MATLAB: How to obtain all possible combinations from a set of values without nested for loops

Question

Hi people! I wanted to know if there is an elegant and general approach to generate all possible vectors of a given length where the components are being taken from a known set of values. In my example I have:

set={-1,0,1}; %set of possible values for vector components
n=10; % length of vector

A possible combination for a vector could be

 [0,0,0,0,0,0,0,0,0,0]
or
 [0,0,0,0,0,0,0,0,0,1]
or
 [1,0,0,0,0,0,0,0,0,-1]

So there are 3^10=59049 possible combinations for the components of the vector. I would like to have a method where my result is a 59049-by-10 matrix, each row being a unique combination of the values {-1,0,1}.

The only way I found is extremly inefficient and not parametric, simply nesting 10 for loops, so I would be really thankful for a "real" method. I already tried different matlab functions such as combvec, combnk, but they didn't do what I wanted. Maybe I just used them wrongly.

Answer 1

n=10;
[combs{1:n}]=ndgrid([-1,0,1]);
result=reshape( cat(n+1,combs{:})   ,[],n);