How to generate an *M^N* by *N* integer matrix consiting of all possible length N row vectors whose elements are between 0 and M-1?

I need to generate an M^N by N matrix consisting of all possible length N (N>=2) row vectors whose elements are integer numbers between 0 and M-1 (M>=2). Since there are a total of M^N such row vectors, the matrix has M^N rows, each corresponding to one particular row vector. I also want the row vectors in an "incremental" order, for example, when M = 2 and N = 3, I want to generate the following matrix:

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

In my code, a typical value of M would be 16 and N would be 3. So my matrix would be a large matrix. Does anybody know how to generate such a matrix in an efficient way?

Thanks

Answer 1

[Jan]

There are several corresponding submissions in the FileExchange. When speed matters, use FEX: VChooseKRO. When you do not want to compile C-code, try FEX: combinator.

Using UINT8 arrays will save a lot of RAM and processing time.

[Peng Liu]

Thank you so much! This is exactly what I want

[Peng Liu]

Hi Jan,

With your help I solved this problem. Recently, I also solve this problem in a different way using Matlab built-function. So I would like to share it with you.

    M = 2; N = 3;  % M^N by N integer matrix
    levels = M*ones(1,N);
    Int_Matrix = fliplr(fullfact(levels))-1

Answer 2

[Walter Roberson]

https://groups.google.com/group/comp.lang.c/browse_thread/thread/d98842738fa27a55/2f6d5ff877063de1

with the adjustment by Chris Torek.

I don't think I have posted the MATLAB code, but it is not difficult to write.

[Peng Liu]

Thanks for you reply. But I couldn't find the answer to my question from the link. Could you provide the Matlab code?