function g = svd_compress(imname,r)

f_in = double(imread(imname)); %load image
f = f_in(:,:,1);

[mr,mc] = size(f);
m = mr*mc;
g = zeros(mr,mc);

%compute SVD
[U,S,V] = svd(f);
%load U; load S; load V; %shortcut, can load from memory if using same image with different r
sv = diag(S); %singular values
svlen = length(find(sv>0));
s = round(r*svlen); %number of singular values to keep

%compress
Uc = U(:,1:s);
svc = sv(1:s);
Vc = V(:,1:s);
numval = s + mr*s + mc*s; %total number of values that we must store

%approximate image using only the stored elements
g = Uc*(svc(:,ones(1,mc)).*Vc');

%full grayscale map for L intensity values
L = 256;
cmap = zeros(L,3);
cmap(:,1) = [0:(1/(L-1)):1]';
cmap(:,2) = [0:(1/(L-1)):1]';
cmap(:,3) = [0:(1/(L-1)):1]';

%compression factor
cf = numval/m; %ratio of number of stored elements to number of pixels in original image

%plot stuff
figure(18)
subplot(1,2,1); colormap(cmap); image(f); axis off; title('original image');
subplot(1,2,2); colormap(cmap); image(g); axis off; 
title([num2str(100*s/svlen) '% singular values, ' num2str(100*cf) '% storage']);