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a/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant.sln b/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant.sln new file mode 100644 index 0000000..e615178 --- /dev/null +++ b/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant.sln @@ -0,0 +1,25 @@ + +Microsoft Visual Studio Solution File, Format Version 12.00 +# Visual Studio Version 17 +VisualStudioVersion = 17.9.34728.123 +MinimumVisualStudioVersion = 10.0.40219.1 +Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "CalcMatrixDeterminant", "CalcMatrixDeterminant\CalcMatrixDeterminant.csproj", "{5F8B8E19-17FF-4A0A-AE65-FE857168ED9D}" +EndProject +Global + GlobalSection(SolutionConfigurationPlatforms) = preSolution + Debug|Any CPU = Debug|Any CPU + Release|Any CPU = Release|Any CPU + EndGlobalSection + GlobalSection(ProjectConfigurationPlatforms) = postSolution + {5F8B8E19-17FF-4A0A-AE65-FE857168ED9D}.Debug|Any CPU.ActiveCfg = Debug|Any CPU + {5F8B8E19-17FF-4A0A-AE65-FE857168ED9D}.Debug|Any CPU.Build.0 = Debug|Any CPU + {5F8B8E19-17FF-4A0A-AE65-FE857168ED9D}.Release|Any CPU.ActiveCfg = Release|Any CPU + {5F8B8E19-17FF-4A0A-AE65-FE857168ED9D}.Release|Any CPU.Build.0 = Release|Any CPU + EndGlobalSection + GlobalSection(SolutionProperties) = preSolution + HideSolutionNode = FALSE + EndGlobalSection + GlobalSection(ExtensibilityGlobals) = postSolution + SolutionGuid = {3540E666-E1FE-42C7-B319-5653E19EDF25} + EndGlobalSection +EndGlobal diff --git a/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/CalcMatrixDeterminant.csproj b/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/CalcMatrixDeterminant.csproj new file mode 100644 index 0000000..206b89a --- /dev/null +++ b/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/CalcMatrixDeterminant.csproj @@ -0,0 +1,10 @@ + + + + Exe + net8.0 + enable + enable + + + diff --git a/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/Program.cs b/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/Program.cs new file mode 100644 index 0000000..1d92d6d --- /dev/null +++ b/yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/Program.cs @@ -0,0 +1,138 @@ +using System; +using System.Diagnostics; +using System.Threading.Tasks; + +class Program +{ + // Вычисление детерминанта методом Гаусса + public static double SequentialDeterminant(double[,] matrix) + { + int n = matrix.GetLength(0); + double det = 1; + + for (int i = 0; i < n; i++) + { + int pivot = i; + for (int j = i + 1; j < n; j++) + { + if (Math.Abs(matrix[j, i]) > Math.Abs(matrix[pivot, i])) + pivot = j; + } + + if (Math.Abs(matrix[pivot, i]) < 1e-10) + return 0; + + if (i != pivot) + { + SwapRows(matrix, i, pivot); + det = -det; + } + + det *= matrix[i, i]; + for (int j = i + 1; j < n; j++) + { + matrix[i, j] /= matrix[i, i]; + } + + for (int j = i + 1; j < n; j++) + { + for (int k = i + 1; k < n; k++) + { + matrix[j, k] -= matrix[j, i] * matrix[i, k]; + } + } + } + + return det; + } + + // Вычисление детерминанта с параллельными вычислениями + public static double ParallelDeterminant(double[,] matrix, int threads = 1) + { + int n = matrix.GetLength(0); + double det = 1; + + for (int i = 0; i < n; i++) + { + int pivot = i; + for (int j = i + 1; j < n; j++) + { + if (Math.Abs(matrix[j, i]) > Math.Abs(matrix[pivot, i])) + pivot = j; + } + + if (Math.Abs(matrix[pivot, i]) < 1e-10) + return 0; + + if (i != pivot) + { + SwapRows(matrix, i, pivot); + det = -det; + } + + det *= matrix[i, i]; + for (int j = i + 1; j < n; j++) + { + matrix[i, j] /= matrix[i, i]; + } + + Parallel.For(i + 1, n, new ParallelOptions { MaxDegreeOfParallelism = threads }, j => + { + for (int k = i + 1; k < n; k++) + { + matrix[j, k] -= matrix[j, i] * matrix[i, k]; + } + }); + } + + return det; + } + + private static void SwapRows(double[,] matrix, int row1, int row2) + { + int n = matrix.GetLength(1); + for (int i = 0; i < n; i++) + { + double temp = matrix[row1, i]; + matrix[row1, i] = matrix[row2, i]; + matrix[row2, i] = temp; + } + } + + // Запуск и замер времени + public static void Benchmark(int size) + { + var random = new Random(); + double[,] matrix = new double[size, size]; + for (int i = 0; i < size; i++) + for (int j = 0; j < size; j++) + matrix[i, j] = random.NextDouble(); + + var stopwatch = new Stopwatch(); + + // Обычный алгоритм + stopwatch.Start(); + double detSeq = SequentialDeterminant((double[,])matrix.Clone()); + stopwatch.Stop(); + Console.WriteLine($"Обычный алгоритм, размер {size}x{size}: {stopwatch.ElapsedMilliseconds} мс"); + + // Параллельный алгоритм с разным количеством потоков + int[] threadCounts = { 1, 2, 4, 8 }; + foreach (var threads in threadCounts) + { + stopwatch.Restart(); + double detPar = ParallelDeterminant((double[,])matrix.Clone(), threads); + stopwatch.Stop(); + Console.WriteLine($"Параллельный алгоритм, потоки: {threads}, размер {size}x{size}: {stopwatch.ElapsedMilliseconds} мс"); + } + } + + public static void Main() + { + int[] sizes = { 100, 300, 500 }; + foreach (var size in sizes) + { + Benchmark(size); + } + } +} diff --git a/yakovleva_yulia_lab_6/README.md b/yakovleva_yulia_lab_6/README.md new file mode 100644 index 0000000..4227c63 --- /dev/null +++ b/yakovleva_yulia_lab_6/README.md @@ -0,0 +1,17 @@ +# Лабораторная работа №6 - Определение детерминанта матрицы с помощью параллельных вычислений + +## Описание +Были реализованы 2 алгоритма для определения детерминанта матрицы: обычный и параллельный. Для больших матриц лучше использовать метод Гаусса, который имеет временную сложность 𝑂(𝑛^3) и более подходящий для бенчмаркинга. + +# Результат +Общий результат +![результат работы](./images/image1.jpg) + +# Описание работы алгоритмов с матрицами 100x100 и 300x300 +Здесь мы видим, что в случае с матрицами 100x100 и 300x300 самым быстрым алгоритмом является обычный. Параллельный алгоритм при одном потоке выполняет задачу медленнее, чем при обычном алгоритме и при большем количестве потоков. Также здесь заметно, что начиная с двух потоков задача выполняется дольше. Это связано с тем, что на управление большим количеством потоков тратятся ресурсы. Чем больше потоков, тем больше ресурсов требуется процессору для управления ими, возникает конкуренция за ресурсы. + +# Описание работы алгоритмов с матрицей 500x500 +В случае с матрицей 500x500 мы видим, что параллельный алгорит быстрее выполняет свою задачу, чем обычный. Чем больше потоков - тем быстрее расчитывается детерминант. Это связано с тем, что потоки распределяют между собой задачи по расчетам детерминанта, и соотвественно заканчивают быстрее. Из этого можем сделать вывод, что параллельный алгоритм больше подходит для работы с большими матрицами. + +## Отчет +Работоспособность: [Видео](https://vk.com/video372869030_456239959) \ No newline at end of file diff --git a/yakovleva_yulia_lab_6/images/image1.jpg b/yakovleva_yulia_lab_6/images/image1.jpg new file mode 100644 index 0000000..30740e4 Binary files /dev/null and b/yakovleva_yulia_lab_6/images/image1.jpg differ