MATLAB: Generalizing algorithm to find all combinations of sums of vectors.

combinatoricsMATLAB

Hello all. I need some help with generalizing an algorithm I wrote. Here is my code:
% Define vectorfield
g1=[5,0,0];
g2=[0,3,0];
g3=[0,0,4];
% Define on-off
u=[0;1];
 % Define set to make field symmetric
symm=[1;-1];
k=1;
 % Generate possible combinations of vector fields
for a=1:length(u)
 for b=1:length(symm)
   for c=1:length(u)
     for d=1:length(symm)
       for e=1:length(u)
         for f=1:length(symm)
           allvecfields(k,:)=u(a).*symm(b).*g1+u(c).*symm(d).*g2+u(e).*symm(f).*g3;
           k=k+1;
         end
       end
     end
   end
 end
end
 realfields=transpose(unique(allvecfields,'rows'));
Each column of realfields is a unique positive, negative or zero combination of the g's. I need some help generalizing this. That is the size of each g can be n, and the number of g's can be m. The code should still return all the unique possible combinations of the g's. I have a feeling that recursion will have to be used but all my attempts have failed so far.
I have looked at combvec and the allcomb file but they don't do what I need. For example
transpose(unique(combvec(g1,g2,g3,-g1,-g2,-g3)','rows'))
returns a 6×63 matrix not the 3×27 that I want.
I have been able to rewrite the above as
 u=[-1,0,1];
 k=1;
 for a=1:length(u)
   for b=1:length(u)
    for c=1:length(u)
        uMat(k,:)=[u(a) u(b) u(c)];
        k=k+1;
    end
  end
 end
 g1=[5,0,0];
 g2=[0,3,0];
 g3=[0,0,4];
 gMat=[g1' g2' g3'];
 for a=1:size(uMat,1)
    allvecfields(k,:)=sum(bsxfun(@times,gMat,uMat(a,:)),2);
 end
 realfields=transpose(unique(allvecfields,'rows'))
which I think this is slightly more elegant but I am still stuck at how to dynamically generate uMat given the number of columns in gMat. Any help would be appreciated.

Best Answer

Let’s suppose that the g’s are the rows in an m by n matrix, G. That is, each n-element row is one of the g’s and there are m of them.
   T = zeros(3^m,m);
   for k = 1:3^m
     T(k,:) = double(dec2base(k-1,3,m)-‘1’); % The T values will be -1, 0, or 1
   end
   A = T*G;
Then A will be your desired ‘allvecfields’ array.
Note: In your first code there is duplication of the possible values of u*symm. Its four combinations yield the values 0,0,1,-1 with only three different values. The code above does not have these duplications and A has only 3^m rows rather than 4^m.
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