All possible combinations for fixed columns?

Hey folks,

I'm attempting to build an algorithm that generates a 2^n x n matrix of values where n is the size of an input matrix made of two vectors that represent the minimum (first column) and maximum (second column) of values, respective.

For instance, if: input = [-1 1; -2 2]; output should be something like: [1 2; -1 -2; 1 -2; -1 2];

I looked at using nchoosek for this. However, when finding all possible combination, it includes columns being shifted around as such:

Theta =

    -1     1    -2     2

>> C = nchoosek(Theta,2)

C =

    -1     1
    -1    -2
    -1     2
     1    -2
     1     2
    -2     2

For higher order systems (n >= 3), this becomes even more complicated. Is there anyway I can use nchoosek or another algorithm with if statements to solve for the correct output, am I using the incorrect function to solve this, or should I build my own algorithm?

I appreciate any feedback.

- Dan

Answer 1

[Henrik]

I don't know how fast this will be for large n, but this seems to do what you want. You can probably vectorize at least one of the loops.

input=[-1 0 1; 2 4 6];
sz=size(input);
output=zeros(sz(2)^2,2);
for k=0:sz(2)-1
  for l=1:sz(2)
      output(k*sz(2)+l,:)=[input(1,k+1) input(2,l)];
  end
end
output

EDIT: changed the preallocation.

[Henrik]

Here I vectorized one loop:

input=[-1 0 1; 2 4 6];
sz=size(input);
output=zeros(sz(2)^2,2);
l=1:sz(2);
for k=0:sz(2)-1
      output(k*sz(2)+l,:)=[ones(sz(2),1)*input(1,k+1) input(2,:).'];
end

[Henrik]

... And here's a full vectorization

input=[-1 0 1; 2 4 6];
sz=size(input);
C1=repmat(input(1,:),sz(2),1);
C1=C1(:);
C2=repmat(input(2,:).',sz(2),1);
output=[C1 C2]