Fastest pairwise row sums

I have two matrices A and B, and I would like to compute a matrix C whose rows are all possible combinations of the sum of a row of A and a row of B. What would be the fastest way to perform the computation?

Additional question - what if A and B are both gpuArrays?

Update - Example

Say A is a matrix of 3 rows and B is a matrix of 2 rows, then I would like C to be the matrix

C = [A(1, :) + B(1, :);
     A(1, :) + B(2, :);
     A(2, :) + B(1, :);
     A(2, :) + B(2, :);
     A(3, :) + B(1, :);
     A(3, :) + B(2, :)];

[madhan ravi]

illustrate with a short example

[Alexander Shtof]

Done.

Answer 1

[Adam]

C = repelem( A, size( B, 1 ), 1 ) + repmat( B, size( A, 1 ), 1 );

Should be the same for gpuArrays too. Whether it is fastest for runtime or not is another matter entirely. There are any number of possible ways of doing it - this is just one. I certainly don't have time to think up, implement and time all of them!

[Alexander Shtof]

This actually works great! Did not know that a function like repelem exists. I used meshgrid to construct pairwise indices, and it resulted in a slower computation.

Thank you!

[Adam]

Yeah, it's one of those useful components to know. It is a relatively recent addition, added in R2015a, although the years seem to be flying past so I guess that is already 4 years ago now!

Answer 2

[Jos (10584)]

% An old-school 20th century indexing trick:
A = randi(9,3,2) 
B = 100*randi(9,4,2) 
[ia, ib] = ndgrid(1:size(A,1),1:size(B,1))
C = A(ia,:) + B(ib,:)