tasks/khalitova-am/lab_6/App/.gitignore

@@ -0,0 +1,454 @@
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tasks/khalitova-am/lab_6/App/App.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>net6.0</TargetFramework>
+    <ImplicitUsings>enable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <PackageReference Include="BenchmarkDotNet" Version="0.13.11" />
+  </ItemGroup>
+
+</Project>

tasks/khalitova-am/lab_6/App/Program.cs

@@ -0,0 +1,187 @@
+using System;
+using System.Diagnostics;
+using System.Threading.Tasks;
+using BenchmarkDotNet.Attributes;
+using BenchmarkDotNet.Running;
+
+public class MatrixDeterminant
+{
+    public static double DeterminantSequential(double[][] matrix)
+    {
+        int size = matrix.Length;
+
+        if (size == 1)
+        {
+            return matrix[0][0];
+        }
+
+        if (size == 2)
+        {
+            return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
+        }
+
+        double determinant = 0;
+
+        for (int i = 0; i < size; i++)
+        {
+            double sign = (i % 2 == 0) ? 1 : -1;
+            double cofactor = sign * matrix[0][i] * DeterminantSequential(GetSubMatrix(matrix, 0, i));
+            determinant += cofactor;
+        }
+
+        return determinant;
+    }
+
+    public static double DeterminantParallel(double[][] matrix, int numThreads)
+    {
+        int size = matrix.Length;
+
+        if (size == 1)
+        {
+            return matrix[0][0];
+        }
+
+        if (size == 2)
+        {
+            return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
+        }
+
+        double determinant = 0;
+
+        Parallel.For(0, size, new ParallelOptions { MaxDegreeOfParallelism = numThreads }, i =>
+        {
+            double sign = (i % 2 == 0) ? 1 : -1;
+            double cofactor = sign * matrix[0][i] * DeterminantSequential(GetSubMatrix(matrix, 0, i));
+            determinant += cofactor;
+        });
+
+        return determinant;
+    }
+
+
+    [Benchmark]
+    public void DeterminantSequential_2x2()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantSequential(matrix);
+    }
+
+    [Benchmark]
+    public void DeterminantParallel_2x2_4TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantParallel(matrix, 4);
+    }
+    [Benchmark]
+    public void DeterminantParallel_2x2_8TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantParallel(matrix, 8);
+    }
+    [Benchmark]
+    public void DeterminantParallel_2x2_16TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantParallel(matrix, 16);
+    }
+    [Benchmark]
+    public void DeterminantSequential_4x4()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantSequential(matrix);
+    }
+
+    [Benchmark]
+    public void DeterminantParallel_4x4_4TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantParallel(matrix, 4);
+    }
+    [Benchmark]
+    public void DeterminantParallel_4x4_8TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantParallel(matrix, 8);
+    }
+    [Benchmark]
+    public void DeterminantParallel_4x4_16TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantParallel(matrix, 16);
+    }
+    [Benchmark]
+    public void DeterminantSequential_8x8()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantSequential(matrix);
+    }
+
+    [Benchmark]
+    public void DeterminantParallel_8x8_4TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantParallel(matrix, 4);
+    }
+    [Benchmark]
+    public void DeterminantParallel_8x8_8TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantParallel(matrix, 8);
+    }
+    [Benchmark]
+    public void DeterminantParallel_8x8_16TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantParallel(matrix, 16);
+    }
+    public static double[][] GenerateRandomMatrix(int rows, int cols)
+    {
+        double[][] matrix = new double[rows][];
+
+        Random rand = new Random();
+
+        for (int i = 0; i < rows; i++)
+        {
+            matrix[i] = new double[cols];
+            for (int j = 0; j < cols; j++)
+            {
+                matrix[i][j] = rand.Next(1, 10);
+            }
+        }
+
+        return matrix;
+    }
+
+    private static double[][] GetSubMatrix(double[][] matrix, int rowToRemove, int colToRemove)
+    {
+        int size = matrix.Length;
+        double[][] subMatrix = new double[size - 1][];
+
+        for (int i = 0, newRow = 0; i < size; i++)
+        {
+            if (i != rowToRemove)
+            {
+                subMatrix[newRow] = new double[size - 1];
+                for (int j = 0, newCol = 0; j < size; j++)
+                {
+                    if (j != colToRemove)
+                    {
+                        subMatrix[newRow][newCol] = matrix[i][j];
+                        newCol++;
+                    }
+                }
+                newRow++;
+            }
+        }
+        return subMatrix;
+    }
+}
+
+class Program
+{
+    static void Main(string[] args)
+    {
+        var summary = BenchmarkRunner.Run<MatrixDeterminant>();
+        Console.ReadLine();
+    }
+}

