%  MATLAB code to use CGM to solve 2x2 system
%        [a b][x1] = [b1]
%        [c d][x2] = [b2]

x=[1, 1];

xd=linspace(0,100,20);
yd=linspace(-100,0,20);
[X,Y]=meshgrid(xd,yd);
a=5; b=4.99; c=b; d=5; b1=1; b2=-1;
Z = 0.5*(a*X.^2 + 2*b*X.*Y + d*Y.*Y) - b1*X - b2*Y;

tol=0.001;
xpoints=x(1);
ypoints=x(2);
r=[b1-a*x(1)-b*x(2),b2-c*x(1)-d*x(2)];
dd=r;
diff=[1,1];
counter=1;
while norm(diff)>tol
     counter=counter+1;
     if counter<3
		 beta=0;
	 else
		 beta=dot(r,r)/dot(r0,r0);
	 end;
     dd=r+beta*dd;
	 q=[a*dd(1)+b*dd(2),c*dd(1)+d*dd(2)];
	 alpha=dot(r,r)/dot(dd,q);
	 diff=alpha*dd;
     x=x+diff;
	 r0=r;
	 r=r-alpha*q;

     fprintf('\n  %i  Computed Solution =  %e  %e \n\n',counter,x);

     xpoints=[xpoints, x(1)];
     ypoints=[ypoints, x(2)];
%     pcolor(X,Y,Z)
     shading interp
     hold on
     contour(X,Y,Z,20,'b')
     plot(xpoints,ypoints,'ko-')
     hold off
     pause
end;