%svd chengxu 

A = [5 5 0 5;5 0 3 4; 3 4 0 3; 0 0 5 3; 5 4 4 5; 5 4 5 5];
A = A';

[U S V] = svd(A);

U = U(:,1:4);
S = S(1:4,1:4);
V = V(:,1:4);

reA = U*S*V';

%give one new user

bob = [5 5 0 0 0 5];

uservector = bob*V*S;

for i = 1:1:size(A,1)
    temp = U(i,:);
    similarity = temp*uservector'/(sqrt(temp*temp')*sqrt(uservector*uservector'));
    userlist(i) = similarity;
end

rank = sort(userlist);
l = size(rank,2);
t = zeros(1,size(A,2));
for i=l:-1:l-1
    indx = find(rank(i)==userlist);
    sim = rank(i);
    t = t + A(indx,:)*sim;
end

index = find(bob==0);
rank = t(index);
rank