function Blatt2()

h=1;
tol=0.01;


z0=[-10,10];
disp(['Funktion aus (a), Startpunkt z0']);
[x,y]=Minimum(z0, h, tol, @f1)

z0=[0,5];
disp(['Funktion aus (b), Startpunkt z01']);
[x,y]=Minimum(z0, h, tol, @f2)

z0=[0.5,5];
disp(['Funktion aus (b), Startpunkt z02']);
[x,y]=Minimum(z0, h, tol ,@f2)




end

function u=f1(z)

u=1/6*z(1)^2+z(2)^2+1/4*z(1)+1;


end

function u=f2(z)

u=1/4*(z(1)^4*z(2)^2 + z(1)^4) - z(1)^3*z(2)^2 - z(1)^3 + z(1)*z(2)^2 + z(1) + 5*z(2)^2 + 5;

end




function [fznew, z_current] = Minimum(z0, h0, tol, f)
% exercise 2.6

i = 1;
z_current = z0;
dir = [0,1;... %N
      -1,0;... %W
       1,0;... %O
       0,-1];  %S
% compute first value at current point and save some output - ensure column vectors for convenience
fz(i,1) = f(z_current);
h_it(i,1) = h0;
z(i,:) = z_current;
h=h0;


while h > tol % as long as tolerance isn't reached

    % compute function value in each direction
    fzN = f(z_current + h*dir(1,:));
    fzW = f(z_current + h*dir(2,:));
    fzO = f(z_current + h*dir(3,:));
    fzS = f(z_current + h*dir(4,:));

    % compute min and argmin
    [fznew, ind] = min([fzN, fzW, fzO, fzS, fz(i,1)]);

    % If minimal function value doesn't differ from the current halve the step size
    if abs(fz(i,1) - fznew) < 1e-12
        h = h/2;
    else % else move in the respective direction
        z_current = z_current + h*dir(ind,:);
        h=h0;
    end
    i = i+1;
    % save function value at new point and some output
    fz(i,1) = fznew;
    h_it(i,1) = h;
    z(i,:) = z_current;
end
a=[h_it,z,fz]


end