[U,S,V] = svd(D);
A = S*V';
% D=U*A
range(D-U*A)

K = 1:5;
[Ur,R]=varimax_kaplan(U(:,K));

% Ur = U*R;
range(Ur-U(:,K)*R)

% U(:,K)*R*inv(R)*A(K,:)
Ar = inv(R)*A(K,:);

% The Ur remain orthogonal, but the Ar do not

m = 1;

subplot(221)
pcolorjw(lon,lat,reshape(U(:,1),[nlats nlons]));colorbar;
subplot(222)
pcolorjw(lon,lat,reshape(Ur(:,1),[nlats nlons]));colorbar;

subplot(223)
plot(year,A(m,:))

subplot(224)
plot(year,Ar(m,:))
ff


diag(A*A') = diag(S*S')