From b36b4f8587a0ea4fd05df735322c17f4e06ae0d4 Mon Sep 17 00:00:00 2001 From: ruden Date: Tue, 12 Dec 2023 22:43:39 +0300 Subject: [PATCH] mironov-eo-lab-6 --- tasks/mironov-eo/lab_6/.gitignore | 484 ++++++++++++++++++ .../lab_6/ConsoleApp1/ConsoleApp1.sln | 25 + .../ConsoleApp1/ConsoleApp1.csproj | 14 + .../ConsoleApp1/ConsoleApp1/MatrixHelper.cs | 177 +++++++ .../lab_6/ConsoleApp1/ConsoleApp1/Program.cs | 63 +++ tasks/mironov-eo/lab_6/README.md | 143 ++++++ tasks/mironov-eo/lab_6/pic/1.png | Bin 0 -> 71614 bytes tasks/mironov-eo/lab_6/pic/2.png | Bin 0 -> 72005 bytes tasks/mironov-eo/lab_6/pic/3.png | Bin 0 -> 97820 bytes tasks/mironov-eo/lab_6/pic/4.png | Bin 0 -> 76143 bytes tasks/mironov-eo/lab_6/pic/5.png | Bin 0 -> 25504 bytes 11 files changed, 906 insertions(+) create mode 100644 tasks/mironov-eo/lab_6/.gitignore create mode 100644 tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln create mode 100644 tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/ConsoleApp1.csproj create mode 100644 tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs create mode 100644 tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/Program.cs create mode 100644 tasks/mironov-eo/lab_6/README.md create mode 100644 tasks/mironov-eo/lab_6/pic/1.png create mode 100644 tasks/mironov-eo/lab_6/pic/2.png create mode 100644 tasks/mironov-eo/lab_6/pic/3.png create mode 100644 tasks/mironov-eo/lab_6/pic/4.png create mode 100644 tasks/mironov-eo/lab_6/pic/5.png diff --git a/tasks/mironov-eo/lab_6/.gitignore b/tasks/mironov-eo/lab_6/.gitignore new file mode 100644 index 0000000..104b544 --- /dev/null +++ b/tasks/mironov-eo/lab_6/.gitignore @@ -0,0 +1,484 @@ +## Ignore Visual Studio temporary files, build results, and +## files generated by popular Visual Studio add-ons. +## +## Get latest from `dotnet new gitignore` + +# dotenv files +.env + +# User-specific files +*.rsuser +*.suo +*.user +*.userosscache +*.sln.docstates + +# User-specific files (MonoDevelop/Xamarin Studio) +*.userprefs + +# Mono auto generated files +mono_crash.* + +# Build results +[Dd]ebug/ +[Dd]ebugPublic/ +[Rr]elease/ +[Rr]eleases/ +x64/ +x86/ +[Ww][Ii][Nn]32/ +[Aa][Rr][Mm]/ +[Aa][Rr][Mm]64/ +bld/ +[Bb]in/ +[Oo]bj/ +[Ll]og/ +[Ll]ogs/ + +# Visual Studio 2015/2017 cache/options directory +.vs/ +# Uncomment if you have tasks that create the project's static files in wwwroot +#wwwroot/ + +# Visual Studio 2017 auto generated files +Generated\ Files/ + +# MSTest test Results +[Tt]est[Rr]esult*/ +[Bb]uild[Ll]og.* + +# NUnit +*.VisualState.xml +TestResult.xml +nunit-*.xml + +# Build Results of an ATL Project +[Dd]ebugPS/ +[Rr]eleasePS/ +dlldata.c + +# Benchmark Results +BenchmarkDotNet.Artifacts/ + +# .NET +project.lock.json +project.fragment.lock.json +artifacts/ + +# Tye +.tye/ + +# ASP.NET Scaffolding +ScaffoldingReadMe.txt + +# StyleCop +StyleCopReport.xml + +# Files built by Visual Studio +*_i.c +*_p.c +*_h.h +*.ilk +*.meta +*.obj +*.iobj +*.pch +*.pdb +*.ipdb +*.pgc +*.pgd +*.rsp +*.sbr +*.tlb +*.tli +*.tlh +*.tmp +*.tmp_proj +*_wpftmp.csproj +*.log +*.tlog +*.vspscc +*.vssscc +.builds +*.pidb +*.svclog +*.scc + +# Chutzpah Test files +_Chutzpah* + +# Visual C++ cache files +ipch/ +*.aps +*.ncb +*.opendb +*.opensdf +*.sdf +*.cachefile +*.VC.db +*.VC.VC.opendb + +# Visual Studio profiler +*.psess +*.vsp +*.vspx +*.sap + +# Visual Studio Trace Files +*.e2e + +# TFS 2012 Local Workspace +$tf/ + +# Guidance Automation Toolkit +*.gpState + +# ReSharper is a .NET coding add-in +_ReSharper*/ +*.