demo hadamard fix

misc/demo/run_all_demo.m

@@ -52,7 +52,7 @@ Fig_BSL;
 
 %% Hadamard factorization
 disp('*********** Hadamard Factorization *************');
-%demo_fact_hadamard; %!!! BROKEN DEMO !!!
+demo_fact_hadamard; 
  speed_up_hadamard; 
 
 

misc/demo/tools/hadamard_mat.m

-%% Description hadamard_mat
-%  Computation of tha Hadamard matrix and its "native" factorization
-%  [H, Fact] = hadamard_mat(M) computes the Hadamard matrix H of size 
-%  2^M*2^M and its factorization Fact.
+%% Description speed_up_hadamard
 %
-% For more information on the FAuST Project, please visit the website of 
+%  This demo makes some time comparison between (Hadamard matrix)-vector multiplication and
+%  (Hadamard factorisation i.e a FAµST)-vector multiplication 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:
@@ -11,15 +12,15 @@
 %			INRIA Rennes, FRANCE
 %			http://www.inria.fr/
 %
-% The FAuST Toolbox is distributed under the terms of the GNU Affero 
+% 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 
+% 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.  
+% 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
@@ -27,37 +28,124 @@
 %
 %% Contacts:
 %   Nicolas Bellot : nicolas.bellot@inria.fr
-%   Adrien Leman   : adrien.leman@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 
+% [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=500;
+Ms=6:11;
+ns=2.^Ms;
+nb_dim=length(Ms);
+threshold=10^(-10);
+dense_times=zeros(nb_mult,nb_dim);
+faust_times=zeros(nb_mult,nb_dim);
+
+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);
+
+%     figure,
+%         for i=1:M
+%             subplot(2,M,i);
+%             imagesc(facts{i});
+%             axis image
+%             subplot(2,M,M+i);
+%             imagesc(cum_Hbis{i});
+%             axis image
+%         end
+hadamard_faust=matlab_faust(facts);
+hadamard_dense=dvp(facts);
+
+h = waitbar(0,'speed up hadamard : multiplication time comparison ...');
+for i=1:nb_mult
+    waitbar(i/nb_mult);
+    for k=1:nb_dim
+        n=ns(k);
+        hadamard_dense=full(Hadamard_matrices{k});
+        hadamard_faust=matlab_faust(Hadamard_facts{k});
+        
+        x=rand(n,1);
+        ydense=zeros(n,1);
+        yfaust=zeros(n,1);
+        
+        tic
+        ydense=hadamard_dense*x;
+        t1=toc;
+        
+        tic
+        yfaust=hadamard_faust*x;
+        t2=toc;
+        
+        if(norm(ydense-yfaust)>threshold)
+            error('speed_up hadamard : multiplication problem');
+        end
+        
+        
+        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;
+
+%% Plot the result
+
+f=figure;
+subplot(1,2,1);
+semilogy(Ms,mean_faust_t,'linewidth',1.5);
+hold on
+semilogy(Ms,mean_dense_t,'r','linewidth',1.5);
+ymin=min([min(mean_dense_t),mean_faust_t(1)]);
+ymax=max([max(mean_dense_t),mean_faust_t(end)]);
+grid on
+axis([Ms(1) Ms(end)  ymin ymax]);
+legend('faust','dense');
+ylabel('Computed Time (sec)');
+xlabel('log(dim)');
+title('Hadamard-vector multiplication');
+set(gca,'XTick',Ms);
+
+
+subplot(1,2,2);
+semilogy(Ms,speed_up,'linewidth',1.5);
+hold on
+semilogy(Ms,ones(1,nb_dim),'g','linewidth',1.5);
+grid on
+axis([Ms(1) Ms(end)  min([speed_up,1]) max([speed_up,1])]);
+title('Hadamard-vector multiplication');
+xlabel('log(dim)');
+ylabel('speedup');
+legend('speed-up','neutral speed-up');
+set(gca,'XTick',Ms);
+f.Name =['Hadamard Faust-vector multiplication'];
+%% save the figure
+runPath=which(mfilename);
+pathname = fileparts(runPath);
+fig_filename = [pathname filesep 'output' filesep 'speed_up_hadamard.png'];
+print(fig_filename,'-dpng','-r300');
 
-function [H,Fact] = hadamard_mat(M)
 
-bloc = (1/sqrt(2))*[1 1;1 -1];
-matbase = bloc;
-matbase=kron(speye(2^(M-1)),matbase);
-n=size(matbase,1);
 
-L=(1:n/2);
-id_i=[2*L-1,2*L];
-id_j=[L,L+n/2];
-values=ones(n,1);
 
-Perm = sparse(id_i,id_j,values,n,n);
-same_fact=matbase*Perm;
 
-Fact = cell(1,M);
-for i=1:M
-    Fact{i} = same_fact;
-end
-    H=dvp(Fact);
-end