Huge modification of the file: uses now the PCA to orthogonalize the state variables to resample

in order to use independent smooth resampling; modification of the input of the procedure since
now no partition is required

matlab/particle/multivariate_smooth_resampling.m

-function new_particles = multivariate_smooth_resampling(weights,particles,number_of_new_particles,number_of_partitions)
+function new_particles = multivariate_smooth_resampling(particles,weights)
 % Smooth Resampling of the  particles.
 
 %@info:
@@ -59,63 +59,15 @@ function new_particles = multivariate_smooth_resampling(weights,particles,number
 %           stephane DOT adjemian AT univ DASH lemans DOT fr
 
 number_of_particles = length(weights);
+weights = weights' ;
 number_of_states = size(particles,2);
-number = number_of_particles/number_of_partitions ;
-tout = sortrows([particles weights],1) ;
-particles = tout(:,1:number_of_states) ;
-weights = tout(:,1+number_of_states) ;
-if number_of_partitions>1 
-    cum_weights = cumsum(weights) ;
-    indx = 1:number_of_particles ;
-    for i=1:number_of_partitions
-        if i==number_of_partitions
-          tmp = bsxfun(@gt,cum_weights,(i-1)/number_of_partitions) ;
-          kp = indx( tmp ) ;
-        else
-          tmp = bsxfun(@and,bsxfun(@gt,cum_weights,(i-1)/number_of_partitions),bsxfun(@lt,cum_weights,i/number_of_partitions)) ;
-          kp = indx( tmp ) ;
-        end
-        if numel(kp)>2
-            Np = length(kp) ;
-            wtilde = [ ( number_of_partitions*( cum_weights(kp(1)) - (i-1)/number_of_partitions) ) ;
-                       ( number_of_partitions*weights(kp(2:Np-1)) ) ;
-                       ( number_of_partitions*(i/number_of_partitions - cum_weights(kp(Np)-1) ) ) ] ;
-        elseif numel(kp)==2
-            Np = length(kp) ;
-            wtilde = [ ( number_of_partitions*( cum_weights(kp(1)) - (i-1)/number_of_partitions) ) ;
-                       ( number_of_partitions*(i/number_of_partitions - cum_weights(kp(Np)-1) ) ) ] ;        
-        elseif numel(kp)==1 
-            new_particles = ones(number,1).*particles(kp,:) ;    
-            return ;
-        else
-            % probleme
-        end
-        test = sum(wtilde) ;
-        disp(test)
-        new_particles = zeros(number_of_particles,number_of_states) ;
-        new_particles_j = zeros(number,number_of_states) ;
-        for j=1:number_of_states
-          particles_j = particles(kp,j) ;
-          if j>1
-            tout = sortrows( [ particles_j wtilde],1) ;
-            particles_j = tout(:,1) ;
-            wtilde = tout(:,2) ;
-          end
-          new_particles_j(:,j) = univariate_smooth_resampling(wtilde,particles_j,number) ;
-        end
-        new_particles((i-1)*number+1:i*number,:) = new_particles_j;
-    end
-else
-    new_particles = zeros(number,number_of_states) ;
-    for j=1:number_of_states
-      if j>1
-        tout = sortrows( [ particles(:,j) weights],1) ;
-        particles_j = tout(:,1) ;
-        weights_j = tout(:,2) ;
-      else
-        particles_j = particles(:,j) ;
-        weights_j = weights ;
-      end
-      new_particles(:,j) = univariate_smooth_resampling(weights_j,particles_j,number) ;
-    end
-end
\ No newline at end of file
+[P,D] = eig(particles'*(bsxfun(@times,1/number_of_particles,particles))) ;
+D = diag(D) ;
+vectors = bsxfun(@times,P,sqrt(D)') ;
+orthogonalized_particles = bsxfun(@rdivide,particles*vectors,D') ; 
+new_particles = zeros(number_of_particles,number_of_states) ;
+for j=1:number_of_states
+  tout = sortrows( [orthogonalized_particles(:,j) weights],1) ;
+  new_particles(:,j) = univariate_smooth_resampling(tout(:,2),tout(:,1),number_of_particles) ;
+end
+new_particles = new_particles*(vectors') ;