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kuzarin_maxim_lab_6/.gitignore
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kuzarin_maxim_lab_6/.gitignore
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## Ignore Visual Studio temporary files, build results, and
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25
kuzarin_maxim_lab_6/DeterminantCalculation.sln
Normal file
25
kuzarin_maxim_lab_6/DeterminantCalculation.sln
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@ -0,0 +1,25 @@
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Microsoft Visual Studio Solution File, Format Version 12.00
|
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# Visual Studio Version 17
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VisualStudioVersion = 17.10.34916.146
|
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MinimumVisualStudioVersion = 10.0.40219.1
|
||||
Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "DeterminantCalculation", "DeterminantCalculation\DeterminantCalculation.csproj", "{31083870-167F-45D9-8205-4E908E4DEAEC}"
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EndProject
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@ -0,0 +1,10 @@
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||||
<Project Sdk="Microsoft.NET.Sdk">
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||||
|
||||
<PropertyGroup>
|
||||
<OutputType>Exe</OutputType>
|
||||
<TargetFramework>net8.0</TargetFramework>
|
||||
<ImplicitUsings>enable</ImplicitUsings>
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||||
<Nullable>enable</Nullable>
|
||||
</PropertyGroup>
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||||
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||||
</Project>
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||||
184
kuzarin_maxim_lab_6/DeterminantCalculation/Program.cs
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184
kuzarin_maxim_lab_6/DeterminantCalculation/Program.cs
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using System.Diagnostics;
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||||
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internal class Program
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||||
{
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private static string[] _resTableColumnsNames = new string[] { "m*m", "1 t", "2 t", "3 t", "4 t", "5 t", "6 t"};
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||||
private static void Main(string[] args)
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||||
{
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||||
Console.WriteLine(string.Join("\t", _resTableColumnsNames));
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||||
for (int i = 8; i < 13; i++)
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||||
{
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||||
var e = CreateMatrix(i, i);
|
||||
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||||
List<long> times = new() { i };
|
||||
|
||||
for (int j = 1; j <= 6; j++)
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||||
{
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||||
var sw = new Stopwatch();
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||||
sw.Start();
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||||
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||||
CalculateDeterminant(e, j);
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||||
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sw.Stop();
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||||
times.Add(sw.ElapsedMilliseconds);
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||||
}
|
||||
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||||
Console.WriteLine(string.Join("\t", times));
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||||
}
|
||||
}
|
||||
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||||
private static int[,] CreateMatrix(int x, int y)
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||||
{
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||||
var rnd = new Random();
|
||||
|
||||
var res = new int[y, x];
|
||||
|
||||
for (int i = 0; i < y; i++)
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||||
{
|
||||
for (int j = 0; j < x; j++)
|
||||
{
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||||
res[i, j] = rnd.Next(0, 100);
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||||
}
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||||
}
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return res;
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||||
}
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|
||||
private static void PritMatrix(int[,] mx)
|
||||
{
|
||||
for (int i = 0; i < mx.GetLength(0); i++)
|
||||
{
|
||||
for (int j = 0; j < mx.GetLength(1); j++)
|
||||
{
|
||||
Console.Write($"{mx[i, j].ToString("000")}\t");
|
||||
}
|
||||
Console.WriteLine();
|
||||
}
|
||||
}
|
||||
|
||||
public static long CalculateDeterminant(int[,] matrix, int maxThreads)
|
||||
=> CalculateDeterminantParalel(
|
||||
matrix,
|
||||
Enumerable.Range(0, matrix.GetLength(0)).ToArray(),
|
||||
Enumerable.Range(0, matrix.GetLength(1)).ToArray(),
|
||||
maxThreads
|
||||
);
|
||||
|
||||
private static long CalculateDeterminant(int[,] matrix, int[] rows, int[] columns)
|
||||
{
|
||||
if (rows.Length <= 3)
|
||||
return GetSimpleDeterminant(matrix, rows.ToList(), columns.ToList());
|
||||
|
||||
(int fixIndex, bool isFixRow) = GetTheBestRowColumn(matrix, rows, columns);
|
||||
|
||||
long res = 0;
