The complexity of such function run in Matlab

Question

The below function is representing an algorithm, so how can I get its complexity? I don't mean the time of running by using the tic .. toc, I mean how many operation (Additions and multiplications) are performed in this loop.

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'*Yy;          
    r_n=Yy-Aug_t*aug_y;                            
    pos_array(times)=pos;                        
end

Size of parameters, m = 256 , N = 256, T= [256,256] and M = [256,1]

Answer 1

You should know what each operator (i.e., *) and each called function (i.e. product) does. Then add up those operations. For instance, I'm pretty sure that in Matlab, the way you're building up Aug_t means that Aug_t' * Aug_t generates a vector dot-product, so for each element in Aug_t there's a multiply-accumulate.