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

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

[Matt J]

n=10;

[combs{1:n}]=ndgrid([-1,0,1]);

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

[Friedrich Maack]

Wow thanks, fast, neat and simple! Great, thank you very much!

[Vivek kumar]

Great solution... Works for me. Now, how to export the output to a text file? And what if the original vector is an string?

Thanks.

[Matt J]

To write to a text file, there is fprintf and friends,

https://www.mathworks.com/help/matlab/ref/fprintf.html

To get combinations of text instead of numbers, just use indexing, e.g.,

n=2;
s='abcdef';

[combs{1:n}]=ndgrid(1:numel(s));
combs=reshape( cat(n+1,combs{:})   ,[],n);

result=s(combs)

[Vivek kumar]

For numbers, I created a string of numbers like A="123". Using for loop selected and concatenated the elements with the help of _ num2str_. Then exported as a text file using dlmwrite.

[Vivek kumar]

Could u suggest anything better?

[Matt J]

I think the loop-free approach in my last comment would be faster, if that matters...