/// <summary>
/// Finds minimum of given function using the Gradient Descent algorithm.
/// </summary>
/// <param name="function">Function used in algorithm.</param>
/// <param name="e">Precision.</param>
/// <param name="startingPoint">Starting point of algorithm.</param>
/// <param name="usingGoldenSection">Flag used for tracking whether user wants to use Golden Section algorithm or not.</param>
/// <returns>Minimum of function.</returns>
public static Matrica FindMinimum(Function function, double e, Matrica startingPoint, bool usingGoldenSection)
{
Matrica x = new Matrica();
x.Equals(startingPoint);
function.SetParametersSize(x.NoOfRows);
Matrica v = new Matrica();
int brojac = 0;
Matrica xs = new Matrica();
if (usingGoldenSection == false)
{
do
{
xs.Equals(x);
v = function.CalculateGradientValue(x.VectorToArray());
function.IncreaseCounterGradientValue(algorithmName);
v.MultiplyByScalar(-1);
x.AddValue(v);
brojac++;
function.IncreaseCounterValue(algorithmName);
function.IncreaseCounterValue(algorithmName);
} while (brojac < 10000);
}
else
{
do
{
xs.Equals(x);
v = function.CalculateGradientValue(x.VectorToArray());
function.IncreaseCounterGradientValue(algorithmName);
v.MultiplyByScalar(-1);
v.MultiplyByScalar(1.0 / function.GetGradientNorm());
for (int i = 0; i < x.NoOfRows; i++)
{
double value = x.LoadedMatrix[i][0];
double vectorValue = v.LoadedMatrix[i][0];
Expression expression = lambda => value + lambda * vectorValue;
function.SetParameters(i, expression);
}
UnimodalInterval interval = UnimodalInterval.FindUnimodalInterval(function, 0, 1, algorithmName);
UnimodalInterval lambdaInterval = GoldenSection.FindMinimum(function, interval.Minimum, interval.Maximum, e, algorithmName);
double lambdaMin = (lambdaInterval.Minimum + lambdaInterval.Maximum) / 2;
v.MultiplyByScalar(lambdaMin);
x.AddValue(v);
function.IncreaseCounterValue(algorithmName);
function.IncreaseCounterValue(algorithmName);
} while (function.GetGradientNorm() >= e);
}
function.DeleteParameters();
return(x);
}
/// <summary>
/// Finds minimum of function using Newton-Raphson algorithm.
/// </summary>
/// <param name="function">Function used in algorithm.</param>
/// <param name="e">Precision</param>
/// <param name="startingPoint">Starting point of algorithm.</param>
/// <param name="usingGoldenSection">Flag used for tracking whether user wants to use Golden Section algorithm or not.</param>
/// <returns>Minimum of function.</returns>
public static Matrica FindMinimum(Function function, double e, Matrica startingPoint, bool usingGoldenSection)
{
Matrica x = new Matrica();
x.Equals(startingPoint);
function.SetParametersSize(x.NoOfRows);
Matrica gradient = new Matrica();
Matrica hessianMatrix = new Matrica();
int brojac = 0;
Matrica xs = new Matrica();
if (usingGoldenSection == false)
{
do
{
xs.Equals(x);
gradient = function.CalculateGradientValue(x.VectorToArray());
function.IncreaseCounterGradientValue(algorithmName);
hessianMatrix = function.CalculateHessianMatrix(x.VectorToArray());
function.IncreaseCounterHessian(algorithmName);
Matrica LU = hessianMatrix.LUPDecomposition(e, gradient);
Matrica y = Matrica.ForwardSubstitution(LU, gradient);
Matrica deltaX = Matrica.BackwardSubstitution(LU, gradient, e);
x.AddValue(deltaX);
brojac++;
function.IncreaseCounterValue(algorithmName);
function.IncreaseCounterValue(algorithmName);
} while (brojac < 100);
}
else
{
do
{
xs.Equals(x);
gradient = function.CalculateGradientValue(x.VectorToArray());
function.IncreaseCounterGradientValue(algorithmName);
hessianMatrix = function.CalculateHessianMatrix(x.VectorToArray());
function.IncreaseCounterHessian(algorithmName);
Matrica LU = hessianMatrix.LUPDecomposition(e, gradient);
Matrica y = Matrica.ForwardSubstitution(LU, gradient);
Matrica deltaX = Matrica.BackwardSubstitution(LU, gradient, e);
x.AddValue(deltaX);
for (int i = 0; i < x.NoOfRows; i++)
{
double value = x.LoadedMatrix[i][0];
double vectorValue = deltaX.LoadedMatrix[i][0];
Expression expression = lambda => value + lambda * vectorValue;
function.SetParameters(i, expression);
}
UnimodalInterval interval = UnimodalInterval.FindUnimodalInterval(function, 0, 1, algorithmName);
UnimodalInterval lambdaInterval = GoldenSection.FindMinimum(function, interval.Minimum, interval.Maximum, e, algorithmName);
double lambdaMin = (lambdaInterval.Minimum + lambdaInterval.Maximum) / 2;
deltaX.MultiplyByScalar(lambdaMin);
x.AddValue(deltaX);
function.IncreaseCounterValue(algorithmName);
function.IncreaseCounterValue(algorithmName);
} while (function.GetGradientNorm() >= e);
}
function.DeleteParameters();
return(x);
}