function [ED2 A]=transD2tf(tf,doclen,T)
%TRANSD2TF   Expected (Translated) (L2Distance)^2
%
%   Arguments:
%      tf   document term frequency (i.e., normalized)
%      N    document lengths
%      T    translation matrix
%
%   Returns:
%      ED2  E_{p(y|x)} ( ||x_i-x_j||_2^2 )
%      A    E_{p(y|x)} ( ||x_i||_2^2 )
%
%   Authors:
%       Joshua V. Dillon; Feb. 26, 2007; jvdillon AAT purdue DDOT edu

if nargin~=3
	error('insufficient arguments');
end

[Mv Nd] = size(tf);
N = doclen'.^-1;

TT  = T*T';
B   = tf' * TT * tf;
A   = diag(B) - N.*(tf'*diag(TT)) + N;
ED2 = repmat(A,1,Nd) + repmat(A',Nd,1) - 2 * B;

%tc=ceil(10*rand(5,3));tf=normalizeRows(tc')';N=sum(tc);T=normalizeRows(rand(5,5));transD2(tc,T)-transD2tf(tf,sum(tc),T)