% Labuppgift 2 a och b, sök nollställen

x=0:.05:1.5;
y=-1.5:.05:.5;
[X,Y] = meshgrid(x,y);
F1=X.*exp(X.*Y+0.8)+exp(Y.^2)-3;
F2=X.^2-Y.^2-0.5*exp(X.*Y);

figure(1)
contour(X,Y,F1,[0,0],'r')
hold on
contour(X,Y,F2,[0,0],'g')

G=ginput(2);
format long

for j=1:2
    disp(['Nollställe ', num2str(j)])
    A=G(j,:)';
    for i=1:10
     F=[A(1)*exp(A(1)*A(2)+0.8)+exp(A(2)^2)-3; A(1)^2-A(2)^2-0.5*exp(A(1)*A(2))];   %funktionsmatris
        J=[exp(A(1)*A(2)+.8)+A(1)*exp(A(1)*A(2)+.8)*A(2) A(1)^2*exp(A(1)*A(2)+.8)+2*A(2)*exp(A(2)^2)
         2*A(1)-.5*A(2)*exp(A(1)*A(2)) 2*A(2)-.5*A(1)*exp(A(1)*A(2))];
     A=A-J\F;
     disp([A' norm(F)])
    end
end

figure(2)
colormap jet
surfc(X,Y,F1)
hold on
contour(X,Y,F1,[0,0],'r')
surfc(X,Y,F2)
contour(X,Y,F2,[0,0],'g')
axis([0.5 1.5 -1.5 .5 -10 10])