 function [H] = HShannon_DKL_N_estimation(Y,co)
%Estimates the Shannon entropy (H) of Y (Y(:,t) is the t^th sample) using the relation H(Y) = H(G)  D(Y,G), where G is Gaussian [N(E(Y),cov(Y)] and D is the KullbackLeibler divergence.
%This is a "meta" method, i.e., the KullbackLeibler divergence estimator can be arbitrary.
%
%We make use of the naming convention 'H<name>_estimation', to ease embedding new entropy estimation methods.
%
%REFERENCE: Quing Wang, Sanjeev R. Kulkarni, and Sergio Verdu. Universal estimation of information measures for analog sources. Foundations And Trends In Communications And Information Theory, 5:265353, 2009.
%
%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/>.
%co.mult:OK.
[d,num_of_samples] = size(Y); %dimension, number of samples
%estimate the mean and covariance of Y:
m = mean(Y,2);
C = cov(Y.');
%entropy of N(m,C):
H_normal = 1/2 * log( (2*pi*exp(1))^d * det(C) );
%generate samples from N(m,C):
R = chol(C); %R'*R=C
Y_normal = R.' * randn(d,num_of_samples) + m;
H = H_normal  D_estimation(Y,Y_normal,co.member_co);
