% test SVD
clear
clc

A = [0 1 1 0 1 1 0;  ...
     1 1 1 1 1 1 1;  ...
     1 1 1 1 1 1 1;  ...
     0 1 1 1 1 1 0;  ...
     0 0 1 1 1 0 0;  ...
     0 0 0 1 0 0 0];
A = 1 - A;
[U, S, V] = svd(A);
V=V';

iter1 = S(1,1)*U(:,1)*V(1,:);
iter2 = S(2,2)*U(:,2)*V(2,:);
iter3 = S(3,3)*U(:,3)*V(3,:);
iter4 = S(4,4)*U(:,4)*V(4,:);
iter5 = S(5,5)*U(:,5)*V(5,:);
iter6 = S(6,6)*U(:,6)*V(6,:);
iter12 = iter1 + iter2;
iter123 = iter1 + iter2 + iter3;
iter1234 = iter1 + iter2 + iter3 + iter4;

subplot(3,6,1), imshow(A), title('Original image')
subplot(3,6,7), imshow(iter1), title('Iteration1')
subplot(3,6,8), imshow(iter2), title('Iteration2')
subplot(3,6,9), imshow(iter3), title('Iteration3')
subplot(3,6,10), imshow(iter4), title('Iteration4')
subplot(3,6,13), imshow(iter1), title('Iteration1')
subplot(3,6,14), imshow(iter12), title('Iteration 1+2')
subplot(3,6,15), imshow(iter123), title('Iteration 1+2+3')
subplot(3,6,16), imshow(iter1234), title('Iteration 1+2+3+4')