию мейн. +Нужно последовательно запустить функцию мейн у файлов simple_app.py, benchmark.py. + +# Описание работы: +Развернули два приложения + +1. Приложение 1 - веб приложение для умножения матриц +2. Приложение 2 - консольное приложение для сравнения эффективности работы алгоритмов. + +Первое приложение дает нам возможность умножить матрицы, получить результат в интерактивном режиме +с указанием используемого алгоритма и с указанием размера матрицы. +В программе предусмотрена возможность задания количества процессов для распараллеливания. +Используется библиотека python multiprocessing. + +На рис 3 видно, что с использованием параллельного алгоритма скорость обработки увеличивается довольно +существенно. Но оптимальная скорость достигается при кол-ве потоков = кол-ву потоков процессора +У меня их 16. + +

+

Форма веб приложения для указания парметров умножения матриц
+ +

+

+

Результат умножения в интерактивном режиме
+ +

+

+

Сравнение бенчмарков
+ +

+

+

Параллельное умножение в коде
+ +

+ +* Время обычное: 0.43517565727233887 с +* Размер матрицы: 100x100 +* Время обычное: 11.15409231185913 с +* Размер матрицы: 300x300 +* Время обычное: 53.64867091178894 с +* Размер матрицы: 500x500 +* Размер матрицы: 100x100 +* Время параллельное: 0.582118034362793 с +* Потоков: 2 +* Размер матрицы: 300x300 +* Время параллельное: 6.083630800247192 с +* Потоков: 2 +* Размер матрицы: 500x500 +* Время параллельное: 26.892888069152832 с +* Потоков: 2 +* Размер матрицы: 100x100 +* Время параллельное: 0.9034981727600098 с +* Потоков: 16 +* Размер матрицы: 300x300 +* Время параллельное: 2.9237937927246094 с +* Потоков: 16 +* Размер матрицы: 500x500 +* Время параллельное: 10.55041241645813 с +* Потоков: 16 +* Размер матрицы: 100x100 +* Время параллельное: 1.5674595832824707 с +* Потоков: 32 +* Размер матрицы: 300x300 +* Время параллельное: 4.185227394104004 с +* Потоков: 32 +* Размер матрицы: 500x500 +* Время параллельное: 11.912990808486938 с +* Потоков: 32 + + + +# Ссылка на видео +https://disk.yandex.ru/i/I_1oUuNTveYUdg + diff --git a/antonov_dmitry_lab_5/benchmark.py b/antonov_dmitry_lab_5/benchmark.py index 1d4db87..ca0a66f 100644 --- a/antonov_dmitry_lab_5/benchmark.py +++ b/antonov_dmitry_lab_5/benchmark.py @@ -66,13 +66,13 @@ def benchmark_parallel(size, num_threads): if __name__ == "__main__": - sizes = [300] + sizes = [100, 300, 500] threads = [2, 16, 32] - # - # for size in sizes: - # sequential_time = benchmark_sequential(size) - # print(f"Время обычное: {sequential_time} с") - # print(f"Размер матрицы: {size}x{size}") + + for size in sizes: + sequential_time = benchmark_sequential(size) + print(f"Время обычное: {sequential_time} с") + print(f"Размер матрицы: {size}x{size}") for thread in threads: for size in sizes: diff --git a/antonov_dmitry_lab_5/screens/img.png b/antonov_dmitry_lab_5/screens/img.png new file mode 100644 index 0000000000000000000000000000000000000000..ba5b28ad2cf663da0dacbcf45c075f49ce598d08 GIT binary patch literal 25713 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znijdE?FJ0#)4@5wglL9WyWY0Q$uB)NaS^dOuf6n6EL|CwkkxF}p$#jAftVK9fvWLk zMW>Cyh9D$kL^kcqm~_C*+FapWa(9AZjAX&x_BNkvi`DwRb9ctlUi3pNB3$C15V@M`X~WjoI*eYnYeCwh#vo%~=w`@O}D zCr^ElxX;5T{xbucKm+xXPTc{bt7V;he^g+?o#y46Xs9@WEy63(>u~$HgZC!^%R7)f z+_LGWgU%jXABURVB7uN&+Jsv=Aq~zs-TWfO#m#fSv9U@bS+ckQn_-gHF~JSlSAXp1 zU-S|BXwjkdw@mKRM2R@74ij}sr!ryYkxxBIjJ&+JMhhKlw{rXX<4YyIdjyF&jIct8 zyroCN!)U1j*y45vxw?`K2CGkBg1JyoSi%8Rz(_iIdVg={0chRG2X1vfCfvr*fA+&r z&_)~*gFmyGWjh@<)~Hh9Y@B$Fy0vS6Odt0O0 - Matrix Multiplication + Умножение матриц -

Matrix Multiplication

+

Умножение матриц

- +
diff --git a/antonov_dmitry_lab_5/templates/result.html b/antonov_dmitry_lab_5/templates/result.html index 74775bd..23bdc89 100644 --- a/antonov_dmitry_lab_5/templates/result.html +++ b/antonov_dmitry_lab_5/templates/result.html @@ -4,15 +4,15 @@ - Matrix Multiplication Result + Результат

Результат

-

Matrix A:

+

Матрица A:

{{ matrix_a }}
-

Matrix B:

+

Матрица B:

{{ matrix_b }}
-

Result:

+

Результат:

{{ result }}
Назад -- 2.25.1