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Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio Version 17
VisualStudioVersion = 17.8.34322.80
MinimumVisualStudioVersion = 10.0.40219.1
Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "ConsoleApp1", "ConsoleApp1\ConsoleApp1.csproj", "{24793D16-F80E-48B2-8A04-76BD2CB61C1C}"
EndProject
Global
GlobalSection(SolutionConfigurationPlatforms) = preSolution
Debug|Any CPU = Debug|Any CPU
Release|Any CPU = Release|Any CPU
EndGlobalSection
GlobalSection(ProjectConfigurationPlatforms) = postSolution
{24793D16-F80E-48B2-8A04-76BD2CB61C1C}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
{24793D16-F80E-48B2-8A04-76BD2CB61C1C}.Debug|Any CPU.Build.0 = Debug|Any CPU
{24793D16-F80E-48B2-8A04-76BD2CB61C1C}.Release|Any CPU.ActiveCfg = Release|Any CPU
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SolutionGuid = {D17B9FEE-F4BF-4559-899B-434F4545FF67}
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>
<ItemGroup>
<PackageReference Include="BenchmarkDotNet" Version="0.13.11" />
</ItemGroup>
</Project>

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namespace ConsoleApp1
{
public class MatrixService
{
static readonly Random rand = new Random();
object lockObject = new object();
public double[,] RandomGenerateMatrix(int dimensionsCount)
{
double[,] result = new double[dimensionsCount, dimensionsCount];
for (int i = 0; i < dimensionsCount; i++)
{
for (int j = 0; j < dimensionsCount; j++)
{
result[i, j] = rand.NextDouble() * 10;
}
}
return result;
}
public double DeterminantOfMatrix(double[,] matrix, int threadCount)
{
int size = matrix.GetLength(0);
if (size == 1)
{
return matrix[0, 0];
}
else if (size == 2)
{
return matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
double determinant = 0;
Parallel.For(0, size, new ParallelOptions { MaxDegreeOfParallelism = threadCount },
(i) =>
{
double[,] subMatrix = GetSubMatrix(matrix, i);
double subDeterminant = matrix[0, i] * Determinant(subMatrix);
double value = Math.Pow(-1, i) * subDeterminant;
lock (lockObject)
{
determinant += value;
}
});
return determinant;
}
}
static double[,] GetSubMatrix(double[,] matrix, int columnIndex)
{
int size = matrix.GetLength(0);
double[,] subMatrix = new double[size - 1, size - 1];
for (int i = 1; i < size; i++)
{
for (int j = 0; j < size; j++)
{
if (j < columnIndex)
{
subMatrix[i - 1, j] = matrix[i, j];
}
else if (j > columnIndex)
{
subMatrix[i - 1, j - 1] = matrix[i, j];
}
}
}
return subMatrix;
}
static double Determinant(double[,] matrix)
{
int size = matrix.GetLength(0);
if (size == 1)
{
return matrix[0, 0];
}
else if (size == 2)
{
return matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
double determinant = 0;
for (int i = 0; i < size; i++)
{
double[,] subMatrix = GetSubMatrix(matrix, i);
determinant += (int)Math.Pow(-1, i) * matrix[0, i] * Determinant(subMatrix);
}
return determinant;
}
}
}
}

