Efficient calculation of 3d matrix of distances

Dear;

I would like to calculate the 3D matrix of distances between one point an each element of a 3D matrix in an efficient way.

Without vectorization the code is:

    MDistances=zeros(size(M));
    for i=1:size(M,1)
       for j=1:size(M,2)
          for k=1:size(M,3)
             MDistances(i,j,k)=(i-ip)^2+(j-jp)^2+(k-kp)^2
          end
       end
    end
    MDistances=sqrt(MDistances);

Thanks a lot!!

Answer 1

[Adam]

[x, y, z] = meshgrid( (j-jp)^2, (i-ip)^2, (k-kp)^2 );
distSq = x + y + z;
MDistances = sqrt( distSq );

should give the correct answer I think. I always get confused with meshgrid though how my x and y inputs and outputs always seem to be the wrong way round. When I did the obvious approach I ended up with an answer that didn't match expectations so swapping i and j around in the inputs seems to give the right answer.

Maybe someone else can expand on why that is the case as I don't have the time to re-remember!

[Luis Isaac]

Great answered!! The only evident thing is that i,j and k must be integer vector now:

i=1:size(M,1);
j=1:size(M,2);
k=1:size(M,3);
[x, y, z] = meshgrid( (j-jp)^2, (i-ip)^2, (k-kp)^2 );
distSq = x + y + z;
MDistances = sqrt( distSq );

[Adam]

Ah yes, I forgot to include that I had created those in the same way you do for each of your loops.