function gradient2d()
%%%%%%%%%%%%%%
close all
x(1)=-1.2
x(2)=1.0
t=0.0001
kmax=1000
for i=1:kmax
    i
    if (norm(g(x))<1e-5)
        break
    end
    d=-g(x)
    t=RL(x,d)
    x=x+t*d
    abs_grad_f=norm(g(x))
    f_val=f(x)
    y(i,:)=x;
end
%%%%%%%%%%%%%%%%%
%%% Partie Plot
%%%%%%%%%%%%%%%%%
x1 = -1.5:0.1:1.5;
x2= -1.5:0.1:1.5;
[x1,x2] = meshgrid(x1,x2);
Z = 100*(x2-x1.^2).^2 + (1-x2).^2;
contourf(x1,x2,Z,30);
hold on
plot(y(:,1),y(:,2),'w-o')
colormap jet
fontsz=16;
xlabel('$x$','Interpreter','latex','FontSize',fontsz)
ylabel('$y$','Interpreter','latex','FontSize',fontsz)
title({'Acheminement des iter\''ees de la m\''ethode du gradient'},'Interpreter','latex')
%%%%%%%%%%%%%%%%%
function d=f(x);
% d = (x(1)-1).^2+(x(2)-1).^2;
 d=100*(x(2)-x(1).^2).^2 + (1-x(1)).^2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 function d=g(x);
 %d(1) = 2*(x(1)-1);%d(2) = 2*(x(2)-1);
 d(1)=-(400*(x(2)-x(1).^2)).*x(1)-2+2*x(1);
 d(2)=200*x(2)-200*x(1).^2;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 function y=theta(t,x,d);
 y=f(x+t*d);
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 function y=thetap(t,x,d);
 y=g(x+t*d)*d';
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%Recherche lineaire
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 function tk=RL(x,d);
    kmax=150;    
    tg=0.0;
    td=1e-3;
    beta=10;
    %%%%Chercher le premier pas td
    for i=1:100;        
        if (thetap(td,x,d)>=0)
            break            
        else
            td=beta*td;
        end
    end
 %%%%%%%%
    for i=1:kmax;
        tk=(tg+td)/2;
        if (abs(thetap(tk,x,d))<1e-5)
            break
        elseif (thetap(tk,x,d)<0)
            tg=tk;            
        else
            td=tk;
        end
    end
%%%%%%%%%%%%%%%%%%%%%%%%%%%