How to do a double sum in MATLAB given the explicit values of the function

Question

I have a double summation which I am trying to compute as follows

$$\sum_i^3\sum_j^3 h_{i,j} w_{i,j}$$

which I am trying to implement in MATLAB.. My application gives me the explicit values of both $h_{i,j} $ and $w_{i,j}$ and gives them as vector such as

For example $${\bf h} = [ h_{11}\,\, h_{12}\,\, h_{13} \,\,h_{21}\,\, h_{22}\,\, h_{23} ]^T$$ $${\bf w} = [ w_{11}\,\, w_{12}\,\, w_{13} \,\,w_{21}\,\, w_{22}\,\, w_{23} ]^T$$

where $T$ means transpose. In order to find the double summation, I do the following in MATLAB

   for l =1: 6 
    v(i)=  h(i)*w(i)
  end 

for i = 1:6 
summation = sum_initial+ v(i)
end

Am I doing things correctly here?

Thanks,

Answer 1

you defined your vectors as two rows, then

just $h.'*w$ or if $h$ is real then $h'*w$ enough, this is a row vector times column vector, i.e. a dot\inner product

however, if you want them to be matrices (as it looks from your mathematical definition), then $h(:).'*w(:)$ will do the trick.

Your code could work if you fix it as following

for l =1: 6 
   v(i)=  h(i)*w(i);
end 

summation=0;
for i = 1:6 
   summation = summation + v(i);
end

Answer 2

Assuming h and w are 3x3 matrices:

h(:).'*w(:)

Answer 3

Maybe you are looking for something like the bsxfun function, which performas a binary operation, such as addition or multiplication, element-wise on two arrays:

summation = sum( bsxfun(@times, h, w) )