Matrix of all possible combinations of some indices in Matlab

问题

Consider a Matlab vector A of size 1xL, reporting some strictly positive integers. I want to construct a matrix T of size prod(A,2)xL reporting all the possible L-tuples from 1:1:A(1), 1:1:A(2), ..., 1:1:A(L).

For example, take L=3 and A=[2 3 1]. Then T can be constructed as

[ca, cb, cc] = ndgrid(1:1:A(1), 1:1:A(2), 1:1:A(3));
T= [ca(:), cb(:), cc(:)]; 

How can I generalise the code above to a generic L?

回答1:

A minor modification of this answer works. The required changes are:

1. Define the vectors to be "combined" based on A.
2. Replace {end:-1:1} indexing there by {:} indexing here, to get the results in reverse lexicographical order.

A = [2 3 1];
vectors = arrayfun(@(x) {1:x}, A); % 1. Define input vectors from A
n = numel(vectors);
T = cell(1,n);
[T{:}] = ndgrid(vectors{:}); % 2. Results will be in reverse lexicographical order 
T = cat(n+1, T{:});
T = reshape(T,[],n); 

来源：https://stackoverflow.com/questions/62593020/matrix-of-all-possible-combinations-of-some-indices-in-matlab