Possible combinations for a vector

Hi!

I have a vector s =[0,0,0,0,0,0,0,0,0] for which i wish to find out all possible combinations and also generate all possbile vectors for. A limit on each element to not be bigger than, lets say 2. So maximum would be like: s=[2,2,2,2,2,2,2,2,2]. Can someone helt me with this, please? Im going to use all the possible vectors for a plot where im going to plot all the vector values.

Best regards,

Daniel

Answer 1

[Stephan]

You could use allcomb from FEX:

k = 0:2;
coms = allcomb(k,k,k,k,k,k,k,k,k);

as expected there are 3^9 = 19683 results

[Daniel Arvidsson]

Thanks alot, Stephan!

Answer 2

[Rik]

s=[0,0,0,0,0,0,0,0,0];
max_value_of_s=2;
num_combinations=(max_value_of_s+1)^numel(s);
disp(num_combinations)

       19683

That is going to go up very quickly if you increase the max value.

Edit:

You can also generate the full array with this code:

N=9;
max_value_of_s=5;
% %naive method (this will cost extreme amounts of memory and processing time
% s=unique(nchoosek(repmat(1:max_value_of_s,1,N),N),'rows');

num_combinations=(max_value_of_s+1)^N;
s=zeros(num_combinations,N);
for row=2:num_combinations %leave row 1 as 0
    s(row,:)=s(row-1,:);
    s(row,1)=s(row,1)+1;%increment position 1
    for col=1:(N-1)
        if s(row,col)>max_value_of_s %overflow to the next 'digit'
            s(row,col)=0;
            s(row,col+1)=s(row,col+1)+1;
        end
    end
end

If you're curious, the naive approach results in this fairly quickly:

@Stephan, thank you for pointing this out, I had already found this when writing my edit, but I'll edit my original code as well.

[Daniel Arvidsson]

Thanks, Rik! But, i would like to generate all those possible vectors, can you help me with that to?

[Stephan]

I think the max value is 3 - due to 0,1 and 2 can be elements.

Answer 3

[Bruno Luong]

dec2base(0:3^9-1,3)-'0'