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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tasks/mironov-eo/lab_6/.gitignore
vendored
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||||
25
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1.sln
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||||
|
||||
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}"
|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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@ -0,0 +1,14 @@
|
||||
<Project Sdk="Microsoft.NET.Sdk">
|
||||
|
||||
<PropertyGroup>
|
||||
<OutputType>Exe</OutputType>
|
||||
<TargetFramework>net8.0</TargetFramework>
|
||||
<ImplicitUsings>enable</ImplicitUsings>
|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
|
||||
</Project>
|
||||
177
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs
Normal file
177
tasks/mironov-eo/lab_6/ConsoleApp1/ConsoleApp1/MatrixHelper.cs
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@ -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.
|
||||
BIN
tasks/mironov-eo/lab_6/pic/1.png
Normal file
BIN
tasks/mironov-eo/lab_6/pic/1.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 70 KiB |
BIN
tasks/mironov-eo/lab_6/pic/2.png
Normal file
BIN
tasks/mironov-eo/lab_6/pic/2.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 70 KiB |
BIN
tasks/mironov-eo/lab_6/pic/3.png
Normal file
BIN
tasks/mironov-eo/lab_6/pic/3.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 96 KiB |
BIN
tasks/mironov-eo/lab_6/pic/4.png
Normal file
BIN
tasks/mironov-eo/lab_6/pic/4.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 74 KiB |
BIN
tasks/mironov-eo/lab_6/pic/5.png
Normal file
BIN
tasks/mironov-eo/lab_6/pic/5.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 25 KiB |
Loading…
Reference in New Issue
Block a user