[Rr]e[Ss]harper +*.DotSettings.user + +# TeamCity is a build add-in +_TeamCity* + +# DotCover is a Code Coverage Tool +*.dotCover + +# AxoCover is a Code Coverage Tool +.axoCover/* +!.axoCover/settings.json + +# Coverlet is a free, cross platform Code Coverage Tool +coverage*.json +coverage*.xml +coverage*.info + +# Visual Studio code coverage results +*.coverage +*.coveragexml + +# NCrunch +_NCrunch_* +.*crunch*.local.xml +nCrunchTemp_* + +# MightyMoose +*.mm.* +AutoTest.Net/ + +# Web workbench (sass) +.sass-cache/ + +# Installshield output folder +[Ee]xpress/ + +# DocProject is a documentation generator add-in +DocProject/buildhelp/ +DocProject/Help/*.HxT +DocProject/Help/*.HxC +DocProject/Help/*.hhc +DocProject/Help/*.hhk +DocProject/Help/*.hhp +DocProject/Help/Html2 +DocProject/Help/html + +# Click-Once directory +publish/ + +# Publish Web Output +*.[Pp]ublish.xml +*.azurePubxml +# Note: Comment the next line if you want to checkin your web deploy settings, +# but database connection strings (with potential passwords) will be unencrypted +*.pubxml +*.publishproj + +# Microsoft Azure Web App publish settings. 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https://github.com/github/gitignore/blob/master/Global/macOS.gitignore +# General +.DS_Store +.AppleDouble +.LSOverride + +# Icon must end with two \r +Icon + + +# Thumbnails +._* + +# Files that might appear in the root of a volume +.DocumentRevisions-V100 +.fseventsd +.Spotlight-V100 +.TemporaryItems +.Trashes +.VolumeIcon.icns +.com.apple.timemachine.donotpresent + +# Directories potentially created on remote AFP share +.AppleDB +.AppleDesktop +Network Trash Folder +Temporary Items +.apdisk + +# content below from: https://github.com/github/gitignore/blob/master/Global/Windows.gitignore +# Windows thumbnail cache files +Thumbs.db +ehthumbs.db +ehthumbs_vista.db + +# Dump file +*.stackdump + +# Folder config file +[Dd]esktop.ini + +# Recycle Bin used on file shares +$RECYCLE.BIN/ + +# Windows Installer files +*.cab +*.msi +*.msix +*.msm +*.msp + +# Windows shortcuts +*.lnk + +# Vim temporary swap files +*.swp diff --git a/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln new file mode 100644 index 0000000..fc4fd95 --- /dev/null +++ b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln @@ -0,0 +1,25 @@ + +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 + {24793D16-F80E-48B2-8A04-76BD2CB61C1C}.Release|Any CPU.Build.0 = Release|Any CPU + EndGlobalSection + GlobalSection(SolutionProperties) = preSolution + HideSolutionNode = FALSE + EndGlobalSection + GlobalSection(ExtensibilityGlobals) = postSolution + SolutionGuid = {D17B9FEE-F4BF-4559-899B-434F4545FF67} + EndGlobalSection +EndGlobal diff --git a/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/ConsoleApp1.csproj b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/ConsoleApp1.csproj new file mode 100644 index 0000000..272dc0e --- /dev/null +++ b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/ConsoleApp1.csproj @@ -0,0 +1,14 @@ + + + + Exe + net8.0 + enable + enable + + + + + + + diff --git a/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs new file mode 100644 index 0000000..5e1183e --- /dev/null +++ b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs @@ -0,0 +1,177 @@ +using CommandLine; +using System; +using System.Collections.Concurrent; +using System.Collections.Generic; +using System.Linq; +using System.Runtime.CompilerServices; +using System.Text; +using System.Threading.Tasks; +using static ConsoleApp1.MatrixHelper; + +namespace ConsoleApp1 +{ + + public class MatrixHelper + { + + 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 determinantOfMatrixGaus(double[,] mat) + { + int n = mat.GetLength(0); + int i, j, k; + for (i = 0; i < n - 1; i++) + { + for (j = i + 1; j < n; j++) + { + if (j == i) + continue; + + double someDet = mat[j, i] / mat[i, i]; + for (k = i; k < n; k++) + mat[j, k] -= someDet * mat[i, k]; + } + } + double det = 1; + for (i = 0; i < n; i++) + det = det * mat[i, i]; + return det; + } + + + + public double determinantOfMatrixParallelGaus(double[,] mat, int threadCount) + { + int n = mat.GetLength(0); + + Parallel.For(0, n - 1, + new ParallelOptions() + { + MaxDegreeOfParallelism = threadCount + }, + (i) => + { + for (int j = i + 1; j < n; j++) + { + if (j == i) + continue; + + double det = mat[j, i] / mat[i, i]; + + for (int k = i; k < n; k++) + mat[j, k] = mat[j, k] - det * mat[i, k]; + }; + }); + double det = 1; + for (int i = 0; i < n; i++) + det = det * mat[i, i]; + return det; + } + + public double determinantOfMatrixLaplas(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; + } + } + + + } +} + diff --git a/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/Program.cs b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/Program.cs new file mode 100644 index 0000000..d22e38a --- /dev/null +++ b/tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/Program.cs @@ -0,0 +1,63 @@ +using BenchmarkDotNet.Attributes; +using BenchmarkDotNet.Running; +using ConsoleApp1; +using System.Collections.Concurrent; + +BenchmarkRunner.Run(); + +[MemoryDiagnoser] +public class MatrixTest +{ + + double[,] Matrix100; + double[,] Matrix10; + + + MatrixHelper matrixHelper; + + + public MatrixTest() + { + matrixHelper = new MatrixHelper(); + + Matrix10 = matrixHelper.RandomGenerateMatrix(10); + Matrix100 = matrixHelper.RandomGenerateMatrix(100); + + } + + [Benchmark] + public double MatrixDeterminantLaplas10() + { + return matrixHelper.determinantOfMatrixLaplas(Matrix10, 1); + } + + [Benchmark] + public double MatrixDeterminantLaplasParallel10() + { + return matrixHelper.determinantOfMatrixLaplas(Matrix10, 15); + } + + [Benchmark] + public double MatrixDeterminantGausParallel10() + { + return matrixHelper.determinantOfMatrixParallelGaus(Matrix10, 15); + } + + [Benchmark] + public double MatrixDeterminantGaus10() + { + return matrixHelper.determinantOfMatrixGaus(Matrix10); + } + + [Benchmark] + public double MatrixDeterminantGausParallel100() + { + return matrixHelper.determinantOfMatrixParallelGaus(Matrix100, 15); + } + + [Benchmark] + public double MatrixDeterminantGaus100() + { + return matrixHelper.determinantOfMatrixGaus(Matrix100); + } +} \ No newline at end of file diff --git a/tasks/mironov-eo/lab_6/README.md b/tasks/mironov-eo/lab_6/README.md new file mode 100644 index 0000000..6a05e92 --- /dev/null +++ b/tasks/mironov-eo/lab_6/README.md @@ -0,0 +1,143 @@ +# Отчет по лабораторной работе №6 + +Выполнил студент гр. ИСЭбд-41 Миронов Е.