What can be the vectorization of this code?

I am trying to vectorize this code.. what can be the vectorization of this code with input data

      function hat_y=omp(s,T,N)

      Size=size(T);                                    
      M=Size(1);                                        
      hat_y=zeros(1,N);                                                    
      Aug_t=[];                                         
      r_n=s;                                           

      for times=1:M;                                    

          for col=1:N;                                  
              product(col)=abs(T(:,col)'*r_n);          
          end
          [val,pos]=max(product);                       
          Aug_t=[Aug_t,T(:,pos)];                      
          T(:,pos)=zeros(M,1);                          
          aug_y=(Aug_t'*Aug_t)^(-1)*Aug_t'*s;           
          r_n=s-Aug_t*aug_y;                            
          pos_array(times)=pos;                         

          if (abs(aug_y(end))^2/norm(aug_y)<0.05)      
              break;
          end
      end

      hat_y(pos_array)=aug_y;

[Geoff Hayes]

Abeera - why do you wan to vectorize this function? Is the performance too slow (only takes a couple of seconds for me)?

[James Tursa]

Is this yet another function that you are going to implement on a GPU?

[Abeera Tariq]

@James Tursa I had the impression that the last algorithm was slow because of its inherent design, not of the implementation. but I was not convinced this will lead to great improvement in performance in Matlab. and left the other one nd started working on this..

[Abeera Tariq]

Geoff I need to implement this on GPU It is the sub part of the code my whole code has many loops inside loops like

       for times=1:M;                                    
            for col=1:N;                                  
                product(col)=abs(T(:,col)'*r_n);          
            end
            .........................            

        end

There are many loops in the major function which call this function.. I tried this version of algorithm on gpu but it tool longer time bcoz of loops .. so now em trying to remove them ..

[Abeera Tariq]

till now i did this

 function hat_y=omp(s,T,N)

      Size=size(T);                                     
      M=Size(1);                                        
      hat_y=zeros(1,N);                                                     
      Aug_t=[];                                         
      r_n=s;                                            

      for times=1:M;

           product(1:N)=abs(T(:,1:N).'*r_n);              
          [val,pos]=max(product);                      
          Aug_t=[Aug_t,T(:,pos)];                     
          T(:,pos)=zeros(M,1);                         
          aug_y=(Aug_t'*Aug_t)^(-1)*Aug_t'*s;          
          r_n=s-Aug_t*aug_y;                           
          pos_array(times)=pos;                        
      end
      hat_y(pos_array)=aug_y;