From ffb4c2a8a48980fa2d48e9da3052534bd1340440 Mon Sep 17 00:00:00 2001 From: JulYakJul <137865717+JulYakJul@users.noreply.github.com> Date: Sun, 27 Oct 2024 13:04:11 +0400 Subject: [PATCH] yakovleva_yulia_lab_6 is ready --- yakovleva_yulia_lab_6/.gitignore | 923 ++++++++++++++++++ .../CalcMatrixDeterminant/.gitignore | 484 +++++++++ .../CalcMatrixDeterminant.sln | 25 + .../CalcMatrixDeterminant.csproj | 10 + .../CalcMatrixDeterminant/Program.cs | 138 +++ yakovleva_yulia_lab_6/README.md | 17 + yakovleva_yulia_lab_6/images/image1.jpg | Bin 0 -> 70913 bytes 7 files changed, 1597 insertions(+) create mode 100644 yakovleva_yulia_lab_6/.gitignore create mode 100644 yakovleva_yulia_lab_6/CalcMatrixDeterminant/.gitignore create mode 100644 yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant.sln create mode 100644 yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/CalcMatrixDeterminant.csproj create mode 100644 yakovleva_yulia_lab_6/CalcMatrixDeterminant/CalcMatrixDeterminant/Program.cs create mode 100644 yakovleva_yulia_lab_6/README.md create mode 100644 yakovleva_yulia_lab_6/images/image1.jpg diff --git a/yakovleva_yulia_lab_6/.gitignore b/yakovleva_yulia_lab_6/.gitignore new file mode 100644 index 0000000..c1f59e6 --- /dev/null +++ b/yakovleva_yulia_lab_6/.gitignore @@ -0,0 +1,923 @@ +## 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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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 0000000000000000000000000000000000000000..30740e4d25b35d54a471a569a744672fbe93ac2b GIT binary patch literal 70913 zcmeFY1yo$ywk=w?ySo!8AUMI@-KubRcLD@L&;UUTcXuz`-2()7f(0i50t89mv+v&b zoPExJ=e~1VyZ68Q-unw0jl~*kF>8)F`sjU(xt^AvwgA|QvI?>Q7#J9U{PP#!X$>F+ zfQN(o?He8r9swR60TC4m@%g|&K}ANz!obGH!ob4B!6U}U!6m}Q#3CRkAR-|lBO}Ac zr=X%Br6MLJBmM0mFz^TnhzN-2NJ!|UI9NEO|MKzF55Pf&@rHd32SW>h#esptfq5DP zkO2U&aKDZAuLmML0umey?DIv!=L>(n@@(_`_f-Ho91H*!8xH&Vv=0N*-D)^IpH0t= z)sQ`ZMPEQF+4Ad*BEo5crDqf{daI6W93Kg|Y$BB03+=`m&P~!K?F5r9vr8tYCz3KMZF*r{5S~yR{sHDbWG3Vg%LL%1jw6{Uw``E@A{1R$<+yDR+3a@M$ac>ef`5lXKS65>Irwn2>u~s)1Q?X01(^6Urr(C}Vu(V^7?Pdfhs}7{q9B{Sy3aF* zI3oN`C8tm%=4IgvYUZ6aPCW4a*pQFM5S&`m@PJMEM1-B;4)`=YN;Wxnh(#qEqEFWq zE6bwYSTIQej(P&{1y!q;ETWIrPY=!-0cG_`k=ibZ@VCK}ZCl1OCZEt%R!%MFeXaWH z7p!R-{4G)-%{E({Emp%N6C>0NvlX-Q^L}3#GSLn5Qg*U{KO{#1UW#}sG1-uJ>HvVP zS0JWs2+e%~h}aK46T4WsS^IF6=u^Jz;sFW%l9K*7v9Y}dW_htYSbxI{z2tZ-cj2e? z%4lTY_%H}l%>9}P=;>v+$^u;M5EVJ>W$`uJ8LIJ!r}gK10}Ok141|nj1%17%fZ?;N zvkX3(5; z!566v4a`gK>c~$#@Z`>&7~%jP!FoU5y$CRI{)#52B8cmT6U;L+Nb9*;#8_7l=>THl zU0mQ8SR`~}v(WA4a7{^b+EpUDs1Rp`G}>N+!qpJ^3R=t99%-wf)p;EjOiX}mvZnJY zPXB`2k)4`V7NoaKS+<=F60DWBLIM#31@+ixJ|ButQA~rx z;Vg2*8K*UJhEp{X}lsiZ7OFIUri<9_-k?Or~SQfLp))5an9(8auuFZE(oxkzOEny9P?f0V z&O-wrjjbQxACu;Kj$5t0Qp%K?v$3a@daF5{xJqynv&#nAP~)X!M@$FDz<6i|gTup8 zhnzBjUxv;IAm3VF(Z)@*(8x_9mT7#KyG@315uctoso39;S6^)%&zHO~V9mHu`;)KY zXDbVn+}O7D5IiKN8=UT&r{)!mt@WnfvHmTDJUdU^ECF=@UkE76tXN_^3>?nj4^_?7 z4qe1Au57AEB0aHBGdm$?BDK&nApI8FIN(C6%T^&dTk}7P$RFlq0Hwdg<4j2ZJ4=Ii z-Rpn&lIWN~|v+Q$+R+sgbOz zxYkg!Ib-#8V$}IT6k@JJO!%}`D)wyKVD$2Eg1mS|HWAAz>8;Z z6Ly9>(Y>`ECH8VXjEaXeUv83WM;oCFPK>>#GSiDj%6=CZhBo8~byyK;tJxYMbP)Uv zrlk~XVw1DTgSCcZw zby%j7?jn0MIYSAV&+O1o`*<|^YElu9Sz@27Z4D4DFrxA~+UWTRv;nFytG8g{ZVi8n z3mqp$A9eH(u0%^um>#!n8XsyxQHc`2YqTvF-nagHiMhF*i~3eGS;0CW8` zHJ(k`w1raH*eI$`^GE50Zm63v`Gxr0nOoh;vHK3G4u5h7O+iAj&4uEejb%#2H;aU* z1vaJzIZ#2*WS)aIb5jTxtH%XTs$xP)c+gjWnIV2HI!0%rMx84-JnuIoyp(#bj$V2Z zj-QFY6ji6+qMxZzD*9_aEA6nJtib@3dI?h>U|a0IsvyocM1%-1VJ}AAHFDI_2PNTt3p4xh zh3MP8Ph}xe7+|yo@cF_#y>LKVqCdKlM{)GoZ3qYm$xf;!AMh$F{Y4+H=8e;X|mI9D#X+fTsgn`DM@*8 z*s!&7mE|5LvO^>~BaXF|Pq1o`&n4P@7X0xi;&4^b{EE*Wd^^aV-yzFA;Sb8Az43w> zgTl>GX`CZfAv=kXn>FO9~~c{(%7O zivb&G8F*c5Mf7Xr>Ey&JtJ*K<71yoVnCjf39+abyA=W|{M4w~PRWTAI8 zBbfI>@h`q&OS`%zJUK7&$19<;4W0A3e!1I3;ix^J;LgwFtalApg zDs)$7i~2bhDK_9GCh{PB<>LRPu?T8#_W6ggh!LZw@b9tcy2Ss5){)aa*dWTaTu{~! 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