A=[3 2;2 6];
b=[5 6]';

f=@(x,y) (3*x.^2+4*x.*y+6*y.^2)/2-5*x-6*y+12;

[X Y]=meshgrid(-3:0.01:3,-3:0.01:3);

mesh(X,Y,f(X,Y)); hold on
set(gca,'FontSize',30);
xlabel('x','FontSize',30); ylabel('y','FontSize',30);
title('Minimum of quadratic function by CG')

x0=ones(2,1);
tol=1e-7;
itmax=200;

[x,k]=cg(A,b,tol)

Exact_sol=A\b
plot3(x(1),x(2),f(x(1),x(2)),'r*','MarkerSize',20); hold off
view(-30,50);
f(x(1),x(2))

function [x,k]= cg(A,b,tol)

x = b;
r = b - A*x;
if norm(r) < tol
    return
end
d = r;
z = A*d;
s = d'*z;
t = (r'*d)/s;
x = x + t*d;

for k = 1:numel(b)
    r = r - t*z;
    if( norm(r) < tol )
        return;
    end
    B = -(r'*z)/s;
    d = r + B*d;
    z = A*d;
    s = d'*z;
    t = (r'*d)/s;
    x = x + t*d;
end
end