% Two arguments: The filename to save image as. And the quality 1-64. Where
% 64 is best, but also unnecssary since no compression will occur. 

% Author: Magnus Lundstedt, 810109-8617

function [uncomp,raw,avg,base]=compress (filename,quality)
    load lena;
    M = extract(lena);
    
    %--- Find average image element
    avgImg = zeros(64,1);
    for i = 1:1024
        avgImg = avgImg + 1/1024 * M(:,[i]);
    end
    
    %--- Translate all elements by average element
    translated = zeros(64,1024);
    for i = 1:1024
        translated(:,[i]) = M(:,[i])-avgImg;
    end
    
    %--- Find covariance-matrix on transponate of translated matrix
    C = cov(translated');
    
    %--- Calculate eigenvalues and eigenvectors of the covariance matrix
    [eigvect,eigval] = eig(C);
    
    %--- Select 10 biggest eigenvalues and their corresponding eigenvectors
    %these eigenvectors will be our new base
    intrVal = eigval([65-quality:64],[1]);
    intrVect = eigvect(:,[65-quality:64]);
    %intrVect = eigvect(:,[1:quality]);
    
    %--- Change base-loop
    for i = 1:1024
        %--- Compressed data in our new base
        raw(:,[i]) = intrVect' * translated(:,[i]);
        
        %--- At the same time reconstruct the image so that we dont have to
        % do a separate decoder :) 
        newSubImages(:,[i]) = intrVect*raw(:,[i])+avgImg;
    end

    %Find a suitable factor to maximize useage of the 256 possible states    
    %when we convert the double into an signed int later.. (Here one could
    %prioritize some colors where humans notice difference more eaisily)
    factor = 128/max(max(abs(raw)));
    
    uncomp = newSubImages;

    avg = avgImg;
    raw = int8(round(raw*factor));
    base = int8(round(intrVect*factor));
    
    save(filename,'raw','avg','base','factor');
    
end