tasks/khalitova-am/lab_6/README.md

@@ -0,0 +1,199 @@
+# Отчёт по лабораторной работе №6
+
+Выполнила: студентка гр. ИСЭбд-41 Халитова А.М.
+
+## Создание приложения
+
+В приложении были созданы следующие методы:
+
+- Заполнение матрицы рандомными значениями:
+```
+    public static double[][] GenerateRandomMatrix(int rows, int cols)
+    {
+        double[][] matrix = new double[rows][];
+
+        Random rand = new Random();
+
+        for (int i = 0; i < rows; i++)
+        {
+            matrix[i] = new double[cols];
+            for (int j = 0; j < cols; j++)
+            {
+                matrix[i][j] = rand.Next(1, 10);
+            }
+        }
+        return matrix;
+    }
+```
+
+- Метод создания подматрицы для удаления строки и столбца в вычислении определителя:
+```
+ private static double[][] GetSubMatrix(double[][] matrix, int rowToRemove, int colToRemove)
+    {
+        int size = matrix.Length;
+        double[][] subMatrix = new double[size - 1][];
+
+        for (int i = 0, newRow = 0; i < size; i++)
+        {
+            if (i != rowToRemove)
+            {
+                subMatrix[newRow] = new double[size - 1];
+                for (int j = 0, newCol = 0; j < size; j++)
+                {
+                    if (j != colToRemove)
+                    {
+                        subMatrix[newRow][newCol] = matrix[i][j];
+                        newCol++;
+                    }
+                }
+                newRow++;
+            }
+        }
+        return subMatrix;
+    }
+```
+
+- Метод вычисления детерминанта обычным алгоритмом:
+```
+    public static double DeterminantSequential(double[][] matrix)
+    {
+        int size = matrix.Length;
+
+        if (size == 1)
+        {
+            return matrix[0][0];
+        }
+
+        if (size == 2)
+        {
+            return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
+        }
+
+        double determinant = 0;
+
+        for (int i = 0; i < size; i++)
+        {
+            double sign = (i % 2 == 0) ? 1 : -1;
+            double cofactor = sign * matrix[0][i] * DeterminantSequential(GetSubMatrix(matrix, 0, i));
+            determinant += cofactor;
+        }
+        return determinant;
+    }
+```
+
+- Метод вычисления детерминанта параллельным алгоритмом:
+```
+public static double DeterminantParallel(double[][] matrix, int numThreads)
+    {
+        int size = matrix.Length;
+
+        if (size == 1)
+        {
+            return matrix[0][0];
+        }
+
+        if (size == 2)
+        {
+            return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
+        }
+
+        double determinant = 0;
+
+        Parallel.For(0, size, new ParallelOptions { MaxDegreeOfParallelism = numThreads }, i =>
+        {
+            double sign = (i % 2 == 0) ? 1 : -1;
+            double cofactor = sign * matrix[0][i] * DeterminantSequential(GetSubMatrix(matrix, 0, i));
+            determinant += cofactor;
+        });
+        return determinant;
+    }
+```
+
+- Методы генерации матриц различных размеров и с различным числом потоков. Поскольку ресурсы машины не позволяют вычислить детерминанту для больших матриц (процесс занимает большое количество времени и памяти, происходит зависание), вычислять будем для матриц меньших размеров (2, 4, 8): 
+```
+
+    [Benchmark]
+    public void DeterminantSequential_2x2()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantSequential(matrix);
+    }
+
+    [Benchmark]
+    public void DeterminantParallel_2x2_4TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantParallel(matrix, 4);
+    }
+    [Benchmark]
+    public void DeterminantParallel_2x2_8TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantParallel(matrix, 8);
+    }
+    [Benchmark]
+    public void DeterminantParallel_2x2_16TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(2, 2);
+        DeterminantParallel(matrix, 16);
+    }
+    [Benchmark]
+    public void DeterminantSequential_4x4()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantSequential(matrix);
+    }
+
+    [Benchmark]
+    public void DeterminantParallel_4x4_4TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantParallel(matrix, 4);
+    }
+    [Benchmark]
+    public void DeterminantParallel_4x4_8TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantParallel(matrix, 8);
+    }
+    [Benchmark]
+    public void DeterminantParallel_4x4_16TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(4, 4);
+        DeterminantParallel(matrix, 16);
+    }
+    [Benchmark]
+    public void DeterminantSequential_8x8()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantSequential(matrix);
+    }
+
+    [Benchmark]
+    public void DeterminantParallel_8x8_4TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantParallel(matrix, 4);
+    }
+    [Benchmark]
+    public void DeterminantParallel_8x8_8TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantParallel(matrix, 8);
+    }
+    [Benchmark]
+    public void DeterminantParallel_8x8_16TH()
+    {
+        double[][] matrix = GenerateRandomMatrix(8, 8);
+        DeterminantParallel(matrix, 16);
+    }
+```
+
+Запуск приложения происходит с помощью строки `var summary = BenchmarkRunner.Run<MatrixDeterminant>();`.
+
+
+## Результаты работы приложения
+
+![](shot.PNG)
+
+Вывод: по результатам работы, для малых матриц парралельный алгоритм не дает прироста в скорости работы. Для матрицы 8 на 8 дает прирост только распараллеливание на малое число потоков. Для вычисления детерминанта больших матриц (больше, чем 8 на 8) не хватает вычислительной мощности моего процессора, но можно предположить что в этом случае увеличение числа потоков приводило бы к увеличению скорости работы.