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# Отчет по лабораторной работе №6
Выполнила студентка гр. ИСЭбд-41 Зиновьева А. Д.
## Создание приложения
Было выбрано консольное приложение, язык программирования - c#.
Обычный алгоритм:
```cs
static double CalculateDeterminantSequential(int[,] matrix)
{
int size = matrix.GetLength(0);
double determinant = 0;
if (size == 1)
{
determinant = matrix[0, 0];
}
else if (size == 2)
{
determinant = matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
for (int j = 0; j < size; j++)
{
determinant += matrix[0, j] * CalculateMinor(matrix, 0, j) * Math.Pow(-1, j);
}
}
return determinant;
}
```
Параллельный алгоритм:
```cs
static double CalculateDeterminantParallel(int[,] matrix, int threads)
{
int size = matrix.GetLength(0);
double determinant = 0;
if (size == 1)
{
determinant = matrix[0, 0];
}
else if (size == 2)
{
determinant = matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
Parallel.For(0, size, new ParallelOptions { MaxDegreeOfParallelism = threads }, j =>
{
determinant += matrix[0, j] * CalculateMinor(matrix, 0, j) * Math.Pow(-1, j);
});
}
return determinant;
}
```
## Бенчмарки
Для примера была взята матрица размерностью 10х10, поскольку для матриц больших размеров детерминант вычисляется слишком долго.
![](pic/pic1.jpg)
``Вывод``: Обычный (последовательный) алгоритм работает быстрее, если количество элементов не слишком много. Параллельный же алгоритм работает быстрее только при наличии большого количества операций и данных.

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Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio Version 17
VisualStudioVersion = 17.8.34330.188
MinimumVisualStudioVersion = 10.0.40219.1
Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "ConsoleAppLab6", "ConsoleAppLab6\ConsoleAppLab6.csproj", "{BB915677-B73E-45C7-85DD-F66D7FC9E97E}"
EndProject
Global
GlobalSection(SolutionConfigurationPlatforms) = preSolution
Debug|Any CPU = Debug|Any CPU
Release|Any CPU = Release|Any CPU
EndGlobalSection
GlobalSection(ProjectConfigurationPlatforms) = postSolution
{BB915677-B73E-45C7-85DD-F66D7FC9E97E}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
{BB915677-B73E-45C7-85DD-F66D7FC9E97E}.Debug|Any CPU.Build.0 = Debug|Any CPU
{BB915677-B73E-45C7-85DD-F66D7FC9E97E}.Release|Any CPU.ActiveCfg = Release|Any CPU
{BB915677-B73E-45C7-85DD-F66D7FC9E97E}.Release|Any CPU.Build.0 = Release|Any CPU
EndGlobalSection
GlobalSection(SolutionProperties) = preSolution
HideSolutionNode = FALSE
EndGlobalSection
GlobalSection(ExtensibilityGlobals) = postSolution
SolutionGuid = {20D650BB-330E-48AD-8607-6220061D9FDE}
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;
using System.Diagnostics;
using System.Threading.Tasks;
class Program
{
static void Main(string[] args)
{
Console.WriteLine("Выберите задание для выполнения:");
//Console.WriteLine("1 - Нахождение детерминанта квадратной матрицы");
Console.WriteLine("2 - Бенчмарки");
string choice = Console.ReadLine();
if (choice == "1")
{
//int threads = GetNumberOfThreads(); // Запрашиваем количество потоков у пользователя
//int matrixSize = 10; // Размер матрицы
//int[,] matrixA = GenerateRandomMatrix(matrixSize);
//int[,] matrixB = GenerateRandomMatrix(matrixSize);
//Console.WriteLine("Выполняется обычное умножение матриц...");
//Stopwatch stopwatch = Stopwatch.StartNew();
//int[,] result1 = MultiplyMatrices(matrixA, matrixB, matrixSize);
//stopwatch.Stop();
//Console.WriteLine($"Результат (обычное умножение матриц): \n {GetMatrixString(result1)}");
//Console.WriteLine($"Время выполнения: {stopwatch.Elapsed.TotalSeconds} секунд \n");
//Console.WriteLine("Выполняется параллельное умножение матриц...");
//stopwatch.Restart();
//int[,] result2 = ParallelMultiplyMatrices(matrixA, matrixB, matrixSize, threads);
//stopwatch.Stop();
