%obtain principal component vectors and related quantities
function P=princomp(X,q)
[K,n]=size(X);
X=double(X);
[P.Cx,P.mx]=covmatrix(X);
P.mx=P.mx';
[V,D]=eig(P.Cx);
d=diag(D);
[d,idx]=sort(d);
d=flipud(d);
idx=flipud(idx);
D=diag(d);
V=V(:,idx);
P.A=V(:, 1:q)';
Mx=repmat(P.mx,K,1);
P.Y=P.A*(X-Mx)';
P.X=(P.A'*P.Y)'+Mx;
P.Y=P.Y';
P.mx=P.mx';
d=diag(D);
P.ems=sum(d(q+1:end));
P.Cy=P.A*P.Cx*P.A';