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using BenchmarkDotNet.Attributes;
using BenchmarkDotNet.Running;
using ConsoleApp1;
BenchmarkRunner.Run<MatrixTest>();
//var matrixService = new MatrixService();
//var matrix = matrixService.RandomGenerateMatrix(3);
//for(int i = 0; i < matrix.GetLength(0); i++)
//{
// for (int j = 0; j < matrix.GetLength(0); j++)
// {
// Console.Write(matrix[i, j] + " ");
// }
// Console.WriteLine();
//}
//var result1 = matrixService.DeterminantOfMatrix(matrix, 1);
//var result2 = matrixService.DeterminantOfMatrix(matrix, 12);
//Console.WriteLine(result1);
//Console.WriteLine(result2);
//Console.ReadLine();
[MemoryDiagnoser]
public class MatrixTest
{
double[,] Matrix5;
double[,] Matrix8;
double[,] Matrix11;
MatrixService matrixService;
public MatrixTest()
{
matrixService = new MatrixService();
Matrix5 = matrixService.RandomGenerateMatrix(5);
Matrix8 = matrixService.RandomGenerateMatrix(8);
Matrix11 = matrixService.RandomGenerateMatrix(11);
}
[Benchmark]
public double MatrixDeterminant5()
{
return matrixService.DeterminantOfMatrix(Matrix5, 1);
}
[Benchmark]
public double MatrixDeterminantParallel5()
{
return matrixService.DeterminantOfMatrix(Matrix5, 12);
}
[Benchmark]
public double MatrixDeterminant8()
{
return matrixService.DeterminantOfMatrix(Matrix8, 1);
}
[Benchmark]
public double MatrixDeterminantParallel8()
{
return matrixService.DeterminantOfMatrix(Matrix8, 12);
}
[Benchmark]
public double MatrixDeterminant11()
{
return matrixService.DeterminantOfMatrix(Matrix11, 1);
}
[Benchmark]
public double MatrixDeterminantParallel11()
{
return matrixService.DeterminantOfMatrix(Matrix11, 12);
}
}

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# Отчет по лабораторной работе №6
Выполнил студент гр. ИСЭбд-41 Савицкий А.В.
## Создание приложения
Выбрал язык C#, Консольное приложение.
Установил библиотеку BenchmarkDotNet для замера производительности.
Сам алгоритм.
``` cs
public double DeterminantOfMatrix(double[,] matrix, int threadCount)
{
int size = matrix.GetLength(0);
if (size == 1)
{
return matrix[0, 0];
}
else if (size == 2)
{
return matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
double determinant = 0;
Parallel.For(0, size, new ParallelOptions { MaxDegreeOfParallelism = threadCount },
(i) =>
{
double[,] subMatrix = GetSubMatrix(matrix, i);
double subDeterminant = matrix[0, i] * Determinant(subMatrix);
double value = Math.Pow(-1, i) * subDeterminant;
lock (lockObject)
{
determinant += value;
}
});
return determinant;
}
}
static double[,] GetSubMatrix(double[,] matrix, int columnIndex)
{
int size = matrix.GetLength(0);
double[,] subMatrix = new double[size - 1, size - 1];
for (int i = 1; i < size; i++)
{
for (int j = 0; j < size; j++)
{
if (j < columnIndex)
{
subMatrix[i - 1, j] = matrix[i, j];
}
else if (j > columnIndex)
{
subMatrix[i - 1, j - 1] = matrix[i, j];
}
}
}
return subMatrix;
}
static double Determinant(double[,] matrix)
{
int size = matrix.GetLength(0);
if (size == 1)
{
return matrix[0, 0];
}
else if (size == 2)
{
return matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0];
}
else
{
double determinant = 0;
for (int i = 0; i < size; i++)
{
double[,] subMatrix = GetSubMatrix(matrix, i);
determinant += (int)Math.Pow(-1, i) * matrix[0, i] * Determinant(subMatrix);
}
return determinant;
}
}
```
Проверка работы на матрице 3х3
![](pic/1.png)
## Бенчмарки
Протестируем обычный и параллельный алгоритм определение детерминанта на различной размерности матрицы.
В ходе экспериментов было установлено, что обработка матрицы размеров больше 12х12 занимает слишком много времени, поэтому для тестирования возьмем матрицы 5х5, 8х8 и 11х11.
Для тестирование запускаю алгоритм в 1 поток и в 12 потоков
![](pic/2.png)
Вывод: Параллельный алгоритм работает быстрее только при наличии большого количества операций. Если операций не так много, то обычный алгоритм справляется быстрее.

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