Optimization of double loop

Question

I have written a code where i have to control, if the position (x,y) (saved in the Matrix Mat) is inside of a circular object which is centered at (posx,posy). If so the point gets a value val otherwise its zero.
My Code looks like this but as a matter of fact it is advertised to NOT use loops in matlab. Since i use not 1 but 2 loops, i was wondering if there is a more effective way for solving my problem.

Mat = zeros(300); %creates my coordinate system with zeros
...
for i =lowlimitx:highlimitx %variable boundary of my object
   for j=lowlimity:highlimity
      helpsqrdstnc = abs(posx-i)^2 + abs(posy-j)^2; %square distance from center
      if helpsqrdstnc < radius^2
         Mat(i,j)= val(helpsqrdstnc); 
       end
   end
end

Answer 1

the usual way to optimize matlab code is to vectorize the operations. This is because built in functions and operators is in general much faster. For your case this would leave you with this code:

Mat = zeros(300); %creates my coordinate system with zeros
...
xSq = abs(posx-(lowlimitx:highlimitx)).^2;
ySq = abs(posy-(lowlimity:highlimity)).^2;

helpsqrdstnc = bsxfun(@plus,xSq,ySq.'); %bsxfun to do [xSq(1)+ySq(1),xSq(2)+ySq(1),...; xSq(1)+ySq(2),xSq(2)+ySq(2)...; ...]
Mat(helpsqrdstnc < radius^2)= val(helpsqrdstnc(helpsqrdstnc < radius^2)); 

where helpsqrdstnc must be the same size as Mat. There may also be neseccary to do a reshape here, but you will notice that by yourself if you get a column vector.

This does of course assume that radius, posx and posy is constant, but reading the question this seems to be the case. However, I do not know exactly how val looks, so it I have not managed to test the code. I also think that val(helpsqrdstnc) is tedious, since this refer to the distance, which does not neseccarily need to be an integer.