//Console.WriteLine($"Результат (параллельное умножение матриц): \n {GetMatrixString(result2)}");
//Console.WriteLine($"Время выполнения: {stopwatch.Elapsed.TotalSeconds} секунд \n");
//Console.WriteLine("\nНажмите Enter, чтобы вернуться в главное меню...");
//Console.ReadLine();
}
else if (choice == "2")
{
int threads = GetNumberOfThreads(); // Запрашиваем количество потоков у пользователя
Console.WriteLine("\nВыполнение алгоритма по нахождению детерминанта квадратной матрицы размером 10x10:");
RunDeterminantBenchmark(10, threads);
Console.ReadLine();
}
else
{
Console.WriteLine("Некорректный выбор.");
Console.WriteLine("\nНажмите Enter, чтобы вернуться в главное меню...");
Console.ReadLine();
}
Console.ReadLine();
}
static void RunDeterminantBenchmark(int size, int threads)
{
int[,] matrix = GenerateRandomMatrix(size);
Console.WriteLine("Исходная матрица:");
GetMatrixString(matrix);
Stopwatch stopwatch = Stopwatch.StartNew();
stopwatch.Restart();
double sequentialDeterminant = CalculateDeterminantSequential(matrix);
stopwatch.Stop();
Console.WriteLine($"Последовательное выполнение: детерминант = {sequentialDeterminant}, время выполнения = {stopwatch.Elapsed.TotalSeconds} секунд");
stopwatch.Restart();
double parallelDeterminant = CalculateDeterminantParallel(matrix, threads);
stopwatch.Stop();
Console.WriteLine($"Параллельное выполнение: детерминант = {parallelDeterminant}, время выполнения = {stopwatch.Elapsed.TotalSeconds} секунд");
}
static int[,] GenerateRandomMatrix(int size)
{
Random random = new Random();
int[,] matrix = new int[size, size];
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
matrix[i, j] = random.Next(10);
}
}
return matrix;
}
static double CalculateDeterminantSequential(int[,] matrix)
{
int size = matrix.GetLength(0);
double determinant = 0;
if (size == 1)
{
determinant = matrix[0, 0];
}
else if (size == 2)
{
determinant = matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
for (int j = 0; j < size; j++)
{
determinant += matrix[0, j] * CalculateMinor(matrix, 0, j) * Math.Pow(-1, j);
}
}
return determinant;
}
static double CalculateDeterminantParallel(int[,] matrix, int threads)
{
int size = matrix.GetLength(0);
double determinant = 0;
if (size == 1)
{
determinant = matrix[0, 0];
}
else if (size == 2)
{
determinant = matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
Parallel.For(0, size, new ParallelOptions { MaxDegreeOfParallelism = threads }, j =>
{
determinant += matrix[0, j] * CalculateMinor(matrix, 0, j) * Math.Pow(-1, j);
});
}
return determinant;
}
static double CalculateMinor(int[,] matrix, int row, int col)
{
int size = matrix.GetLength(0);
int[,] minor = new int[size - 1, size - 1];
int minorRow = 0;
for (int i = 0; i < size; i++)
{
if (i == row)
{
continue;
}
int minorCol = 0;
for (int j = 0; j < size; j++)
{
if (j == col)
{
continue;
}
minor[minorRow, minorCol] = matrix[i, j];
minorCol++;
}
minorRow++;
}
return CalculateDeterminantSequential(minor);
}
static double MeasureExecutionTime(Action action)
{
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
action();
stopwatch.Stop();
return stopwatch.Elapsed.TotalSeconds;
}
static int GetNumberOfThreads()
{
int threads = 1;
Console.WriteLine("Введите количество потоков:");
int.TryParse(Console.ReadLine(), out threads);
return threads;
}
static void PrintMatrix(int[,] matrix)
{
int size = matrix.GetLength(0);
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
Console.Write(matrix[i, j] + " ");
}
Console.WriteLine();
}
}
static string GetMatrixString(int[,] matrix)
{
int rows = matrix.GetLength(0);
int columns = matrix.GetLength(1);
string matrixString = "";
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
matrixString += matrix[i, j] + " ";
}
matrixString += "\n";
}
return matrixString;
}
}

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