clear;
rankK = 2;

%Create data 
X = [1 0 0 1 0 0 0 0 0;
     1 0 1 0 0 0 0 0 0;
     1 1 0 0 0 0 0 0 0;
	 0 1 1 0 1 0 0 0 0;
	 0 1 1 2 0 0 0 0 0;
	 0 1 0 0 1 0 0 0 0;
	 0 1 0 0 1 0 0 0 0;
	 0 0 1 1 0 0 0 0 0;
	 0 1 0 0 0 0 0 0 1;
	 0 0 0 0 0 1 1 1 0;
	 0 0 0 0 0 0 1 1 1;
	 0 0 0 0 0 0 0 1 1];

[U S V] = svd(X);
size(U);
size(S);
size(V);

Uk = U(:,1:rankK);
Sk = S(1:rankK,1:rankK);
Vk = V(:,1:rankK);

%Create a query that is the same as the first document
q=[1 1 1 0 0 0 0 0 0 0 0 0]';

qconcept = inv(Sk)*transpose(Uk)*q;

dot = qconcept' * Vk';

angle = dot ./ norm(qconcept);

for i = 1:9
	angle(1,i)=angle(1,i)./norm(Vk(i,:));
end;