nonlin_gg.m

Sparse Estimation Algorithms by Blumensath and Davies min ||x||_0 subject to ||y - Ax||_2<e

iter = 1;

while ~done


    % Select element with largest derivative

        
    if grad_given
        if verbose
            display('Calculating gradient...') 
        end
        grad                    = Grad(s,x);
      else
        if verbose
            display('Estimating gradient...') 
            tt=toc;
        end
        grad                    = zeros(m,1);
        for cm=1:m
            DELTA               = zeros(m,1);
            DELTA(cm)           = 0.5*g_tol;
            grad(cm)            = (C(s+DELTA,x)-C(s-DELTA,x))/g_tol;
        end
        if verbose
            display(['Elapsed time: ' num2str(toc-tt)])
        end
    end

  

    [val ind]=max(abs(w.*grad));


    if ~sum(IND==ind)
        IND=[IND ind];
        if verbose
            display(sprintf('New coefficient selected.')) 
        end
    end


    N_IND=1:m;
    N_IND(IND)=[];

    
    
    if optimiser_given
        if verbose
            display(sprintf('Optimising using supplied function.')) 
        end
        s   = OPT(s,x,IND);
        ne  = C(s,x);
    else
        
        if verbose
            display(sprintf('Optimising using gradient optimisation.')) 
            tt=toc;
        end
        CHANGE=1;
        count=0;

        while norm(grad)>grad_tol && count<Max_Grad && abs(CHANGE)>1e-12 && ~isempty (find(grad, 1))
            count=count+1;
            

            % ESTIMATE GRADIENT
            if count==1
                grad(N_IND)=zeros(size(N_IND));
            else
                if grad_given
                    grad                    = Grad(s,x);
                    grad(N_IND)             = 0;
                else
                    grad                    = zeros(m,1);
                    for cm=1:length(IND)
                        DELTA               = zeros(m,1);
                        DELTA(IND(cm))      = 0.5*g_tol;
                        grad(IND(cm))       = (C(s+DELTA,x)-C(s-DELTA,x))/g_tol;
                    end
                end
            end
            if count == Max_Grad
               display(sprintf('Maximum number of gradient steps reached.')) 
            end
            

      
            % Update s

            it          = 0;
            as          = step_size*grad;
            nne         = C(s-as,x);
            count       = 0;
            while ne    <= nne && ~isempty (find(grad, 1)) && count < 15
                count   = count+1; 
                it      = it+1;
                as      = step_size*10^(-it)*grad;
                nne     = C(s-as,x);
            end
            s           = s-as;

            % Calculate error and change in error
            CHANGE      = ne-nne;
            ne          = nne;
    
            if verbose && toc-tt>10
                display(sprintf('Norm of gradient --- %i,',norm(grad)));
                tt=toc;
            end

        end
    end

    ERR=ne^2/n;

    if comp_err
         err_cost(iter)=ERR;
    end

    if comp_time
         iter_time(iter)=toc;
    end
        
        


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                        Are we done yet?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
     if strcmp(STOPCRIT,'M')
         if length(IND) >= STOPTOL
             done =1;
         elseif verbose && toc-t>10
            display(sprintf('Nonzero elements %i --- %i iterations to go --- current cost %i',length(IND) ,STOPTOL-length(IND),ne)) 
            if do_plot
                    PlotFunc(s)
            end
            t=toc;
         elseif do_plot && toc-t>10
            PlotFunc(s)
            t=toc;
         end
    elseif strcmp(STOPCRIT,'cost')
         if comp_err
            if err_cost(iter)<STOPTOL;
                done = 1; 
            elseif verbose && toc-t>10 
                display(sprintf('Iteration %i. --- %i cost',iter ,err_cost(iter))) 
                if do_plot
                    PlotFunc(s)
                end
                t=toc;
            elseif do_plot && toc-t>10
                PlotFunc(s)
                t=toc;
            end
         else
             if ERR<STOPTOL;
                done = 1; 
             elseif verbose && toc-t>10 
                display(sprintf('Iteration %i. --- %i cost',iter ,ERR)) 
                if do_plot
                    PlotFunc(s)
                end
                t=toc;
            elseif do_plot && toc-t>10
                PlotFunc(s)
                t=toc;
             end
         end
     elseif strcmp(STOPCRIT,'cost_change') && iter >=2
         if comp_err && iter >=2
              if ((err_cost(iter-1)-err_cost(iter))/sigsize <STOPTOL);
                done = 1; 
             elseif verbose && toc-t>10 
                display(sprintf('Iteration %i. --- %i cost change',iter ,(err_cost(iter-1)-err_cost(iter))/sigsize )) 
                if do_plot
                    PlotFunc(s)
                end
                t=toc;
            elseif do_plot && toc-t>10
                PlotFunc(s)
                t=toc;
             end
         else
             if ((oldERR - ERR)/sigsize < STOPTOL);
                done = 1; 
             elseif verbose && toc-t>10
                display(sprintf('Iteration %i. --- %i cost change',iter ,(oldERR - ERR)/sigsize)) 
                if do_plot
                    PlotFunc(s)
                end
                t=toc;
            elseif do_plot && toc-t>10
                PlotFunc(s)
                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)))) 
                if do_plot
                    PlotFunc(s)
                end
                t=toc;
          elseif do_plot && toc-t>10
                PlotFunc(s)
                t=toc;
          end
     end
     
    % Also stop if residual gets too small or maxIter reached
     if comp_err
         if err_cost(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_cost = err_cost(1:iter);
end
if nargout ==3
    iter_time = iter_time(1:iter);
end
if verbose
   display('Done') 
end