% Script: gmres_example.m
% investigate gmres parameter settings

% Poisson matrix example
 n = 50;
 A = n^2*gallery('poisson',n);
 b = -ones(n^2,1);

% Wathen matrix
% nx = 28; ny = 28; n = 3*nx*ny+2*(nx+ny)+1;
% A = gallery('wathen',nx,ny);
% b = -ones(n,1);

[x2,f2,rr2,it2,rv2] = gmres(A,b,20);
[x3,f3,rr3,it3,rv3] = gmres(A,b,40);
[x5,f5,rr5,it5,rv5] = gmres(A,b,20,[],20);
figure;
semilogy(1:length(rv2),rv2/norm(b),'ok')
hold on
semilogy(1:length(rv3),rv3/norm(b),'-k')
semilogy(1:length(rv5),rv5/norm(b),'--k')
axis('tight')
hold off
title('GMRES residual vs iteration number','FontSize',14)
xlabel('iteration','FontSize',14); 
ylabel('||b-Ax||/||b||','FontSize',14);
set(gca,'YTick',[10^-6 10^-4 10^-2 10^0],'FontSize',14)
legend('10(20)','10(40)','20(20)',1)