/// <summary>
/// Finds minimum for function using Coordinate Descent Optimization algorithm.
/// </summary>
/// <param name="vector">Starting point.</param>
/// <param name="e">Precision.</param>
/// <param name="function">Function used in algorithm.</param>
/// <param name="h">Shift used for getting unimodal interval.</param>
/// <returns>Minimum of function.</returns>
public static Matrica FindMinimum(Matrica vector, Matrica e, Function function, int h)
{
Matrica x = new Matrica();
x.Equals(vector);
Matrica xs = new Matrica();
function.SetParametersSize(x.NoOfRows);
do
{
xs = new Matrica();
xs.Equals(x);
for (int i = 0; i < vector.NoOfRows; i++)
{
Matrica ei = new Matrica();
ei.NoOfColumns = 1;
ei.NoOfRows = vector.NoOfRows;
for (int j = 0; j < vector.NoOfRows; j++)
{
List <double> row = new List <double>();
if (i == j)
{
row.Insert(0, 1);
}
else
{
row.Insert(0, 0);
}
ei.LoadedMatrix.Add(j, row);
}
for (int j = 0; j < x.NoOfRows; j++)
{
double value = x.LoadedMatrix[j][0];
if (i == j)
{
Expression expression = lambda => value + lambda;
function.SetParameters(j, expression);
}
else
{
Expression expression = lambda => value;
function.SetParameters(j, expression);
}
}
UnimodalInterval interval = UnimodalInterval.FindUnimodalInterval(function, 0, h);
UnimodalInterval lambdaInterval = GoldenSection.FindMinimum(function, interval.Minimum, interval.Maximum, e.LoadedMatrix[i][0]);
double lambdaMin = (lambdaInterval.Minimum + lambdaInterval.Maximum) / 2;
ei.MultiplyByScalar(lambdaMin);
x.AddValue(ei);
}
} while (x.SubtractMatrices(xs).IsLessThanOrEqual(e));
function.DeleteParameters();
return(x);
}
/// <summary>
/// Finds unimodal interval for given function and starting point.
/// </summary>
/// <param name="function">Function.</param>
/// <param name="startingPoint">Starting point.</param>
/// <param name="h">Shift.</param>
/// <returns>Unimodal interval.</returns>
public static UnimodalInterval FindUnimodalInterval(Function function, double startingPoint, double h, string algorithmName)
{
UnimodalInterval result = new UnimodalInterval(startingPoint - h, startingPoint + h);
double m = startingPoint;
double funcValueForMinimum, funcValueForMaximum, funcValueForM;
uint step = 1;
funcValueForM = function.CalculateValue(startingPoint);
function.IncreaseCounterValue(algorithmName);
funcValueForMinimum = function.CalculateValue(result.Minimum);
function.IncreaseCounterValue(algorithmName);
funcValueForMaximum = function.CalculateValue(result.Maximum);
function.IncreaseCounterValue(algorithmName);
if (funcValueForM < funcValueForMaximum && funcValueForM < funcValueForMinimum)
{
return(new UnimodalInterval(startingPoint - h, startingPoint + h));
}
else if (funcValueForM > funcValueForMaximum)
{
do
{
result.Minimum = m;
m = result.Maximum;
funcValueForM = funcValueForMaximum;
result.Maximum = startingPoint + h * (step *= 2);
funcValueForMaximum = function.CalculateValue(result.Maximum);
function.IncreaseCounterValue(algorithmName);
} while (funcValueForM > funcValueForMaximum);
}
else
{
do
{
result.Maximum = m;
m = result.Minimum;
funcValueForM = funcValueForMinimum;
result.Minimum = startingPoint - h * (step *= 2);
funcValueForMinimum = function.CalculateValue(result.Minimum);
function.IncreaseCounterValue(algorithmName);
} while (funcValueForM > funcValueForMinimum);
}
return(result);
}
/// <summary>
/// Executes Golden Section Optimization algorithm for given function.
/// </summary>
/// <param name="f">Function used in algorithm.</param>
public static void GoldenSectionOptimization(Function f)
{
Console.WriteLine("ZLATNI REZ:");
Console.WriteLine("============================================");
Console.WriteLine("Unesite 1 ako želite predati početnu točku za koju će se izračunati unimodalni interval ili 2 ako unosite unimodalni interval iz datoteke sami.");
string line = Console.ReadLine();
int choice = Int32.Parse(line);
if (choice == 1)
{
Console.WriteLine("Upišite putanju do datoteke s početnom točkom:");
string path1 = Console.ReadLine();
double startingPoint = ReadValueFromFile(path1);
Console.WriteLine("Upišite putanju do datoteke s preciznosti e:");
string path2 = Console.ReadLine();
double e = ReadValueFromFile(path2);
Console.WriteLine("Upišite putanju do datoteke s pomakom pretraživanja h:");
string path3 = Console.ReadLine();
double h = ReadValueFromFile(path3);
UnimodalInterval interval = UnimodalInterval.FindUnimodalInterval(f, startingPoint, h);
UnimodalInterval result = GoldenSection.FindMinimum(f, interval.Minimum, interval.Maximum, e);
Console.WriteLine("\nRješenje:");
Console.WriteLine("============");
Console.WriteLine("[" + result.Minimum + ", " + result.Maximum + "]");
}
else if (choice == 2)
{
Console.WriteLine("Upišite putanju do datoteke s unimodalnim intervalom:");
string path1 = Console.ReadLine();
UnimodalInterval interval = GetUnimodalIntervalFromFile(path1);
Console.WriteLine("Upišite putanju do datoteke s preciznosti e:");
string path2 = Console.ReadLine();
double e = ReadValueFromFile(path2);
UnimodalInterval result = GoldenSection.FindMinimum(f, interval.Minimum, interval.Maximum, e);
Console.WriteLine("\nRješenje:");
Console.WriteLine("============");
Console.WriteLine("[" + result.Minimum + ", " + result.Maximum + "]");
}
else
{
throw new ArgumentException("Niste odabrali ni 1 ni 2!");
}
}