permutations and combinations of column

If there are two matrices

A=[1 2 3 4];
B=[5 6 7 8];

How can I create this

C=[ 1   2    3   4;
  1   2    3   8;
  1   2    7   4;
  1   2    7   8;
  1   6    3   4;
  1   6    3   8;
  1   6    7   4;
  1   6    7   8;
  5   2    3   4;
  5   2    3   8;
  5   2    7   4;
  5   2    7   8;
  5   6    3   4;
  5   6    3   8;
  5   6    7   4;
  5   6    7   8]

Answer 1

[Sean de Wolski]

A=[1 2 3 4];
B=[5 6 7 8];
AB = [A;B];

idx = fullfact([2 2 2 2]);

C = AB(sub2ind([2 4],idx,repmat(1:4,size(idx,1),1)))

This won't be sorted. You could presort idx so that it is:

idx = sortrows(idx,1:4)

[Azzi Abdelmalek]

 result=C(idx)

[Sean de Wolski]

@Azzi: That won't work because idx is only referencing the row in AB. We need the column information also. Of course, if speed is the primary goal, a for-loop will smoke sub2ind() and day of the week...

Answer 2

[Azzi Abdelmalek]

A=[1 2 3 4];B=[5 6 7 8];
C=[];n=length(A);
for k=1:n
  un=ones(2^(n-k),1);
  C=[C repmat([A(k)*un; B(k)*un],2^(k-1),1)];
end