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b/kuzarin_maxim_lab_6/DeterminantCalculation.sln new file mode 100644 index 0000000..6c92229 --- /dev/null +++ b/kuzarin_maxim_lab_6/DeterminantCalculation.sln @@ -0,0 +1,25 @@ + +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}") = "DeterminantCalculation", "DeterminantCalculation\DeterminantCalculation.csproj", "{31083870-167F-45D9-8205-4E908E4DEAEC}" +EndProject +Global + GlobalSection(SolutionConfigurationPlatforms) = preSolution + Debug|Any CPU = Debug|Any CPU + Release|Any CPU = Release|Any CPU + EndGlobalSection + GlobalSection(ProjectConfigurationPlatforms) = postSolution + {31083870-167F-45D9-8205-4E908E4DEAEC}.Debug|Any CPU.ActiveCfg = Debug|Any CPU + {31083870-167F-45D9-8205-4E908E4DEAEC}.Debug|Any CPU.Build.0 = Debug|Any CPU + {31083870-167F-45D9-8205-4E908E4DEAEC}.Release|Any CPU.ActiveCfg = Release|Any CPU + {31083870-167F-45D9-8205-4E908E4DEAEC}.Release|Any CPU.Build.0 = Release|Any CPU + EndGlobalSection + GlobalSection(SolutionProperties) = preSolution + HideSolutionNode = FALSE + EndGlobalSection + GlobalSection(ExtensibilityGlobals) = postSolution + SolutionGuid = {15AF4683-8FFA-462B-AEB1-EBC1DC51E24A} + EndGlobalSection +EndGlobal diff --git a/kuzarin_maxim_lab_6/DeterminantCalculation/DeterminantCalculation.csproj b/kuzarin_maxim_lab_6/DeterminantCalculation/DeterminantCalculation.csproj new file mode 100644 index 0000000..2150e37 --- /dev/null +++ b/kuzarin_maxim_lab_6/DeterminantCalculation/DeterminantCalculation.csproj @@ -0,0 +1,10 @@ + + + + Exe + net8.0 + enable + enable + + + diff --git a/kuzarin_maxim_lab_6/DeterminantCalculation/Program.cs b/kuzarin_maxim_lab_6/DeterminantCalculation/Program.cs new file mode 100644 index 0000000..b04446d --- /dev/null +++ b/kuzarin_maxim_lab_6/DeterminantCalculation/Program.cs @@ -0,0 +1,184 @@ +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"}; + private static void Main(string[] args) + { + Console.WriteLine(string.Join("\t", _resTableColumnsNames)); + for (int i = 8; i < 13; i++) + { + var e = CreateMatrix(i, i); + + List times = new() { i }; + + for (int j = 1; j <= 6; j++) + { + var sw = new Stopwatch(); + sw.Start(); + + CalculateDeterminant(e, j); + + sw.Stop(); + times.Add(sw.ElapsedMilliseconds); + } + + Console.WriteLine(string.Join("\t", times)); + } + } + + 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; + } + + private static void PritMatrix(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(); + } + } + + public static long CalculateDeterminant(int[,] matrix, int maxThreads) + => CalculateDeterminantParalel( + matrix, + Enumerable.Range(0, matrix.GetLength(0)).ToArray(), + Enumerable.Range(0, matrix.GetLength(1)).ToArray(), + maxThreads + ); + + private static long CalculateDeterminant(int[,] matrix, int[] rows, int[] columns) + { + if (rows.Length <= 3) + return GetSimpleDeterminant(matrix, rows.ToList(), columns.ToList()); + + (int fixIndex, bool isFixRow) = GetTheBestRowColumn(matrix, rows, columns); + + long res = 0; + int row = isFixRow ? rows[fixIndex] : -1; + int column = isFixRow ? -1 : columns[fixIndex]; + + for (int index = 0; index < rows.Length; index++) + { + if (isFixRow) + column = columns[index]; + else + row = rows[index]; + + res += ((index + fixIndex) % 2 != 0 ? -1 : 1) * matrix[column, row] * + CalculateDeterminant(matrix, rows.Where(x => x != row).ToArray(), columns.Where(x => x != column).ToArray()); + } + + return res; + } + + private static long CalculateDeterminantParalel(int[,] matrix, int[] rows, int[] columns, int maxThread) + { + if (rows.Length <= 3) + return GetSimpleDeterminant(matrix, rows.ToList(), columns.ToList()); + + (int fixIndex, bool isFixRow) = GetTheBestRowColumn(matrix, rows, columns); + + long res = 0; + int row = isFixRow ? rows[fixIndex] : -1; + int column = isFixRow ? -1 : columns[fixIndex]; + + var semaphore = new SemaphoreSlim(maxThread, maxThread); + + for (int index = 0; index < rows.Length; index++) + { + if (isFixRow) + column = columns[index]; + else + row = rows[index]; + + var c_column = column; + var c_row = row; + var c_index = fixIndex + index; + semaphore.Wait(); + Task.Run(() => + { + try + { + res += (c_index % 2 != 0 ? -1 : 1) * matrix[c_column, c_row] * + CalculateDeterminant( + matrix, + rows.Where(x => x != c_row).ToArray(), + columns.Where(x => x != c_column).ToArray() + ); + } + finally { semaphore.Release(); } + }); + } + + semaphore.Wait(maxThread); + return res; + } + + private static (int fixIndex, bool isFixRow) GetTheBestRowColumn(int[,] matrix, int[] rows, int[] columns) + { + Dictionary zerosCount = rows.Select(x => x + 1).Union(columns.Select(x => -x - 1)).ToDictionary(x => x, x => 0); + + foreach (var r in rows) + { + foreach (var c in columns) + { + if (matrix[r, c] == 0) + { + zerosCount[r + 1] += 1; + zerosCount[-c - 1] += 1; + } + } + } + + var best = zerosCount.ToList().OrderByDescending(x => x.Value).FirstOrDefault().Key; + + if (best > 0) + { + return (Array.IndexOf(rows, best - 1), true); + } + else + { + return (Array.IndexOf(columns, -best + 1), false); + } + } + + private static long GetSimpleDeterminant(int[,] matrix, List rows, List columns) + { + if (rows.Count == 1) + { + return matrix[columns[0], rows[0]]; + } + else if (rows.Count == 2) + { + return matrix[columns[0], rows[0]] * matrix[columns[1], rows[1]] - matrix[columns[0], rows[1]] * matrix[columns[1], rows[0]]; + } + else if (columns.Count == 3) + { + return matrix[columns[0], rows[0]] * matrix[columns[1], rows[1]] * matrix[columns[2], rows[2]] + + matrix[columns[0], rows[1]] * matrix[columns[1], rows[2]] * matrix[columns[2], rows[0]] + + matrix[columns[0], rows[2]] * matrix[columns[1], rows[0]] * matrix[columns[2], rows[1]] - + + matrix[columns[0], rows[2]] * matrix[columns[1], rows[1]] * matrix[columns[2], rows[0]] - + matrix[columns[1], rows[0]] * matrix[columns[0], rows[1]] * matrix[columns[2], rows[2]] - + matrix[columns[0], rows[0]] * matrix[columns[1], rows[2]] * matrix[columns[2], rows[1]]; + } + throw new Exception(); + } +} \ No newline at end of file diff --git a/kuzarin_maxim_lab_6/Images/determinant test.png b/kuzarin_maxim_lab_6/Images/determinant test.png new file mode 100644 index 0000000..cddef53 Binary files /dev/null and b/kuzarin_maxim_lab_6/Images/determinant test.png differ diff --git a/kuzarin_maxim_lab_6/README.md b/kuzarin_maxim_lab_6/README.md new file mode 100644 index 0000000..3378bbf --- /dev/null +++ b/kuzarin_maxim_lab_6/README.md @@ -0,0 +1,15 @@ +# Лабораторная работа 6 +Данная работа посвящена параллельному вычислению определителя матриц +## Описание +Вычисление определителей для матрицы порядка более чем 3, сводится к разложению матрицы по строке (столбцу). Из этого следует, что для нахождения определителя 10-го порядка нужно (в худшем случае) 10 определителей 9-го порядка, что в свою очередь в худшем случае означает, что потребуется 8*9 = 72 определителя 8-го порядка и так далее. Это достаточно трудоёмкая процедура, которую желательно распределить +## 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 находления определителя квадратных матриц (размер указан в первой колонке) с использованием разного числа потоков(от 1 до 6). Чем больше размер, тем дольше будет идти расчёт. +## Результаты +Результаты одного из запусков программы представлены ниже. +
+![Resout](Images/determinant test.png) +
+Как можно заметить, на небольших размерах распаралеливание приводит только к увеличению времени выполнения (за счёт времени создания Task и синхронизации). Но с ростом размера матрицы использование нескольким потоков начинает приносить значительный выигрыш по производительности. Но в рамках текущей реализации ускориться сильнее определённого предела не получится, что видно из расчёта матрицы 12/*12 + +## Видеодемонстрация +Был записан видеоролик, демонстрирующий процесс запуска и работы системы. Он расположен по [адресу](https://drive.google.com/file/d/1bwJMBa_zKTvZ5PT_xgmrz9SCtEf_ied2/view?usp=sharing)