how to write code to try every combination of N-dim vector?

Hello, I want to write a code to try every combination of a N-dimentional vector(with entry 0 or 1 or 2). For example, if N=3, all combinations are (0,0,0)(0,0,1)...(2,2,2) and there are 3^N=27.

One brutal way is for commands: for i=0:2->for j=... but I have to write N these for commands, which is not wise. I wonder it there a fast and smart way to try all combinations?

Thanks a lot!

Answer 1

[Sean de Wolski]

[xx yy zz] = ndgrid(0:2);
[xx(:) yy(:) zz(:)]

Generalized (fixed)

n = 4
[C{1:n}] = ndgrid(0:2);
for ii = n:-1:1
  M(:,ii) = C{ii}(:);
end

[C Zeng]

Hello, Sean, thanks, but N is also a parameter her, and I do not know if there is 3. In fact, there might be N=5 or 20. If so, how to make it work?

Thank you!

[Sean de Wolski]

see addendum

[C Zeng]

Oh, great! Thank you so much!

If I want to try all combination and find the maximizer, how could I write the recurrent command? for example, I have a function of the 4-dim vector, and it is the sum of 4 entries, I want to compare and find the maximizer. Of course it would be (2,2,2,2) but I want computer to visit every combination and compare and then find the maximizer and maximum value which is 8. Could you advise?

You are awesome!

[Sean de Wolski]

M = reshape(...from above)

sum(M,2);

[Sean de Wolski]

[~, row_max] = max(sum(M,2))

[C Zeng]

Hi, Sean, thanks!

Sorry I did not make it clear! :-) The function can be complex, and I want to visit every combination (say 3^N) and solve the function value and then compare, what is the general code for it please?

Hope you can understand!

[C Zeng]

Can I write like this:

For i=1 to 3^N

[a1,a2,a3,a4]=M(i,:);

then define function and solve the value;

compare and find the maximizer;

end;

It works well I think.

[C Zeng]

Hi, the code does not work and try all combinations:

n = 4

[C{1:n}] = ndgrid(0:2);

reshape(vertcat(C{:}),[],n)

In deed, it has many same combinations.

[Sean de Wolski]

This is true. I messed up on thinking reshape() would account for the order of the cells being stacked. It did not, see update.

Answer 2

[Daniel Shub]

x = fullfact([3,3,3])-1

[Oleg Komarov]

Thanks again!

[C Zeng]

Thank you, Daniel, it works here!