%% Clown demo


%% 
% First, we load and visualize the demo matrix
load clown
size(X)

figure(1)
image(X)
colormap(map)

%% 
% We compute the SVD of the matrix

[U,S,V] = svd(X);

%%
% Now let's have a look at the singular values 

s = diag(S);

figure(2)
plot(s,'.')
ylabel('Singular values')

%%
% Apparently just the first few singular values are significantly different
% from zero. Let's now assemble an approximating matrix by using just the
% terms corresponding to the few largest singular values.

k = 10
Xred = U(:,1:k)*S(1:k,1:k)*V(:,1:k)';

figure(3)
image(Xred)
colormap(map)