Merge pull request '[Л/Р 6] Островская Софья' (#96) from ostrovsofa/distributed-computing:ostrovskaya-sf-lab-6 into main

Reviewed-on: http://student.git.athene.tech/v.moiseev/distributed-computing/pulls/96
This commit is contained in:
Vladislav Moiseev 2023-12-17 23:45:07 +04:00
commit 5844b9b63c
6 changed files with 720 additions and 0 deletions

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# Отчет по лабораторной работе №6
Выполнила студентка гр. ИСЭбд-41 Островская С. Ф.
## Создание приложения
Было выбрано консольное приложение, язык программирования - c#.
Обычный алгоритм:
```cs
static void SequentialDeterminantCalculation(int matrixSize, int lowerLimit, int upperLimit)
{
int[][] randomMatrix = GenerateRandomMatrix(matrixSize, lowerLimit, upperLimit);
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
int result = Determinant(randomMatrix);
stopwatch.Stop();
TimeSpan elapsedTime = stopwatch.Elapsed;
Console.WriteLine($"Последовательный детерминант: {result}");
Console.WriteLine($"Последовательное время: {elapsedTime.TotalSeconds:F7} секунд");
}
```
Параллельный алгоритм:
```cs
static void ParallelDeterminantCalculation(int matrixSize, int lowerLimit, int upperLimit, int numProcesses)
{
int[][] randomMatrix = GenerateRandomMatrix(matrixSize, lowerLimit, upperLimit);
int[][] matricesToProcess = new int[matrixSize][];
for (int col = 0; col < matrixSize; col++)
{
matricesToProcess[col] = Submatrix(randomMatrix, 0, col)[0];
}
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
int[] determinants = new int[matrixSize];
Parallel.For(0, matrixSize, new ParallelOptions { MaxDegreeOfParallelism = numProcesses }, col =>
{
determinants[col] = Determinant(new int[][] { matricesToProcess[col] });
});
int result = 0;
for (int col = 0; col < matrixSize; col++)
{
result += ((-1) * col) * randomMatrix[0][col] * determinants[col];
}
stopwatch.Stop();
TimeSpan elapsedTime = stopwatch.Elapsed;
Console.WriteLine($"Параллельный детерминант: {result}");
Console.WriteLine($"Параллельное время: {elapsedTime.TotalSeconds:F7} секунд");
}
```
## Бенчмарки
Для примера была взята матрица размерностью 10х10, поскольку для матриц больших размеров детерминант вычисляется слишком долго.
![](pic/pic1.jpg)
``Вывод``: Обыный алгоритм работает быстрее, если количество элементов не слишком много. Параллельный же алгоритм работает быстрее только при наличии большого количества операций и данных.

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using System;
using System.Diagnostics;
using System.Threading.Tasks;
class Program
{
static void SequentialDeterminantCalculation(int matrixSize, int lowerLimit, int upperLimit)
{
int[][] randomMatrix = GenerateRandomMatrix(matrixSize, lowerLimit, upperLimit);
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
int result = Determinant(randomMatrix);
stopwatch.Stop();
TimeSpan elapsedTime = stopwatch.Elapsed;
Console.WriteLine($"Последовательный детерминант: {result}");
Console.WriteLine($"Последовательное время: {elapsedTime.TotalSeconds:F7} секунд");
}
static void ParallelDeterminantCalculation(int matrixSize, int lowerLimit, int upperLimit, int numProcesses)
{
int[][] randomMatrix = GenerateRandomMatrix(matrixSize, lowerLimit, upperLimit);
int[][] matricesToProcess = new int[matrixSize][];
for (int col = 0; col < matrixSize; col++)
{
matricesToProcess[col] = Submatrix(randomMatrix, 0, col)[0];
}
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
int[] determinants = new int[matrixSize];
Parallel.For(0, matrixSize, new ParallelOptions { MaxDegreeOfParallelism = numProcesses }, col =>
{
determinants[col] = Determinant(new int[][] { matricesToProcess[col] });
});
int result = 0;
for (int col = 0; col < matrixSize; col++)
{
result += ((-1) * col) * randomMatrix[0][col] * determinants[col];
}
stopwatch.Stop();
TimeSpan elapsedTime = stopwatch.Elapsed;
Console.WriteLine($"Параллельный детерминант: {result}");
Console.WriteLine($"Параллельное время: {elapsedTime.TotalSeconds:F7} секунд");
}
static int[][] GenerateRandomMatrix(int matrixSize, int lowerLimit, int upperLimit)
{
Random random = new Random();
int[][] matrix = new int[matrixSize][];
for (int i = 0; i < matrixSize; i++)
{
matrix[i] = new int[matrixSize];
for (int j = 0; j < matrixSize; j++)
{
matrix[i][j] = random.Next(lowerLimit, upperLimit);
}
}
return matrix;
}
static int[][] Submatrix(int[][] matrix, int rowToDelete, int colToDelete)
{
int size = matrix.Length - 1;
int[][] submatrix = new int[size][];
int rowIndex = 0;
for (int i = 0; i < matrix.Length; i++)
{
if (i == rowToDelete)
continue;
submatrix[rowIndex] = new int[size];
int colIndex = 0;
for (int j = 0; j < matrix.Length; j++)
{
if (j == colToDelete)
continue;
submatrix[rowIndex][colIndex] = matrix[i][j];
colIndex++;
}
rowIndex++;
}
return submatrix;
}
static int Determinant(int[][] matrix)
{
int n = matrix.Length;
if (n == 1)
{
return matrix[0][0];
}
else if (n == 2)
{
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
}
else
{
int determinant = 0;
for (int j = 0; j < n; j++)
{
int[][] submatrix = Submatrix(matrix, 0, j);
int subDeterminant = Determinant(submatrix);
determinant += ((-1) * j) * matrix[0][j] * subDeterminant;
}
return determinant;
}
}
static void Main(string[] args)
{
SequentialDeterminantCalculation(10, 0, 10);
Console.WriteLine();
int[] numThreads = { 1, 2, 4, 6, 8, 12, 16, 32 };
for (int i = 0; i < 8; i++)
{
Console.WriteLine($"Количество потоков: {numThreads[i]}");
ParallelDeterminantCalculation(10, 0, 10, numThreads[i]);
}
}
}

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