group_pcgp.m

Greedy Group Sparsity Promoting Optmization

if verbose
   display('Main iterations...') 
end
c = max(group);
for j = 1:c
    g{j} = find(group == j);
end
tic
t=0;
p=zeros(m,1);
DR=Pt(Residual);
for j = 1:c
    lg(j) = mean(abs(DR(g{j})));
end
[v L]=sort(lg,'descend');
I = g{L(1)};
IN=[IN I'];
pDDp=1;
done = 0;
iter=1;
selectnew=1;

while ~done

    
    % Select new element
    if isa(GradSteps,'char')
        if strcmp(GradSteps,'auto')
             
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Iteration to automatic selection of the number of gradient steps
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%             finished=0;    
%             while ~finished
            % Inner products
                p(IN)=DR(IN);
            % Update direction    
                 if iter==1
                     p(IN)=1;
                 else
                     if selectnew
                         b=0;
                     else
                         b=-Dp'*P(DR)/pDDp;
                     end
                     p(IN)=DR(IN) +b*p(IN);
                 end
             % Step size
                 Dp=P(p);   
                 pDDp=Dp'*Dp;
                 a=Residual'*Dp/(pDDp);
             % Update coefficients   
                 s=s+a*p;
             % New Residual and inner products
                 Residual=Residual-a*Dp;
                 DR=Pt(Residual);
                 % select new element
                     for j = 1:c
                        lg(j) = mean(abs(DR(g{j})));
                     end
                     [v L]=sort(lg,'descend');
                     I = g{L(1)};
                     IN = union(IN,I);
                     if strcmp(STOPCRIT,'M') & length(IN) >= STOPTOL
                        IN=IN(1:STOPTOL);
                     end

                    % Only if we select new element do we leave the loop    
%                      if isempty(intersect(IN,I))
%                         IN=[IN I'];
%                         finished=1;
%                         selectnew=1;
%                      else
%                         selectnew=0;
%                      end
%             end
        else
            
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                           Is option known?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            error('Undefined option for GradSteps, use ''auto'' or an integer.')
        end
    elseif isa(GradSteps,'numeric') 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%               Iteration for fixed number of gradient steps
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
                
        % Do GradSteps gradient steps
        count=1;
        while count<=GradSteps
                 
            % Inner products
                p(IN)=DR(IN);
            % Update direction    
                 if iter==1
                     p(IN)=1;
                 else
                     if count ==1
                         b=0;
                     else
                        b=-Dp'*P(DR)/pDDp;
                     end
                     p(IN)=DR(IN) +b*p(IN);
                 end
             % Step size
                 Dp=P(p);   
                 pDDp=Dp'*Dp;
                 a=Residual'*Dp/(pDDp);
             % Update coefficients   
                 s=s+a*p;
             % New Residual and inner products
                 Residual=Residual-a*Dp;
                 DR=Pt(Residual);
                  count=count+1;
        end
             % select new element
                 for j = 1:c
                    lg(j) = mean(abs(DR(g{j})));
                 end
                 [v L]=sort(lg,'descend');
                 I = g{L(1)};
                IN=[IN I'];
                
    else
          error('Undefined option for GradSteps, use ''auto'' or an integer.')
    end


     ERR=Residual'*Residual/n;
     if comp_err
         err_mse(iter)=ERR;
     end
     
     if comp_time
         iter_time(iter)=toc;
     end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                        Are we done yet?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
     if strcmp(STOPCRIT,'M')
         if iter >= STOPTOL
             done =1;
         elseif verbose && toc-t>10
            display(sprintf('Iteration %i. --- %i iterations to go',iter ,STOPTOL-iter)) 
            t=toc;
         end
    elseif strcmp(STOPCRIT,'mse')
         if comp_err
            if err_mse(iter)<STOPTOL;
                done = 1; 
            elseif verbose && toc-t>10
                display(sprintf('Iteration %i. --- %i mse',iter ,err_mse(iter))) 
                t=toc;
            end
         else
             if ERR<STOPTOL;
                done = 1; 
             elseif verbose && toc-t>10
                display(sprintf('Iteration %i. --- %i mse',iter ,ERR)) 
                t=toc;
             end
         end
     elseif strcmp(STOPCRIT,'mse_change') && iter >=2
         if comp_err && iter >=2
              if ((err_mse(iter-1)-err_mse(iter))/sigsize <STOPTOL);
                done = 1; 
             elseif verbose && toc-t>10
                display(sprintf('Iteration %i. --- %i mse change',iter ,(err_mse(iter-1)-err_mse(iter))/sigsize )) 
                t=toc;
             end
         else
             if ((oldERR - ERR)/sigsize < STOPTOL);
                done = 1; 
             elseif verbose && toc-t>10
                display(sprintf('Iteration %i. --- %i mse change',iter ,(oldERR - ERR)/sigsize)) 
                t=toc;
             end
         end
     elseif strcmp(STOPCRIT,'corr') 
          if max(abs(DR)) < STOPTOL;
             done = 1; 
          elseif verbose && toc-t>10
                display(sprintf('Iteration %i. --- %i corr',iter ,max(abs(DR)))) 
                t=toc;
          end
     end
     
    % Also stop if residual gets too small or maxIter reached
     if comp_err
         if err_mse(iter)<1e-16
             display('Stopping. Exact signal representation found!')
             done=1;
         end
     else


         if iter>1
             if ERR<1e-16
                 display('Stopping. Exact signal representation found!')
                 done=1;
             end
         end
     end

     if iter >= MAXITER
         display('Stopping. Maximum number of iterations reached!')
         done = 1; 
     end
     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                    If not done, take another round
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   
     if ~done
        iter=iter+1;
        oldERR=ERR;
     end
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                  Only return as many elements as iterations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargout >=2
    err_mse = err_mse(1:iter);
end
if nargout ==3
    iter_time = iter_time(1:iter);
end
if verbose
   display('Done') 
end

% Change history
%
% 8 of Februray: Algo does no longer stop if dictionary is not normaliesd.