% GENFIG_5C Reproduces figure 5c.
%
% USAGE     
%
%       GENFIG_5C(color, display, filename)
%
% INPUTS    
%
%       color     Color (true) or grayscale (false) (optional, default = true)
%       display   Displays (true) or does not display (false) the figure (optional, default = true)
%       filename  Saves the figure in eps format under the name 'filename' (optional, default = not saved)
%
% COPYRIGHT
%
%       This file is part of the Matlab code provided for the following
%       reproducible paper:
%
%       Olivier Roy and Martin Vetterli,
%       "Dimensionality Reduction for Distributed Estimation in the Infinite Dimensional Regime",
%       vol. 54, no. 4, pp. 1655-1669, April 2008.
%
%       This program 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 2 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                       
%       (enclosed in the file GPL).   
% 
%       GNU General Public License,
%       Copyright (C) 2008,
%       Audiovisual Communications Laboratory (LCAV),
%       Ecole Polytechnique F閐閞ale de Lausanne (EPFL),
%       CH-1015 Lausanne.
%
% COMMENTS
%
%       Author: Olivier Roy
%       Latest modifications: April 2, 2008.
function genfig_5c(color, display, filename)

% We set the default values for the input arguments
save = true;
if nargin < 3
    save = false;
end
if nargin < 2
    display = true;
end
if nargin < 1
    color = true;
end

% We set the parameters of the simulation
rho = 0.6;
m_max = 100;

% We compute the approximation error for different values of m
error = zeros(1,m_max);
for m=1:m_max

    % We compute the infinite block-length distortion (IBLD) for different
    % values of alpha
    alpha_val = [0:m]/m;
    IBLD_val = 1 - (2/pi)*atan(((1+rho)/(1-rho))*tan(pi*alpha_val/2));

    % We compute the finite block-length distortion (FBLD) for different values
    % of alpha
    R_X = toeplitz(rho.^[0:m-1]);
    ev = eig(R_X);
    ev = sort(ev, 'descend');    
    FBLD_val = zeros(1,m);
    for k=0:m
        FBLD_val(k+1) = sum(ev(k+1:end))/trace(R_X);
    end

    % We compute the approximation error
    error(m) = sum(abs(FBLD_val - IBLD_val).^2)/m;

end

% We plot the figure
figure;
if (color)
    plot([3:m_max], error(3:end), 'b-');
else
    plot([3:m_max], error(3:end), 'k-');
end
box on
grid on

if save
    xlabel('xLabel');
    ylabel('yLabel');
    title('title');
    saveas(gcf, filename,'psc2');
end
if display
    xlabel('m');
    ylabel('e(m)');
else
    close gcf
end