private static Point GeneralizedNewtonMethod(FunctionWrapper function, Point x0, double h0, double epsilon)
{
var g = function.Gradient(x0);
if (!(g.Normalize() > epsilon))
{
return(x0);
}
double h;
var hessian = function.Hess(x0);
var hessianInverted = hessian.InvertByJordanGauss();
do
{
CountThisLoop();
var x = x0;
x0 = new Point(new double[x0.Length]);
var w = new Vector(new double[x0.Length]);
for (var i = 0; i < w.Length; i++)
{
for (var j = 0; j < w.Length; j++)
{
w[i] += hessianInverted[i, j] * g[j];
}
}
h = function.FindHForFastestDescent(x, w, h0, epsilon);
x0 = x - h * w;
g = function.Gradient(x0);
} while (g.Normalize() >= epsilon && Math.Abs(h) > Math.Sqrt(epsilon));
return(x0);
}
private static Point NewtonMethod(FunctionWrapper function, Point x0, double epsilon)
{
var g = function.Gradient(x0);
if (g.Normalize() > epsilon)
{
do
{
CountThisLoop();
var x = x0;
var hessian = function.Hess(x0);
var hessianInverted = hessian.InvertByJordanGauss();
x0 = new Point(new double[x0.Length]);
var w = new Vector(new double[x0.Length]);
for (var i = 0; i < w.Length; i++)
{
for (var j = 0; j < w.Length; j++)
{
w[i] += hessianInverted[i, j] * g[j];
}
}
x0 = x - w;
g = function.Gradient(x0);
} while (g.Normalize() >= epsilon);
}
return(x0);
}
private static Point FastestDescent(FunctionWrapper function, Point x0, double h0, double epsilon)
{
var g = function.Gradient(x0);
if (g.Normalize() > epsilon)
{
Point x;
do
{
CountThisLoop();
x = x0;
var h = function.FindHForFastestDescent(x, g, h0, epsilon);
x0 = x - h * g;
g = function.Gradient(x0);
} while (!((x - x0).Normalize() < epsilon || g.Normalize() < epsilon));
}
return(x0);
}
