load clowndata.mat;  % This file is downloaded from class website

% At this point, you should have a matrix X and matrix "map".
whos

% This is just to look at some of the matrix values in X
X(1:10,1:10)  

% Show the image of the clown (change the "colormap")
image(X)
colormap(map)

% You can type:  help colormap   
%  to see the different names of the built-in color schemes available.
%  For example,
colormap('jet')

% Or back to the one for the clown:
colormap(map)

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

% Inspect the singular values
plot(log(diag(S)))


% Create a rank-50 approximation (and the error)
N=50; PartialRecon=U(:,1:N)*S(1:N,1:N)*V(:,1:N)';
image(PartialRecon)

M=N+1; Leftover=U(:,M:end)*S(M:end,M:end)*V(:,M:end)';
imagesc(Leftover)

%If you add the images, you get the clown back again
image(round(PartialRecon+Leftover))