Merge pull request '[Л/Р 6] Миронов Евгений' (#60) from MironovEvgeniy/distributed-computing:mironov-eo-lab-6 into main
Reviewed-on: http://student.git.athene.tech/v.moiseev/distributed-computing/pulls/60
This commit is contained in:
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## Ignore Visual Studio temporary files, build results, and
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# Paket dependency manager
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.paket/paket.exe
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paket-files/
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# FAKE - F# Make
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.fake/
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# CodeRush personal settings
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# Cake - Uncomment if you are using it
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# tools/**
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# Backup folder for Package Reference Convert tool in Visual Studio 2017
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|
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# VS Code files for those working on multiple tools
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.vscode/*
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!.vscode/tasks.json
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!.vscode/launch.json
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*.code-workspace
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# Local History for Visual Studio Code
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# Windows Installer files from build outputs
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*.cab
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*.msi
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*.msm
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*.msp
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# JetBrains Rider
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*.sln.iml
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.idea
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##
|
||||||
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## Visual studio for Mac
|
||||||
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##
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# globs
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Makefile.in
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*.userprefs
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*.usertasks
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config.make
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config.status
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aclocal.m4
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install-sh
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autom4te.cache/
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*.tar.gz
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tarballs/
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test-results/
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||||||
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# Mac bundle stuff
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*.dmg
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*.app
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# content below from: https://github.com/github/gitignore/blob/master/Global/macOS.gitignore
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# General
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.DS_Store
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.AppleDouble
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.LSOverride
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# Icon must end with two \r
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Icon
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# Thumbnails
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._*
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# Files that might appear in the root of a volume
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.DocumentRevisions-V100
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.fseventsd
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.Spotlight-V100
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.TemporaryItems
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.Trashes
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.VolumeIcon.icns
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.com.apple.timemachine.donotpresent
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# Directories potentially created on remote AFP share
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.AppleDB
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.AppleDesktop
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Network Trash Folder
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Temporary Items
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.apdisk
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# content below from: https://github.com/github/gitignore/blob/master/Global/Windows.gitignore
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# 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
|
||||||
25
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln
Normal file
25
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln
Normal file
@ -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
|
||||||
@ -0,0 +1,14 @@
|
|||||||
|
<Project Sdk="Microsoft.NET.Sdk">
|
||||||
|
|
||||||
|
<PropertyGroup>
|
||||||
|
<OutputType>Exe</OutputType>
|
||||||
|
<TargetFramework>net8.0</TargetFramework>
|
||||||
|
<ImplicitUsings>enable</ImplicitUsings>
|
||||||
|
<Nullable>enable</Nullable>
|
||||||
|
</PropertyGroup>
|
||||||
|
|
||||||
|
<ItemGroup>
|
||||||
|
<PackageReference Include="BenchmarkDotNet" Version="0.13.11" />
|
||||||
|
</ItemGroup>
|
||||||
|
|
||||||
|
</Project>
|
||||||
177
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs
Normal file
177
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs
Normal file
@ -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;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
63
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/Program.cs
Normal file
63
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/Program.cs
Normal file
@ -0,0 +1,63 @@
|
|||||||
|
using BenchmarkDotNet.Attributes;
|
||||||
|
using BenchmarkDotNet.Running;
|
||||||
|
using ConsoleApp1;
|
||||||
|
using System.Collections.Concurrent;
|
||||||
|
|
||||||
|
BenchmarkRunner.Run<MatrixTest>();
|
||||||
|
|
||||||
|
[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);
|
||||||
|
}
|
||||||
|
}
|
||||||
143
tasks/mironov-eo/lab_6/README.md
Normal file
143
tasks/mironov-eo/lab_6/README.md
Normal file
@ -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.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
|
||||||
|
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
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
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. При этом он является оптимальным по памяти и практически не создает нагрузки на сборщик мусора.
|
||||||
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Loading…
Reference in New Issue
Block a user