demo matlab : norm_hadamard ajoute

misc/demo/Hadamard_factorization/norm_hadamard.m

+%% Description norm_hadamard
+%
+%  This demo makes some time comparison between the 2-norm of the Hadamard matrix and
+%  her Faust representation for different dimension
+%  of the Hadamard matrix.
+%
+% For more information on the FAuST Project, please visit the website of
+% the project :  <http://faust.gforge.inria.fr>
+%
+%% License:
+% Copyright (2016):	Luc Le Magoarou, Remi Gribonval
+%			INRIA Rennes, FRANCE
+%			http://www.inria.fr/
+%
+% The FAuST Toolbox is distributed under the terms of the GNU Affero
+% General Public License.
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU Affero General Public License as published
+% by the Free Software Foundation.
+%
+% This program 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 Affero General Public License for more details.
+%
+% You should have received a copy of the GNU Affero General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%% Contacts:
+%   Nicolas Bellot : nicolas.bellot@inria.fr
+%   Leman Adrien   : adrien.leman@inria.fr
+%	Luc Le Magoarou: luc.le-magoarou@inria.fr
+%	Remi Gribonval : remi.gribonval@inria.fr
+%
+%% References:
+% [1]	Le Magoarou L. and Gribonval R., "Flexible multi-layer sparse
+%	approximations of matrices and applications", Journal of Selected
+%	Topics in Signal Processing, 2016.
+%	<https://hal.archives-ouvertes.fr/hal-01167948v1>
+%%
+
+nb_mult=10;
+Ms=6:11;
+ns=2.^Ms;
+nb_dim=length(Ms);
+threshold=10^(-10);
+
+
+h = waitbar(0,'speed up hadamard : Generation of the data ...');
+Hadamard_matrices=cell(1,nb_dim);
+Hadamard_facts=cell(1,nb_dim);
+
+
+
+
+
+for k=1:nb_dim
+    waitbar(k/nb_dim);
+    M=Ms(k);
+    n=ns(k);
+    % generation of the hadamard factorisation
+    [H,facts] = hadamard_mat(M);
+    Hadamard_matrices{k}=H;
+    Hadamard_facts{k}=facts;
+end
+close(h);
+
+
+
+
+dense_times=zeros(nb_mult,nb_dim);
+faust_times=zeros(nb_mult,nb_dim);
+norm_dense=zeros(1,nb_dim);
+norm_faust=zeros(1,nb_dim);
+RCGs=ns./(Ms*2);
+
+h = waitbar(0,'2-norm hadamard : multiplication time comparison ...');
+for i=1:nb_mult
+    waitbar(i/nb_mult);
+    for k=1:nb_dim
+        n=ns(k);
+        hadamard_dense=Hadamard_matrices{k};
+        hadamard_faust=Faust(Hadamard_facts{k});
+        
+        
+
+	%% 2-norm of the hadamard matrix
+        tic
+        norm_dense(k)=norm(hadamard_dense);
+        t1=toc;
+        
+        tic
+        norm_faust(k)=norm(hadamard_faust);
+        t2=toc;
+        
+
+
+
+        
+        dense_times(i,k)=t1;
+        faust_times(i,k)=t2;
+
+    end
+end
+close(h);
+
+mean_dense_t = mean(dense_times);
+mean_faust_t = mean(faust_times);
+speed_up = mean_dense_t ./ mean_faust_t;
+% expected_norm = ones(1,nb_dim); % version orthonormee
+expected_norm = 2.^(Ms/2); % version non orthonormée 
+err_norm_dense=sqrt((norm_dense - expected_norm).^2);
+err_norm_faust=sqrt((norm_faust - expected_norm).^2);
+
+disp(['speed-up : ' num2str(speed_up)]);
+disp(['norm dense : ' num2str(norm_dense(1,:))]);
+disp(['norm faust : ' num2str(norm_faust(1,:))]);
+
+
+%% Plot the result
+plot_tickness=2.0;
+legend_location = 'NorthWest';
+f=figure;
+
+% runtime comparison
+subplot(1,3,1);
+semilogy(Ms,mean_faust_t,'linewidth',plot_tickness);
+hold on
+semilogy(Ms,mean_dense_t,'r','linewidth',plot_tickness);
+ymin=min([mean_dense_t,mean_faust_t]);
+ymax=max([mean_dense_t,mean_faust_t]);
+grid on
+axis([Ms(1) Ms(end)  ymin ymax]);
+legend('faust','dense','Location',legend_location);
+ylabel('Computed Time (sec)');
+xlabel('log(dim)');
+title('runtime ');
+set(gca,'XTick',Ms);
+
+% speed-up
+subplot(1,3,2);
+semilogy(Ms,speed_up,'linewidth',plot_tickness);
+hold on
+semilogy(Ms,ones(1,nb_dim),'k','linewidth',plot_tickness);
+semilogy(Ms,RCGs,'g','linewidth',plot_tickness);
+grid on
+axis([Ms(1) Ms(end)  min([speed_up,1,RCGs]) max([speed_up,1,RCGs])]);
+title('speed-up norm(A)');
+xlabel('log(dim)');
+ylabel('speedup');
+legend('faust','neutral','theoretical','Location',legend_location);
+set(gca,'XTick',Ms);
+%%
+
+subplot(1,3,3);
+id=find(err_norm_faust ~= 0);% semilogy is not compatible with 0
+semilogy(Ms(id),err_norm_faust(id),'r+-','linewidth',plot_tickness);
+hold on
+semilogy(Ms,err_norm_dense,'linewidth',plot_tickness);
+
+ymin=min([err_norm_dense, err_norm_faust]);
+ymax=max([err_norm_dense, err_norm_faust]);
+
+grid on
+%axis([Ms(1) Ms(end)  ymin ymax]);
+legend('faust','dense','Location',legend_location);
+ylabel('Computed Time (sec)');
+xlabel('log(dim)');
+title('error ');
+set(gca,'XTick',Ms);
+
+
+
+
+
+
+
+
+
+f.Name =['Hadamard 2-norm'];
+%% save the figure
+runPath=which(mfilename);
+pathname = fileparts(runPath);
+figure_dir = [pathname filesep '..' filesep 'Figures'];
+format_fig='-dpng';
+figure_name=[figure_dir filesep 'Hadamard-norm'];
+print(figure_name, format_fig);
+
+
+
+
+
+
+

misc/demo/run_all_demo.m

@@ -53,7 +53,8 @@ Fig_BSL;
 %% Hadamard factorization
 disp('*********** Hadamard Factorization *************');
 demo_fact_hadamard; 
- speed_up_hadamard; 
+speed_up_hadamard;
+norm_hadamard; 
 
 
 %% Runtime comparison

misc/demo/tools/hadamard_mat.m

@@ -41,9 +41,10 @@
 
 function [H,Fact] = hadamard_mat(M)
 
-bloc = (1/sqrt(2))*[1 1;1 -1];
-matbase = bloc;
-matbase=kron(speye(2^(M-1)),matbase);
+% bloc = (1/sqrt(2))*[1 1;1 -1]; % normalized version
+bloc = [1 1;1 -1]; % non-normalized version
+
+matbase=kron(speye(2^(M-1)),bloc);
 n=size(matbase,1);
 
 L=(1:n/2);