function gradient2d0()
%%%%%%%%%%%%%%
close all
x(1)=1.0
x(2)=-1.2
t=0.00001
kmax=1000
for i=1:kmax;
    if (norm(g(x))<1e-5)
        break
    end
    ii=i
    d=-g(x)
    %t=RL(x,d)
    %t=RL_Armijo(x,d)
    t=RL_Goldestein(x,d)
    %t=RL_Wolf(x,d)
    x=x+t*d
    %thep=thetap(t,x,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;    
    a=0.0;
    b=1e-3;
    beta=10;
    %%%%Chercher le premier pas
    for i=1:100;        
        if (thetap(b,x,d)>=0)
            break            
        else
            b=beta*b;
        end
    end
 %%%%%%%%
    for i=1:kmax;
        tk=(a+b)/2;
        if (abs(thetap(tk,x,d))<1e-5) %2.0)
            break
        elseif (thetap(tk,x,d)<0)
            a=tk;            
        else
            b=tk;
        end
    end
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%RL Amijo%%%%%%%%%%%%%%%%%%
function t=RL_Armijo(x,d)
m=.3d0;
t1=0.095;
for i=1:150
    t=(t1^i);
    if (theta(t,x,d) <= (m*t*thetap(0,x,d))+theta(0,x,d))
        break
    end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%RL Goldestein%%%%%%%%
% function t=RL_Goldestein(x,d)
% m1=.3d0;
% m2=.7d0;
% alfa=10d0;
% lambda=.5d0;
% t=0.0001;
% td=0;
% tg=0;
% hhh= (m1*t*thetap(0,x,d))+theta(0,x,d)
% for i=1,150
%     if ((theta(t,x,d) <= (m1*t*thetap(0,x,d))+theta(0,x,d)) && (theta(t,x,d) >= (m2*t*thetap(0,x,d))+theta(0,x,d)))
%         break
%         if(theta(t,x,d) > (m1*t*thetap(0,x,d))+theta(0,x,d))
%             td=t
%         end
%         if (theta(t,x,d) < (m2*t*thetap(0,x,d))+theta(0,x,d)) then
%             tg=t
%         end
%         if (td==0) then
%             t=alfa*tg
%         else
%             t=td*lambda+((1-lambda)*tg)
%         end
%     end
% end
% %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%RL Wolf%%%%%%%%%
function t=RL_Goldestein(x,d)
m1=.3;
m2=.7;
alfa=10;
lambda=.5;
t=0.001;
td=0;
tg=0;
for i=1:50
    if ((theta(t,x,d) <= (m1*t*thetap(0,x,d))+theta(0,x,d)) && (theta(t,x,d) >= (m2*t*thetap(0,x,d))+theta(0,x,d)))
        break
        if(theta(t,x,d) > (m1*t*thetap(0,x,d))+theta(0,x,d)) then
            td=t;
        end
        if ((theta(t,x,d) <= (m1*t*thetap(0,x,d))+theta(0,x,d)) &&(theta(t,x,d) < (m2*t*thetap(0,x,d))+theta(0,x,d)))
            tg=t;
        end
        if (td==0) then
            t=alfa*tg;
        else
            t=td*lambda+((1-lambda)*tg);
        end
    end
end
%%%%%%
%%%%%%%%%RL Wolf%%%%%%%%%
function t=RL_Wolf(x,d)
m1=.3;
m2=.7;
alfa=10;
lambda=.5;
t=0.002;
td=0;
tg=0;
for i=1:150
    if ((theta(t,x,d) <= (m1*t*thetap(0,x,d))+theta(0,x,d)) && (thetap(t,x,d) >= (m2*thetap(0,x,d))))
        break
        if(theta(t,x,d) > (m1*t*thetap(0,x,d))+theta(0,x,d)) then
            td=t;
        end
        if ((theta(t,x,d) <= (m1*t*thetap(0,x,d))+theta(0,x,d)) && (thetap(t,x,d)<(m2*thetap(0,x,d))))
            tg=t;
        end
        if (td==0) then
            t=alfa*tg;
        else
            t=td*lambda+((1-lambda)*tg);
        end
    end
end