|
||||
int row = isFixRow ? rows[fixIndex] : -1;
|
||||
int column = isFixRow ? -1 : columns[fixIndex];
|
||||
|
||||
for (int index = 0; index < rows.Length; index++)
|
||||
{
|
||||
if (isFixRow)
|
||||
column = columns[index];
|
||||
else
|
||||
row = rows[index];
|
||||
|
||||
res += ((index + fixIndex) % 2 != 0 ? -1 : 1) * matrix[column, row] *
|
||||
CalculateDeterminant(matrix, rows.Where(x => x != row).ToArray(), columns.Where(x => x != column).ToArray());
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
private static long CalculateDeterminantParalel(int[,] matrix, int[] rows, int[] columns, int maxThread)
|
||||
{
|
||||
if (rows.Length <= 3)
|
||||
return GetSimpleDeterminant(matrix, rows.ToList(), columns.ToList());
|
||||
|
||||
(int fixIndex, bool isFixRow) = GetTheBestRowColumn(matrix, rows, columns);
|
||||
|
||||
long res = 0;
|
||||
int row = isFixRow ? rows[fixIndex] : -1;
|
||||
int column = isFixRow ? -1 : columns[fixIndex];
|
||||
|
||||
var semaphore = new SemaphoreSlim(maxThread, maxThread);
|
||||
|
||||
for (int index = 0; index < rows.Length; index++)
|
||||
{
|
||||
if (isFixRow)
|
||||
column = columns[index];
|
||||
else
|
||||
row = rows[index];
|
||||
|
||||
var c_column = column;
|
||||
var c_row = row;
|
||||
var c_index = fixIndex + index;
|
||||
semaphore.Wait();
|
||||
Task.Run(() =>
|
||||
{
|
||||
try
|
||||
{
|
||||
res += (c_index % 2 != 0 ? -1 : 1) * matrix[c_column, c_row] *
|
||||
CalculateDeterminant(
|
||||
matrix,
|
||||
rows.Where(x => x != c_row).ToArray(),
|
||||
columns.Where(x => x != c_column).ToArray()
|
||||
);
|
||||
}
|
||||
finally { semaphore.Release(); }
|
||||
});
|
||||
}
|
||||
|
||||
semaphore.Wait(maxThread);
|
||||
return res;
|
||||
}
|
||||
|
||||
private static (int fixIndex, bool isFixRow) GetTheBestRowColumn(int[,] matrix, int[] rows, int[] columns)
|
||||
{
|
||||
Dictionary<int, int> zerosCount = rows.Select(x => x + 1).Union(columns.Select(x => -x - 1)).ToDictionary(x => x, x => 0);
|
||||
|
||||
foreach (var r in rows)
|
||||
{
|
||||
foreach (var c in columns)
|
||||
{
|
||||
if (matrix[r, c] == 0)
|
||||
{
|
||||
zerosCount[r + 1] += 1;
|
||||
zerosCount[-c - 1] += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
var best = zerosCount.ToList().OrderByDescending(x => x.Value).FirstOrDefault().Key;
|
||||
|
||||
if (best > 0)
|
||||
{
|
||||
return (Array.IndexOf(rows, best - 1), true);
|
||||
}
|
||||
else
|
||||
{
|
||||
return (Array.IndexOf(columns, -best + 1), false);
|
||||
}
|
||||
}
|
||||
|
||||
private static long GetSimpleDeterminant(int[,] matrix, List<int> rows, List<int> columns)
|
||||
{
|
||||
if (rows.Count == 1)
|
||||
{
|
||||
return matrix[columns[0], rows[0]];
|
||||
}
|
||||
else if (rows.Count == 2)
|
||||
{
|
||||
return matrix[columns[0], rows[0]] * matrix[columns[1], rows[1]] - matrix[columns[0], rows[1]] * matrix[columns[1], rows[0]];
|
||||
}
|
||||
else if (columns.Count == 3)
|
||||
{
|
||||
return matrix[columns[0], rows[0]] * matrix[columns[1], rows[1]] * matrix[columns[2], rows[2]] +
|
||||
matrix[columns[0], rows[1]] * matrix[columns[1], rows[2]] * matrix[columns[2], rows[0]] +
|
||||
matrix[columns[0], rows[2]] * matrix[columns[1], rows[0]] * matrix[columns[2], rows[1]] -
|
||||
|
||||
matrix[columns[0], rows[2]] * matrix[columns[1], rows[1]] * matrix[columns[2], rows[0]] -
|
||||
matrix[columns[1], rows[0]] * matrix[columns[0], rows[1]] * matrix[columns[2], rows[2]] -
|
||||
matrix[columns[0], rows[0]] * matrix[columns[1], rows[2]] * matrix[columns[2], rows[1]];
|
||||
}
|
||||
throw new Exception();
|
||||
}
|
||||
}
|
||||
BIN
kuzarin_maxim_lab_6/Images/determinant test.png
Normal file
BIN
kuzarin_maxim_lab_6/Images/determinant test.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 14 KiB |
15
kuzarin_maxim_lab_6/README.md
Normal file
15
kuzarin_maxim_lab_6/README.md
Normal file
@ -0,0 +1,15 @@
|
||||
# Лабораторная работа 6
|
||||
Данная работа посвящена параллельному вычислению определителя матриц
|
||||
## Описание
|
||||
Вычисление определителей для матрицы порядка более чем 3, сводится к разложению матрицы по строке (столбцу). Из этого следует, что для нахождения определителя 10-го порядка нужно (в худшем случае) 10 определителей 9-го порядка, что в свою очередь в худшем случае означает, что потребуется 8*9 = 72 определителя 8-го порядка и так далее. Это достаточно трудоёмкая процедура, которую желательно распределить
|
||||
## Запуск
|
||||
Приложение представлет собой консольную программу на C#, которую можно скомпилировать и затем запустит exe файл. В результате в окне консоли появится таблица сравнения времени находления определителя квадратных матриц (размер указан в первой колонке) с использованием разного числа потоков(от 1 до 6). Чем больше размер, тем дольше будет идти расчёт.
|
||||
## Результаты
|
||||
Результаты одного из запусков программы представлены ниже.
|
||||
<br/>
|
||||
|
||||
<br/>
|
||||
Как можно заметить, на небольших размерах распаралеливание приводит только к увеличению времени выполнения (за счёт времени создания Task и синхронизации). Но с ростом размера матрицы использование нескольким потоков начинает приносить значительный выигрыш по производительности. Но в рамках текущей реализации ускориться сильнее определённого предела не получится, что видно из расчёта матрицы 12/*12
|
||||
|
||||
## Видеодемонстрация
|
||||
Был записан видеоролик, демонстрирующий процесс запуска и работы системы. Он расположен по [адресу](https://drive.google.com/file/d/1bwJMBa_zKTvZ5PT_xgmrz9SCtEf_ied2/view?usp=sharing)
|
||||
Loading…
Reference in New Issue
Block a user