MATLAB: Help vectorize for loop please

efficiencyvectorizing

I want to get rid of that for loop and just use/vectors/matrices, so i can optimize my code. if any one can help thanks.
%help compute the average
        d = max(size(x));
        c = 1/(d-1);
        function y1 = f1(r)
              y1 = tanh((1-r)*7) +.7;
        end
        %y2 will be returned
        y2 = zeros(d,1);
         z1 = x(1:2:2*N - 1);
         z2 = x(2:2:2*N );
         for j=1:(d/2)
             Z1 = z1(j) - z1; %x - xj
             Z2 = z2(j) - z2; %y - yj
             Z3 = (Z2.*Z2) + (Z1.*Z1); %(x-xj)^2 + (y - yj)^2
             Z3 = sqrt(Z3);%|X- Xj|
             Z3(j) = 1;
             Z1 = Z3.\Z1;% (x - xj)/|X - Xj|
             Z2 = Z3.\Z2;% (y - yj)/|X - Xj|
             Z4 = f1(Z3); % F( |X - Xj|)
             Z1 = Z1.*Z4;%F( |X - Xj|)*(x - xj)/|X - Xj|
             Z2 = Z2.*Z4;%F( |X - Xj|)*(y - yj)/|X - Xj|
             y2(2*j - 1) = c*sum(Z1);
             y2(2*j) = c*sum(Z2);
         end

Best Answer

As far as I can tell, this seems to replace your code and is a tiny bit faster. (I tested only on small arrays, so maybe the savings will be significant on an actual problem). I assume that N = d/2? I'm also assuming that x is a column vector. I was using x = randi(10,20,1) to test, and I got the same answers as your code.
d = length(x);
c = 1/(d-1);
f1 = @(r) tanh((1-r)*7) +.7;
z1 = x(1:2:2*N - 1);
z2 = x(2:2:2*N );
y2 = zeros(d,1);
Z1 = bsxfun(@minus,z1',repmat(z1,1,d/2));
Z2 = bsxfun(@minus,z2',repmat(z2,1,d/2));
Z3 = sqrt((Z2.*Z2) + (Z1.*Z1));
Z3(1:((d/2)+1):end)=1;
Z1 = Z1./Z3;
Z2 = Z2./Z3;
Z4 = f1(Z3);
Z1 = Z1.*Z4;
Z2 = Z2.*Z4;
y2(1:2:2*N - 1) = sum(Z1)*c;
y2(2:2:2*N) = sum(Z2)*c;
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