how to generate a matrix with all possible combinations in an efficient way

I have n=1:4 and m=3, and I want to generate a matrix S whose rows are all the possible combinations.. i.e., S has 4^3 rows and 3columns. What is the mist efficient way to do this as I want to extend matrix to be of 50^10 rows and 10 columns (very large)

[Bruno Luong]

It's good that you are aware it's very large. Beside "very" do you wonder how big it is and can you deal to store it and have time to process it? If you don't think again.

[Guillaume]

very large is a massive understatement, as Bruno says. Looking a this wikipedia entry, you might be able to store your matrix if you manage to convice google to lend you all of their data centres. Good luck!

[mohamed Faraj]

I agree with you. The matrix may be of a manegable size. e.g., 20^5 or 10^5 rows and 5 columns

Answer 1

[Guillaume]

For reasonable n and m you can either use Jos' allcomb or the following:

%n: a vector of numbers
%m: a scalar integer
allcombs = cell(1, m);
[allcombs{:}] = ndgrid(n);
allcombs = reshape(cat(m+1, allcombs{:}), [], m);