If the only reason you want to vectorize is speed and k, b have the same range (i.e. from 1 to 10) and likewise a, c have the same range you can take advantage of this and make this quadruple for-loop a double one.
The following implementation is about 40 times faster than the posted one on my machine:
N = 10; % nb, nk
M = 10; % na, nc
NM = N*M;
Num = zeros(NM,2);
Den = zeros(NM,3);
k = 1;
for n = 1:N;
for m = 1:M;
Num(k,:) = [n n*m];
Den(k,:) = [1 n+m n*m];
k = k+1;
end
end
Denmp = repmat(Den,NM,1);
Num = reshape(Num, 1,NM,2);
Nump = repmat (Num, NM,1,1);
Nump = reshape(Nump, NM*NM,2);
