genfig_8.m

Dimensionality Reduction for Distributed Estimation in the Infinite Dimensional Regime

% GENFIG_8 Reproduces figure 8.
%
% USAGE     
%
%       GENFIG_8(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_8(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 simulation parameters
randn('state',0); % for reproducible results
m = 30;
rho = 0.6;

% We define the covariance matrices of the involved vectors
R_S     = toeplitz(rho.^[0:2*m-1]);
R_SX1   = R_S(:,1:2:2*m);
R_SX2   = R_S(:,2:2:2*m);
R_X1    = R_S(1:2:2*m,1:2:2*m);
R_X2    = R_S(2:2:2*m,2:2:2*m);
R_X1X2  = R_S(1:2:2*m,2:2:2*m);
R_SX    = [R_SX1 R_SX2];
R_X     = [R_X1 R_X1X2; R_X1X2' R_X2];

% We compute the infinite block-length distortion (IBLD) for different
% values of alpha1 and alpha2
alpha1_val = [0:m]/m;
alpha2_val = [0:m]/m;
dist_val = zeros(length(alpha1_val),length(alpha2_val));
for i=1:length(alpha1_val)
    alpha1 = alpha1_val(i);
    for j=1:length(alpha1_val)
        alpha2 = alpha2_val(j);
        dist_val(i,j) = algo1(R_S, R_X, R_SX, [m m], [floor(m*alpha1), floor(m*alpha2)], 'rand');
    end
    
end

% We normalize the distortion
dist_val = dist_val/trace(R_S);

% We plot the figure
figure;
hold on
box on

surf(alpha2_val, alpha1_val, dist_val);
if (~color)
    map = gray(256);
    map = map(100:256,:);
    colormap(map);
else
    colormap('jet');
end
view(56,16);
a = axis;
axis([0, 1, 0, 1, 0, a(6)]); 
box off
grid on
if save
    xlabel('xLabel');
    ylabel('yLabel');
    zlabel('zLabel');
    title('title');
    saveas(gcf, filename,'psc2');
end
if display
    xlabel('\alpha_1');
    ylabel('\alpha_2');
    zlabel('MSE');
else
    close gcf
end