Matrix with all possible value combinations

Hi everyone,

I have a quick question. Lets say i want to form a matrix with all possible combinations of some acceptable value, eg. lets say i have 3 elements and i the possible values are 0 1 2 so the matrix would be

0  0  0
0  0  1
0  0  2
0  1  0
0  1  1
0  1  2
0  2  0
0  2  1
0  2  2

and so on for all the possible 3^3 combinations. How can i do this with Matlab for cases that could span between many other possible values (0 1 2 3 4 5 6 7 8...) and for many more columns this time (not only 3).

Thanks.

Answer 1

[the cyclist]

There is a slick way to do this when your vector is the N elements [0 1 2 ... N-1]:

N = 3;
m = dec2base(0:N^N-1, N)-'0';

Notice that dec2base gives a string result, and "subtracting" '0' from that string gives the numeric result you want.

For N=8, this takes about 5 seconds to run on my machine. (I think larger N than that is impractical from a memory point of view.)

If your vector is not so super-specialized, but the elements are unique, then I think this method would still be useful. You could generate the above first, then do a substitution to get to the elements you actually want.

[Raldi]

Not exactly what I want,

what if I had 4 samples (columns) and 3 possible values (eg 0 1 2)?

[the cyclist]

There's almost certainly a better solution than this, but in case nothing else surfaces:

NCOL = 8; % Can't be more than 8, by memory constraint
MAXVAL = 2;

m = dec2base(0:NCOL^NCOL-1, NCOL)-'0';

% Excise values that are bigger than the one you want.
m(any(m>MAXVAL,MAXVAL),:) = [];
m(:,any(m>MAXVAL,1)) = [];