Permute matrix elements across rows

Say I have a 2x3 matrix, e.g.

X = [1 2 3; 
     4 5 6]

I would like to be able to create a new n x 3 matrix, where n is the number of all possible combinations of the column elements across rows.

In lack of a better description, here is what this new matrix would look like this:

X2 = [X(1,1) X(1,2) X(1,3); 
      X(1,1) X(1,2) X(2,3); 
      X(1,1) X(2,2) X(1,3); 
      X(1,1) X(2,2) X(2,3); 
      X(2,1) X(1,2) X(1,3); 
      X(2,1) X(1,2) X(2,3); 
      X(2,1) X(2,2) X(1,3); 
      X(2,1) X(2,2) X(2,3)];

I'm sure there is a better way of doing this than just indexing, but I can't seem to find one.

Answer 1

[Sean de Wolski]

 [xx yy zz] = ndgrid(X(:,1),X(:,2),X(:,3));
 X3 = sortrows([xx(:), yy(:),zz(:)],[1 2 3]);
 isequal(X2,X3)
 % ans = 1

[Jos (10584)]

This will not work in general. Try , for instance, with

X = [1 5 4 ; 2 6 3] ;

and X3 will not be the same as X2

Answer 2

[Jos (10584)]

I suggest to split the matrix into the elements you want to make combinations of using MAT2CELL

X = [2 4 1 ; 5 3 6] ; % a disordered matrix! 
C = mat2cell(X, size(X,1), ones(1,size(X,2)))

and combine these cells, using, for instance ALLCOMB on the File Exchange: http://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb

X2 = allcomb(C{:})  % done

or modify allcomb's engine using NDGRID, CAT and RESHAPE (but take special care of the order):

[C{:}] = ndgrid(C{end:-1:1}) 
X3 = reshape(cat(numel(C)+1,C{end:-1:1}),[],numel(C))

Directly passing the columns of X to allcomb (or to NDGRID, etc.) works as well, but is not as versatile, of course:

allcomb(X(:,1),X(:,2),X(:,3))

Answer 3

[Treli]

Just what I needed! Many thanks tr