How to create an N-ary array

Suppose I have K variables, each of which can take the values 1 through N. I want to create a table such that each column corresponds to the Kth variable, and each row corresponds to a particular combination. This table will be N^K entries long and K entries wide. One way to do this would be, for example

[V1 V2 ... VK] = ngrid(1:N,1:N,...,1:N)
    V = [V1 V2 ... VK]

However, this clearly does not generalize nicely to variable N. Is there a simple way to extend this code so it works for different K?

[James Tursa]

How do you have your K variables stored? Hopefully not as named-numbered variables. In a cell array or as columns of a matrix?

[David Cyncynates]

I called them variables just because it makes sense to think of them that way to me, but ultimately I just want to have a N^K by K array with each combination stored in a given row. I suppose I could do this the old-fashioned way, where I create the matrix row by row, but I feel like there aught to be a better way.

[James Tursa]

That doesn't answer my question. How do you have them currently stored?

[David Cyncynates]

They're not stored. I would like it to be stored in an array. To be clear - this is my point of confusion! It feels very cumbersome to make this object in matlab, so I think I am missing something.

[James Tursa]

OK, I will ask it another way. Are the inputs always the exact values 1:N?

[David Cyncynates]

Yes, the only informatino you need to create this array is the values N and K: Basically, each row stores a number written in N symbols.

[David Cyncynates]

Here's an example of what I was trying to write. Perhaps I'll just stick with this:

N = 4;
K = 3;

V = zeros(K,N^K);

ii = 0 : N^K - 1;
for jj = 1 : K
    V(jj,:) = floor((mod(ii,N^jj))/N^(jj-1));
end

[James Tursa]

OK, got it. Looks like you are basically counting in base N with K digits. How large can K and N be? This could easily eat all your memory if they are too large.

Answer 1

[Stephen23]

N = 4;
K = 3;
C = cell(1,K);
[C{:}] = ndgrid(1:N);
C = cellfun(@(m)m(:),C,'uni',0);
M = [C{:}]

M = 64×3

1 1 1 2 1 1 3 1 1 4 1 1 1 2 1 2 2 1 3 2 1 4 2 1 1 3 1 2 3 1

●

... lots more rows here not shown

How it works:

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists

As James Tursa pointed out, you could quickly run out of memory for large values of K.

Answer 2

[Bruno Luong]

N=3
K=5
[~,A] = ismember(dec2base(0:N^K-1,N),['0':'9' 'A':'Z']);
A = A-1