MATLAB: How to create a matrix where every combination of numbers between 0 and 1 (step x) is used and every row sums to one

Question

Hello everybody,

I'm looking for a way to create a matrix where every row sums to one and every combination of numbers between zero and one is used given a specified step parameter.

Example: 3 Columns; Step 0.5:

Row 1:[0 0.5 0.5] Row 2:[0.5 0 0.5] Row 3:[0.5 0.5 0]

I'm using the following code (for 6 columns) which is too slow given a small step parameter:

i=1;
for a = 0:step:0.5
  for b = 0:step:0.5
      for c = 0:step:0.5
          for d = 0:step:0.5
              for e = 0:step:0.5
                  for f = 0:step:0.5
                      weights(i,:)=[a b c d e f];
                      i = i+1;
                  end
              end
          end
      end
  end
 end
clear a b c d e f i 
ind = sum(weights,2) == 1;
weights = weights(ind,:);

Thank you for your help!

Answer 1

for step stp = .5

stp = .5;
ii = cell(1,6);
[ii{:}] = ndgrid(0:stp:1);
out = cell2mat(cellfun(@(x)x(:),ii(:,end:-1:1),'un',0));
out = out(sum(out,2) == 1,:);

OR

x = 0:stp:1;
out = x(fliplr(fullfact(numel(x)*ones(1,6))));
out = out(sum(out,2) == 1,:);