Question

Here is piece of Matlab code. It works very slow. Is there any way to make it work faster? I cant figure out the way to vectorize it.Maybe it can be written like some kind of filter ?

...
for uu=2:length(x)-2;
    for vv= 2:length(y)-2;

     P1=[x(uu+1) y(vv) temp(uu+1,vv)];
     P2=[x(uu) y(vv+1) temp(uu,vv+1)];
     P3=[x(uu-1),y(vv) temp(uu-1,vv)];
     P4=[x(uu) y(vv-1) temp(uu,vv-1)];


     cr=cross((P1-P3),(P2-P4));

     cr=cr/norm(cr);
     theta=acos(dot([0,0,1],px))*180/pi;
     ...
 end
end
...

Answer 1

To vectorize this nested loop, you need to reshape your data properly. The cross product can be performed along a certain dimension, so all you really need to do is to reshape P1 … P4 into vectors containing your data well ordered.

Notice that you have a “cross-shaped” kernel for your operation. P1 could be the bottom part, P3 the top part, P2 the right part and P4 the left part. Assuming that the vectors x and y are only the coordinates of sampled points (temp), each of those vectors could be represented like this :

[x,y] = meshgrid(1:size(temps,1),1:size(temp,2)); % Create a sampling grid or replicate the one you have

tmp1 = x(3:end,2:end-1);
tmp2 = y(3:end,2:end-1);
tmp3 = temp(3:end,2:end-1);
P1 = [tmp1(:), tmp2(:), tmp3(:)] % Vectorization

tmp1 = x(2:end-1,3:end);
tmp2 = y(2:end-1,3:end);
tmp3 = temp(2:end-1,3:end);
P2 = [tmp1(:), tmp2(:), tmp3(:)];

tmp1 = x(1:end-2,2:end-1);
tmp2 = y(1:end-2,2:end-1);
tmp3 = temp(1:end-2,2:end-1);
P3 = [tmp1(:), tmp2(:), tmp3(:)];

tmp1 = x(2:end-1,1:end-2);
tmp2 = y(2:end-1,1:end-2);
tmp3 = temp(2:end-1,1:end-2);
P4 = [tmp1(:), tmp2(:), tmp3(:)];

V1 = P1 - P3;
V2 = P2 - P4;

CR = cross(V1,V2);
NRM = (CR(:,1).^2 + CR(:,2).^2 + CR(:,3).^2).^0.5; % norm(X) cannot be vectorized
CR = CR./NRM;

Theta doesn’t seem to be dependent of any variables in your loop, but acos(X) and dot(v1,v2) can be used with vectorized data, same as cross(v1,v2).

I doubt that you could get any performance boost from decomposing the cross product function in its cofactor expansion, or by trying to implement it as some kind of non-linear filter. If it’s still too slow, you should have a look at the Parallel toolbox.

Hope this helps !