MATLAB: Unique factorial design or number sequence

arraystatistics

Hi,
How would I be able to generate a unique sequence by combining [4 6 8 10 12] and [1 2 3], like the ones below:
4 4 4 4 4 1
4 4 4 4 4 2
4 4 4 4 4 3
4 4 4 4 6 1
4 4 4 4 6 2
4 4 4 4 6 3
. . .. . . . .
12 12 12 12 12 1
12 12 12 12 12 2
12 12 12 12 12 3
However, I do not need repetitions, e.g., I need only one sequence 6 8 8 8 8 1 and NOT 8 6 8 8 8 1

Best Answer

v1 = [4 6 8 10 12]; 
v2 = [1 2 3];
n1 = length(v1);
n2 = length(v2);
ii = flip(fullfact([n2,n1*ones(1,n1)]),2);
ii = ii(all(diff(ii(:,1:end-1),1,2) >= 0,2),:);
out = [v1(ii(:,1:end-1)),v2(ii(:,end))];
or without fullfact:
c = {1:n1,1:n2};
ii = cell(1,numel(v1)+1);
[ii{end:-1:1}] = ndgrid(c{[2,ones(1,n1)]});
ii = cell2mat(cellfun(@(x)x(:),ii,'un',0));
ii = ii(all(diff(ii(:,1:end-1),1,2) >= 0,2),:);
out = [v1(ii(:,1:end-1)),v2(ii(:,end))'];
EDIT
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