О. + +## Выбор алгоритма + +Предложенный алгоритм(теорема Лапласа) имеет асимптотику примерно O(n!). Для подсчета определителя матрицы размерностью более 10х10 он зависает. Запустить его на матрицу 100х100 на моей машине просто невозвожно. + +Поэтому рассматриваю другой алгоритм - метод Гаусса. Он имеет сложность O(n^3), и его уже реально выполнять на больших данных. +Но на каждом шаге изменяется общий ресурс в виде исходной матрицы, поэтому алгоритм должен плохо параллелиться. + +Также ко всему этому определитель матрицы свыше 100х100 слишком большой и не поддерживается типом double. +![](pic/1.png) + +![](pic/2.png) + + +В итоге решил использовать теорему Лапласа на матрицах до 10х10 и метод Гаусса на матрицах до 100х100 + + + +## Создание приложения + +Выбрал язык C#, Консольное приложение. + +Попробуем запустить все алгоритмы на матрицах 3х3 и проверить результат выполнения. +![](pic/3.png) + +Немного разные результаты спишу на погрешность типа double + +Однопоточный метод Гаусса +```cs +public double determinantOfMatrixGaus(double[,] mat, int n) +{ + int i, j, k; + for (i = 0; i < n - 1; i++) + { + for (j = i + 1; j < n; j++) + { + if (j == i) + continue; + + double someDet = mat[j, i] / mat[i, i]; + for (k = i; k < n; k++) + mat[j, k] -= someDet * mat[i, k]; + } + } + double det = 1; + for (i = 0; i < n; i++) + det = det * mat[i, i]; + return det; +} +``` + +Параллельный метод Гаусса +```cs +public double determinantOfMatrixParallelGaus(double[,] mat, int n) +{ + Parallel.For(0, n - 1, + new ParallelOptions() + { + MaxDegreeOfParallelism = threadCount + }, + (i) => + { + for (int j = i + 1; j < n; j++) + { + if (j == i) + continue; + + double det = mat[j, i] / mat[i, i]; + + for (int k = i; k < n; k++) + mat[j, k] = mat[j, k] - det * mat[i, k]; + }; + }); + double det = 1; + for (int i = 0; i < n; i++) + det = det * mat[i, i]; + return det; +} +``` +Почему это работает до конца не понятно. +Возможно потому что алгоритм меняет только строку j, и только на основании данных строк i (счетчик в Parallel.For - синхронизован) и j(текущая строка). + +Сделал вот такую проверку - все ок, ни одной ошибки + +![](pic/4.png) + +Однако я все равно сомневаюсь в прошлой реализации и подозреваю, что где-то есть race condition. +Поэтому вот реализация в которой куча блокировок, и она работает намного медленее, но зато я в ней уверен. + +``` cs +public double determinantOfMatrixParallelGaus(double[,] mat, int n) +{ + lockObjects = new object[n].Select(x => new object()).ToArray(); + + for (int i = 0; i < n - 1; i++) + { + lock (lockObjects[i]) + { + Parallel.For(i + 1, n, + (j) => + { + if (j == i) + return; + + lock (lockObjects[j]) + { + double det = mat[j, i] / mat[i, i]; + + for (int k = i; k < n; k++) + mat[j, k] = mat[j, k] - det * mat[i, k]; + } + }); + } + } + double det = 1; + for (int i = 0; i < n; i++) + det = det * mat[i, i]; + return det; +} +``` + + + + +## Бенчмарки + +Запускаю тесты + +1) Лаплас 10х10 в один поток +2) Лаплас 10х10 в 15 потоков +3) Гаусс 10х10 в 15 потоков +4) Гаусс 10х10 в 1 поток +5) Гаусс 100х100 в 15 потоков +6) Гаусс 100х100 в 1 поток. + +![](pic/5.png) + +Видим, что в нашем тесте параллельные реализации работают быстрее однопоточных. + +Помимо этого и без того понятного вывода видим огромную разницу в алгоритмах Гаусса и Лапласа. С объемом данных большим в 100 раз алгоритм Гаусса справляется быстрее в 40 раз. 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