function out=newton(x)
% solve for n non linear set of equations
% calls f.m and jaco.m
% inputs: x initial values
% outputs: out=answer vector.

% note that you could also input a TOL, max no of steps,...

for i=1:250 % here max no of iteration is 250
    if (det(Jaco(x))==0), error('singular matrix---> NO solution can be found'), end % check if jacobian is singular
    y=-inv(Jaco(x))*f(x); % solves jaco(x)*y=-f(x)
    x=y'+x; % newton iteration (update value)
    val=(sum((y.^2)))^.5; % calculates ||y||
    if (val<0.0001), break, end  % check if it is within tolerance here: 0.0001
end % wow, I can not say more...
out=x'; % output final answer