public static void Optim2D(Graphique G)
{
G.ClearWhite();
DrawFnt2D(Fnt);
G.DrawAxis();
double x = Utils.RND();
double y = Utils.RND();
G.Cross(x, y, Color.White);
//////////////////////////////////////////////////////
double k = 0.1;
double x_prev = 0;
double y_prev = 0;
while ((x_prev == 0 && y_prev == 0) || (Math.Abs(x_prev) - Math.Abs(x) > zero || Math.Abs(y_prev) - Math.Abs(y) > zero))
{
x_prev = x;
y_prev = y;
x = x_prev - (k * Fnt_dx(x_prev, y_prev));
y = y_prev - (k * Fnt_dy(x_prev, y_prev));
G.Cross(x, y, Color.White);
}
//////////////////////////////////////////////////////
}
public static void Optim2Dmax(Graphique G)
{
G.ClearWhite();
DrawFnt2D(Fntmax);
G.DrawAxis();
var r = new Random();
double gamma = .01; // step size multiplier
double x = r.NextDouble() - 0.5;
double y = r.NextDouble() - 0.5;
double z = Fntmax(x, y);
///////////////////////////////////////////////////////////////////
for (int i = 0; i < 1000; i++)
{
if (Fntmax(x, y) == Fntv1(x, y))
{
x += -gamma *dFntv1x(x, y);
y += -gamma *dFntv1y(x, y);
}
else
{
x += -gamma *dFntv2x(x, y);
y += -gamma *dFntv2y(x, y);
}
G.Cross(x, y, Color.White);
}
///////////////////////////////////////////////////////////////////
}
public static void GradLitteral(Graphique G)
{
G.ClearWhite();
DrawFnt(g, Color.Red);
double x = 1;
double y = g(x);
G.Cross(x, y, Color.Blue);
///////////////////////////////////////////////////////
double k = 0.01;
double y_prev = y;
while (y <= y_prev) // if y is larger than the previous y, then the minima has already been found
{
y_prev = y;
x = x - (k * g_d(x));
y = g(x);
G.Cross(x, y, Color.Blue);
}
///////////////////////////////////////////////////////
}
public static void GradEstimation(Graphique G)
{
G.ClearWhite();
DrawFnt(f, Color.Red);
double x = 0.7;
double y = f(x);
G.Cross(x, y, Color.Blue);
////////////////////////////////////////////////////////////
double eps = 0.05;
double k = 0.01; // Rate of steps
while (Math.Abs(x) > zero) // Keep trying to find minima that is located in x=0
{
x = x - (k * f_d(x, eps)); // x progression towards minima
y = f(x);
G.Cross(x, y, Color.Blue);
}
///////////////////////////////////////////////////////
}
public static void GradLitteral(Graphique G)
{
G.ClearWhite();
DrawFnt(g, Color.Red);
double x = 1;
double gamma = 0.01; // step size multiplier
double precision = 0.001; // range limit
double previous_step_size = x;
while (previous_step_size > precision)
{
double prev_x = x;
x += -gamma *dg(prev_x);
previous_step_size = Math.Abs(x - prev_x);
G.Cross(x, g(x), Color.Blue);
}
}
public static void Optim2D(Graphique G)
{
G.ClearWhite();
DrawFnt2D(Fnt);
G.DrawAxis();
var r = new Random();
double gamma = .1; // step size multiplier
//double precision = .1; // range limit
double x = r.NextDouble() - 0.5;
double y = r.NextDouble() - 0.5;
double z = Fnt(x, y);
for (int i = 0; i < 30; i++)
{
x += -gamma *dFntx(x, y);
y += -gamma *dFnty(x, y);
z = Fnt(x, y);
G.Cross(x, y, Color.White);
}
}