function [D_alpha] = estimate_Dalpha(X,Y,co)
%Estimates D_alpha = \int p^{\alpha}(x)q^{1-\alpha}(x)dx, the Rényi and the Tsallis divergences are simple functions of this quantity.
%
%INPUT:
% X: X(:,t) is the t^th sample from the first distribution.
% Y: Y(:,t) is the t^th sample from the second distribution.
% co: cost object (structure).
%
%Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")
%
%This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox.
%
%ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by
%the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
%
%This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
%MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
%
%You should have received a copy of the GNU General Public License along with ITE. If not, see <http://www.gnu.org/licenses/>.
[d,num_of_samplesY] = size(Y);
[d,num_of_samplesX] = size(X);
squared_distancesXX = kNN_squared_distances(X,X,co,1);
squared_distancesYX = kNN_squared_distances(Y,X,co,0);
dist_k_XX = sqrt(squared_distancesXX(end,:));
dist_k_YX = sqrt(squared_distancesYX(end,:));
B = gamma(co.k)^2 / (gamma(co.k-co.alpha+1)*gamma(co.k+co.alpha-1));
D_alpha = mean( ((num_of_samplesX-1)/num_of_samplesY * (dist_k_XX./dist_k_YX).^d).^(1-co.alpha)) * B;