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JulYakJul 2024-10-27 13:04:11 +04:00
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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);
}
}
}

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# 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)

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