Newton to see when the Gradient = 0

Hey i have a Problem i defined the following function:

function Newton(f,df,Hesf,x)
% Newtonverfahren
sigma=1e-4;
beta=0.5;
rho=1e-8;
p=2.1;
eps=1e-6;
kmax=200;
k=0;
fx=feval(f,x);
dfx=feval(df,x);
while norm(dfx) > eps && k<=kmax
    Hf=feval(Hesf,x);
    if condest(Hf) > 1e+15
        d=-dfx;
    else
        d=(-Hf\dfx')';
        if dfx*d' > -rho*norm(d)^p
            d=-dfx;
        end
    end
    xd=x+d;
    fxd=feval(f,xd);
    j=0;
    dfxd=dfx*d';
    while fxd > fx + sigma * beta^j * dfxd
        j=j+1;
        xd=x+beta^j*d;
        fxd=feval(f,xd);
    end
    x=xd;
    fx=fxd;
    dfx=feval(df,x);
    k=k+1;
end
disp(x)
%disp(x(1));
%disp(x(2));
end

this is how i defined my functions:

function fx = Rosenbrock(x)
fx=100*(x(2)-x(1)^2)^2+(1-x(1))^2;
end


function dfx=Gradient(x)
dfx=[-400 * x(1) *(x(2)-x(1)^2)+2*(x(1)-1), 200*(x(2)-x(1)^2)];
end


function dfx=Hessematrix(x)
dfx=[-400 *(x(2)-x(1)^2)+800*x(1)^2+2, -400*x(1); -400*x(1), 200];
end

When im now calling the Newton Function with:

Newton('Rosenbrock', 'Gradient', 'Hessematrix', [1.2;1.2]) 

I get a 2x2 Matrix. But i would expect an output of 2x1 since the output should be the value for the gradient.

I thought maybe something is wrong with my input. Maybe someone can help me

Answer 1

[Jan]

In the line:

xd=x+d;

x is a [2x1] vector and d a [1x2] vector. The implicite expanding replies a [2 x 2] matrix.

Maybe this fixes the problem:

function dfx=Gradient(x)
dfx=[-400 * x(1) * (x(2)-x(1)^2)+2*(x(1)-1); 200*(x(2)-x(1)^2)];
%                                          ^ instead of a ","
end