Please help me vectorize this code

It is a simple nested for loop, I want to learn how to vectorize such loops.

The distance function is an O(1) function with no loops within.

Basically, I have a 2D matrix of size 16x2000. I want to determine the distance between every column with every other column hence making a 2000x2000 matrix.

for i=1:nvoxels
  for j=i:nvoxels
      a=img(1:16,i);
      b=img(1:16,j);
      m(i,j)=distance(a,b);
  end
end

The distance function is :

function lambda = distance(a,b)
var1=var(a);
var2=var(b);
rho=corrcoef(a,b);
rho=rho(1,2);
rho=rho^2;
lambda = (var1 + var2 - sqrt(((var1+var2)^2)-(4*var1*var2*(1-rho))))/2;
if var1==var2
   lambda=0;
end

[Jan]

Please note, that the required changes must appear inside the function distance, not only in the shown code. So please add the code of this function here also by editing the original question (not as a comment, please).

Answer 1

[Jan]

At first cleanup your code for a fair comparison:

for i = 1:nvoxels
  a = img(:, i);
  for j = i:nvoxels
      b = img(:, j);
      m(j,i) = distance(a, b);  % Swapped orientation
  end
end

Afterwards the function distance must be vectorized - so please insert it in your question. But as usual it is not guaranteed, that the vectorized function is faster because the allocation of temporary memory might cost more time than the faster processing of the data saves.

I've swapped the orientation of m, because writing to the array columnwise is usually faster than the rowwise access.

[awi]

I have added the distance code. Please check.