Generating all possible products from set of values

Hi!

I have some variables that can have different values:

X1 can be 1, 2 or 3

X2 can be 4 or 5

X3 can be 6 or 7 or 8 or 9

I need to multiply the values of the variables, and generate all possible combinations. I mean as a result, I need a vector, that contains:

1*4*6; 1*4*7; 1*4*8; 1*4*9; 1*5*6; 1*5*7; 1*5*8; 1*5*9; 2*4*6; 2*4*7; 2*4*8; 2*4*9; 2*5*6; 2*5*7; 2*5*8; 2*5*9; 3*4*6; 3*4*7; 3*4*8; 3*4*9; 3*5*6; 3*5*7; 3*5*8; 3*5*9; 3*4*6; 3*4*7; 3*4*8; 3*4*9; 3*5*6; 3*5*7; 3*5*8; 3*5*9. (in this case 24 elements, because 3*2*4=24).

In this small example I can calculate it by hand, but in reality, I have much more variables with more possible values, so I need a way to automatize this task.

Thank you guys for help :)

[Stephen23]

Your example output repeats the 3*4*X and 3*5*X groups, giving 32 elements. The 24 elements should be:

1*4*6; 1*4*7; 1*4*8; 1*4*9; 1*5*6; 1*5*7; 1*5*8; 1*5*9; 2*4*6; 2*4*7; 2*4*8; 2*4*9; 2*5*6; 2*5*7; 2*5*8; 2*5*9; 3*4*6; 3*4*7; 3*4*8; 3*4*9; 3*5*6; 3*5*7; 3*5*8; 3*5*9

Answer 1

[Stephen23]

One simple solution (although it does change the size of A on each iteration).

C = {[1,2,3],[4,5],[6,7,8,9]}; % much better in a cell array than as separate variables.
A = C{1}(:);
for k = 2:numel(C)
    V = shiftdim(C{k}(:),1-k);
    A = A.*V; % requires >= R2016b
end
B = A(:); % optional

or to get the order you requested:

>> B = reshape(permute(A,numel(A):-1:1),[],1)
B =
    24
    28
    32
    36
    30
    35
    40
    45
    48
    56
    64
    72
    60
    70
    80
    90
    72
    84
    96
   108
    90
   105
   120
   135

For earlier MATLAB versions replace the .* with bsxfun.

[Gabor Pauer]

Thank you Sir, it works :) the order is not important for me :)