%% Example:  The SVD

clear
close all;  %This closes all open figures

load mandrill;  %This loads an "image" in the matrix X, colors are in "map"

fprintf('The original matrix as an image\n');
figure(1)
image(X)
colormap(map)

%% Now perform the SVD
[U,S,V]=svd(X);

%% Look at partial reconstructions of the matrix using the following number of basis vectors

NumVecs=[3,6,10,50,150,480];
for k=1:6
    j=NumVecs(k);
    H=round(U(:,1:j)*S(1:j,1:j)*V(:,1:j)');
    figure(2)
    subplot(2,3,k)
    image(H)
    colormap(map)
end