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Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio Version 17
VisualStudioVersion = 17.10.34916.146
MinimumVisualStudioVersion = 10.0.40219.1
Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "MatrixMultiplication", "MatrixMultiplication\MatrixMultiplication.csproj", "{EF2DB216-9BCD-4FEE-B9C8-4262A5B7CC30}"
EndProject
Global
GlobalSection(SolutionConfigurationPlatforms) = preSolution
Debug|Any CPU = Debug|Any CPU
Release|Any CPU = Release|Any CPU
EndGlobalSection
GlobalSection(ProjectConfigurationPlatforms) = postSolution
{EF2DB216-9BCD-4FEE-B9C8-4262A5B7CC30}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
{EF2DB216-9BCD-4FEE-B9C8-4262A5B7CC30}.Debug|Any CPU.Build.0 = Debug|Any CPU
{EF2DB216-9BCD-4FEE-B9C8-4262A5B7CC30}.Release|Any CPU.ActiveCfg = Release|Any CPU
{EF2DB216-9BCD-4FEE-B9C8-4262A5B7CC30}.Release|Any CPU.Build.0 = Release|Any CPU
EndGlobalSection
GlobalSection(SolutionProperties) = preSolution
HideSolutionNode = FALSE
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GlobalSection(ExtensibilityGlobals) = postSolution
SolutionGuid = {619485C2-FE35-496B-9E25-4F5465D0C1A1}
EndGlobalSection
EndGlobal

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<Project Sdk="Microsoft.NET.Sdk">
<PropertyGroup>
<OutputType>Exe</OutputType>
<TargetFramework>net8.0</TargetFramework>
<ImplicitUsings>enable</ImplicitUsings>
<Nullable>enable</Nullable>
</PropertyGroup>
</Project>

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using System.Diagnostics;
internal class Program
{
private static string[] _resTableColumnsNames = new string[] { "m*m", "1 t", "2 t", "3 t", "4 t", "5 t", "6 t", "7 t", "8 t" };
private static void Main(string[] args)
{
Console.WriteLine(string.Join("\t", _resTableColumnsNames));
for (int i = 10; i < 10000; i *= 2)
{
var a = CreateMatrix(i, i);
var b = CreateMatrix(i, i);
List<long> times = new() { i };
for (int j = 1; j <= 8; j++)
{
var sw = new Stopwatch();
sw.Start();
MultiplyMatrix(a, b, j);
sw.Stop();
times.Add(sw.ElapsedMilliseconds);
}
Console.WriteLine(string.Join("\t", times));
}
}
/// <summary>
/// Создаём матрицу случайных элементов
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
private static int[,] CreateMatrix(int x, int y)
{
var rnd = new Random();
var res = new int[y, x];
for (int i = 0; i < y; i++)
{
for (int j = 0; j < x; j++)
{
res[i, j] = rnd.Next(0, 100);
}
}
return res;
}
/// <summary>
/// Вывести матрицу. Использовался при отладке
/// </summary>
/// <param name="mx"></param>
private static void PrintMatrix(int[,] mx)
{
for (int i = 0; i < mx.GetLength(0); i++)
{
for (int j = 0; j < mx.GetLength(1); j++)
{
Console.Write($"{mx[i, j].ToString("000")}\t");
}
Console.WriteLine();
}
}
/// <summary>
/// Непосредственно умножение матриц
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="maxTask"></param>
/// <returns></returns>
private static int[,] MultiplyMatrix(int[,] a, int[,] b, int maxTask)
{
int[,] res = new int[a.GetLength(0), b.GetLength(1)];
var semaphore = new SemaphoreSlim(maxTask, maxTask);
for (int i = 0; i < a.GetLength(0); i++)
{
for (int j = 0; j < b.GetLength(1); j++)
{
semaphore.Wait();
int ci = i;
int cj = j;
_ = Task.Run(() =>
{
try
{
res[ci, cj] = CalculateElement(a, b, ci, cj);
}
finally
{
semaphore.Release();
}
});
}
}
semaphore.Wait(maxTask);
return res;
}
/// <summary>
/// Вычисление значение одного элемента
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="i"></param>
/// <param name="j"></param>
/// <returns></returns>
private static int CalculateElement(int[,] a, int[,] b, int i, int j)
=> Enumerable.Range(0, a.GetLength(1)).Sum(k => a[i, k] * b[k, j]);
}

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# Лабораторная работа 5
Данная работа посвящена параллельному умножению больших матриц (чтобы это был побыстрее)
## Описание
Основной принцип умножения матриц: строки умножаются на столбцы, таким образом получаются элементы. И так как значения в строках/столбцах не меняется по ходу алгоритма, его достаточно легко можно распаралелить.
## Запуск
Приложение представлет собой консольную программу на C#, которую можно скомпилировать и затем запустит exe файл. В результате в окне консоли появится таблица сравнения времени умножения 2-х квадратных матриц (размер указан в первой колонке) с использованием разного числа потоков(от 1 до 8). Чем больше размер, тем дольше будет идти расчёт.
## Результаты
Результаты одного из запусков программы представлены ниже.
<br/>
![Resout](Images/Resouts.png)
<br/>
Как можно заметить, на небольших размерах распаралеливание не приносит никакого выигрыша, а иногда даже удлиняет время работы. Это связана с тем, что работы с потоками (запуск, получение результата и т. п.) - требует дополнительного времени, а из-за малого числа операций в целом, получаем не прирост производительности, а её падение.
Противоположно обстоят дела в случае с большими матрицами. Так как там расчётов значительно больше, распаралеливание начинает значительно ускорять вычисление результата. Причём, часто можно видеть, что, например, увеличения числа потоков с 1 до 2 (в 2 раза) сокращает время в 2 раза. Но чем больше потоков, тем прирост меньше (так как вновь вступают в силу факторы, описанные ранее). И прирост производительности пусть и есть, но он очень небольшой.
## Видеодемонстрация
Был записан видеоролик, демонстрирующий процесс запуска и работы системы. Он расположен по [адресу](https://drive.google.com/file/d/1dhA3JUAhhpDUh32xVW7jMuW1BKDX02eV/view?usp=sharing)