% Script: pcgcond_example.m
% adds poisson and wathen matrices to matrices with
% controlled condition numbers and plots iteration progress

n = 600;
b = rand(n,1);
b = b/norm(b);
kappa = [2 10 100 1000];  % these will be condition numbers
for k=1:4
    d = linspace(1,kappa(k),n)';
    A = spdiags(d,0,n,n);
    [x,flag,err,m,normr] = pcg(A,b,1e-14,500);
    semilogy( 0:length(normr)-1, normr );
    hold on;
    iter(k) = m;
end
hold on
n = 25;
A = n^2*gallery('poisson',n);
b = -ones(n^2,1);
[x,flag,err,m,normr] = pcg(A,b,1e-14,500);
semilogy( 0:length(normr)-1, normr, '--');
condest(A) % for a sparse matrix
hold on;
A = gallery('wathen',n,n);
A = length(A)*A;
b = -ones(length(A),1);
[x,flag,err,m,normr] = pcg(A,b,1e-14,500);
semilogy( 0:length(normr)-1, normr, '-.' );
condest(A)  % for a sparse matrix