Return all unique rows with unique elements

How would I find all rows of a matrix which contain only unique elements? For example, if I have a matrix containing all 3-way combinations of the numbers 1-3:

>> x = allcomb(1:3, 1:3, 1:3)

x =

     1     1     1
     1     1     2
     1     1     3
     1     2     1
     1     2     2
     1     2     3
     1     3     1
     1     3     2
     1     3     3
     2     1     1
     2     1     2
     2     1     3
     2     2     1
     2     2     2
     2     2     3
     2     3     1
     2     3     2
     2     3     3
     3     1     1
     3     1     2
     3     1     3
     3     2     1
     3     2     2
     3     2     3
     3     3     1
     3     3     2
     3     3     3

I could do the following:

   y = unique(sort(x, 2), 'rows');    
   y(y(:,1) == y(:,2) | y(:,1) == y(:,3) | y(:,2) == y(:,3), :) = [];

But is there a more efficient way to accomplish this for matrices with an arbitrary number of columns?

Thanks, Dan

Answer 1

[Daniel]

@andrei:

This does not work because it returns several rows which contain the same element. What I am looking for is a matrix of rows which only contain unique elements. In the above example, this is a single row [1 2 3], but in principle could be much larger. As an example, consider the following:

x = allcomb(1:5, 1:5, 1:5); 
y = unique(sort(x, 2), 'rows');    
y(y(:,1) == y(:,2) | y(:,1) == y(:,3) | y(:,2) == y(:,3), :) = []

Thanks, Dan

[I accidentally hit the accept this answer button. Please disregard.]

[Andrei Bobrov]

edited

Answer 2

[Andrei Bobrov]

variant (edited 09/28/2011 13:00 MDT)

xu = unique(x);
[~,loc] = ismember(x,xu);
[a,b] = unique(sort(loc,2),'rows','first');
out = x(b(all(diff(a,1,2),2)),:);

variant 2

[xu,b] = unique(sort(x,2),'rows')
out = x(sort(b(all(diff(xu,1,2),2))),:)

Answer 3

[Daniel]

@andrei:

Ah, the last line should be:

out = x(b(all(diff(a,1,2),2), :), :);

That does it! Thanks!!

Answer 4

[Jan]

No need for the time-consuming UNIQUE:

x     = allcomb(1:3, 1:3, 1:3);
index = all(diff(sort(x, 2), 1, 2), 2);
y     = x(index, :);