1. Zoltán Szabó
  2. ITE


ITE / code / estimators / base_estimators / DKL_PSD_SzegoT_estimation.m

function [D] = DKL_PSD_SzegoT_estimation(Y1,Y2,co)
%function [D] = DKL_PSD_SzegoT_estimation(Y1,Y2,co)
%Estimates the Kullback-Leibler divergence using power spectral density representation and Szego's theorem. 
%We use the naming convention 'D<name>_estimation' to ease embedding new divergence estimation methods.
%  Y1: Y1(:,t) is the t^th sample from the first distribution.
%  Y2: Y2(:,t) is the t^th sample from the second distribution. Note: the number of samples in Y1 [=size(Y1,2)] and Y2 [=size(Y2,2)] can be different.
%  co: divergence estimator object.
%   David Ramirez, Javier Via, Ignacio Santamaria, and Pedro Crespo. Entropy and Kullback-Leibler divergence estimation based on Szego's theorem. In European Signal Processing Conference (EUSIPCO), pages 2470-2474, 2009.
%   Robert M. Gray. Toeplitz and circulant matrices: A review. Foundations and Trends in Communications and Information Theory, 2:155-239, 2006. (Szego's theorem)
%   Ulf Grenander and Gabor Szego. Toeplitz forms and their applications. University of California Press, 1958. (Szego's theorem)

%Copyright (C) 2013 Zoltan Szabo ("http://www.gatsby.ucl.ac.uk/~szabo/", "zoltan (dot) szabo (at) gatsby (dot) ucl (dot) ac (dot) uk")
%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. The information theoretical quantity of interest can be (and is!) estimated exactly [co.mult=1]; the computational complexity of the estimation is essentially the same as that of the 'up to multiplicative constant' case [co.mult=0].

    dY1 = size(Y1,1);
    dY2 = size(Y2,1);

    if dY1~=dY2
        error('The dimension of the samples in Y1 and Y2 must be equal.');
    if dY1~=1
        error('The samples must be one-dimensional for this estimator.');
D = KL_est_szego_ar(Y1,Y2,co.p_max,co.K);