Generalizing algorithm to find all combinations of sums of vectors.

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 6x63 matrix not the 3x27 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.

Answer 1

[Roger Stafford]

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.

[Ivan Abraham]

Holy cow it works! I spend all day trying to figure this out. Thank you so much. Now I have to go read about dec2base. :)