How to vectorize for loops

Hello, I am quite new to Matlab but I have typed down the following piece of code. It works as desired, but I have noticed the following:

• Matlab spends a lot of time on exprnd(.). Is there a way to improve this flaw?
• As it is quite visible I am using three 'for' loops but I know that Matlab is much more efficient when loops are vectorized. Is there any way you could help me achieve this?

 %Random Walk
 RW=10;
 nsteps = 10;
 X = -99999:99999;
 L = length(X);    
 m = ['x','d','*','s','o','.','h','^','v','>','<','p','h']; 

 S1 = zeros(nsteps,1);
 MSD1 = zeros(nsteps,1);
 nstepss1 = zeros(nsteps,1);

 for k=1:nsteps+1

        K1 = zeros(RW,1);
        V1 = zeros(RW,1);

            for j=1:RW+1

                position = 0;  
                Xright = 0;     
                Xleft = 0;      

                        u_left = 0;
                        u_right = 0;

                    for i=1:nsteps+1

                        u = exprnd( 1 );
                        z = rand;
                        p = 0.1*(u_right)./(0.3)./0.2*(u_right)./(0.3)+0.1*(u_left)./(0.3)).*(k<(1/20)*nsteps) + 0.1*(u_right)./(3.0)./0.2*(u_right)./(3.0)+0.1*(u_left)./(3.0)).*(k>=(1/20)*nsteps);
                        left_step = -1.*(z<p);
                        right_step = 1.*(z>p);
                        n = left_step+right_step;

                        %Boundary Conditions
                        if position+n > X(L)
                            position = X(1);
                        elseif position+n < X(1)
                            position = X(L);
                        else
                            position = position+n;
                        end
                        % Choice of Step
                        if n == 1
                            Xright = Xright+1;
                            if u_right>=u
                                u_right = u_right;
                            else 
                                u_right=u;
                            end
                        else
                            Xleft = Xleft+1;
                            if u_left>=u
                                u_left = u_left;
                            else 
                                u_left=u;
                            end
                        end

                    end
                K1(j) = position;    %Final position of each RW
                V1(j)  = ((Xright-Xleft)/nsteps);    %Average velocity of each RW

            end

        S1(k) = std(V1);
        MSD1(k)=sqrt(S1(k)^2+(mean(V1))^2);
        nstepss1(k) = k;
    hold all;
    PLO1 = scatter(nstepss1.', MSD1, '+');

end
  hold off;
  drawnow

Sorry for the long piece of code provided and thank you for your answers.

[foboo]

It's not a vectorized version, but you can just draw the random numbers outside of the loop and then access the vector in the loop.

[Evangelos Mitsokapas]

Hello, thanks for taking the time to answer. Would you mind elaborating a little bit on what exactly you are suggesting? Like I mentioned in the beginning of the post, I am not yet quite familiar with the vectorizing concept.

[Eric]

What foboo means is doing

 myexprnd = exprnd(1,[nsteps+1, RW+1, nsteps+1]);

before the first for loop to get all the random numbers at once, since doing it that way is faster. Later, you can retrieve the number by calling

 u = myexprnd(k,j,i);

Answer 1

[Jan]

@Evangelos: Omit useless code like: u_right = u_right; This is a waste of time only and confusing. Better replace

if u_left>=u
   u_left = u_left;
else 
   u_left=u;
end

by

u_left = min(u_lect, u);

Your code contains a bug the line:

p = 0.1*(u_right)./(0.3)./0.2*(u_right)./(0.3)+0.1*(u_left)./(0.3)) ...

There is a right parenthesis too much. After fixing this, this line should be cleaned massively: No parentheses around scalar numbers, (0.3)./0.2 is 1.5, etc.

Replace:

left_step = -1.*(z<p);
right_step = 1.*(z>p);

by

left_step  = -(z<p);
right_step =  (z>p);

and

if position+n > X(L)
   position = X(1);
elseif position+n < X(1)
   position = X(L);
else
   position = position+n;
end

by:

position = position + n;
if position > X(L)
   position = X(1);
elseif position < X(1)
   position = X(L);
end

You can improve the code and accelerate it, but I do not think that it is a candidate for a vectorization.