Merge pull request 'yakovleva_yulia_lab_6 is ready' (#120) from yakovleva_yulia_lab_6 into main
Reviewed-on: #120
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yakovleva_yulia_lab_6/.gitignore
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|
||||
|
||||
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|
||||
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|
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|
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dozorova_alena_lab_4/ConsumerDelay/.vs/ConsumerDelay/v17/.suo
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dozorova_alena_lab_4/ConsumerDelay/.vs/ConsumerDelay/v17/DocumentLayout.json
|
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dozorova_alena_lab_4/ConsumerDelay/.vs/ProjectEvaluation/consumerdelay.metadata.v7.bin
|
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dozorova_alena_lab_4/ConsumerDelay/.vs/ProjectEvaluation/consumerdelay.projects.v7.bin
|
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dozorova_alena_lab_4/ConsumerDelay/obj/ConsumerDelay.csproj.nuget.dgspec.json
|
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dozorova_alena_lab_4/ConsumerDelay/obj/ConsumerDelay.csproj.nuget.g.targets
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dozorova_alena_lab_4/ConsumerDelay/obj/Debug/net6.0/ConsumerDelay.AssemblyInfoInputs.cache
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dozorova_alena_lab_4/ConsumerSimple/.vs/ConsumerSimple/v17/.suo
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|
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|
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dozorova_alena_lab_4/ConsumerSimple/obj/ConsumerSimple.csproj.nuget.dgspec.json
|
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dozorova_alena_lab_4/ConsumerSimple/obj/ConsumerSimple.csproj.nuget.g.props
|
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dozorova_alena_lab_4/ConsumerSimple/obj/ConsumerSimple.csproj.nuget.g.targets
|
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||||
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||||
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dozorova_alena_lab_4/ConsumerSimple/obj/Container/ContainerOperatingSystemFlavor.cache
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||||
dozorova_alena_lab_4/ConsumerSimple/obj/Container/ContainerRunContext.cache
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||||
dozorova_alena_lab_4/ConsumerSimple/obj/Container/DebuggeeArguments.cache
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||||
dozorova_alena_lab_4/ConsumerSimple/obj/Container/DebuggeeKillProcessCommand.cache
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||||
dozorova_alena_lab_4/ConsumerSimple/obj/Container/DebuggeeProgram.cache
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||||
dozorova_alena_lab_4/ConsumerSimple/obj/Container/DebuggeeWorkingDirectory.cache
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484
yakovleva_yulia_lab_6/CalcMatrixDeterminant/.gitignore
vendored
Normal file
484
yakovleva_yulia_lab_6/CalcMatrixDeterminant/.gitignore
vendored
Normal file
@ -0,0 +1,484 @@
|
||||
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|
@ -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
|
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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
|
@ -0,0 +1,10 @@
|
||||
<Project Sdk="Microsoft.NET.Sdk">
|
||||
|
||||
<PropertyGroup>
|
||||
<OutputType>Exe</OutputType>
|
||||
<TargetFramework>net8.0</TargetFramework>
|
||||
<ImplicitUsings>enable</ImplicitUsings>
|
||||
<Nullable>enable</Nullable>
|
||||
</PropertyGroup>
|
||||
|
||||
</Project>
|
@ -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);
|
||||
}
|
||||
}
|
||||
}
|
17
yakovleva_yulia_lab_6/README.md
Normal file
17
yakovleva_yulia_lab_6/README.md
Normal file
@ -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)
|
BIN
yakovleva_yulia_lab_6/images/image1.jpg
Normal file
BIN
yakovleva_yulia_lab_6/images/image1.jpg
Normal file
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