How can i make a partition matrix

I tried to make a mxn partition matrix that all her columns sum 1.0, i have this, but is very slow

c=5; k=3;
matrixTemp = zeros(c, k);
randoms = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];
idx_r = zeros(1,k);
for i = 1:c
    s = 0;
     while s ~= 1
          idx_r = randperm(9,k);
           s = sum(randoms(idx_r));
     end
     matrixTemp(i,:) = randoms(idx_r);
end

It is posible more easy?

The partition matrix is the same that fuzzy c means.

I need this for example:

c1 | 0.5 0.6 0.1

c2 | 0,2 0.2 0.5

c3 | 0.3 0.2 0.4

----------------------

R | 1.0 1.0 1.0 % sum each column equals to 1.0

Answer 1

[JESUS DAVID ARIZA ROYETH]

If you are not interested in decimals, just add one, the solution is easy:

c=5;
k=3;
matrixTemp=rand(c,k);
matrixTemp=matrixTemp./sum(matrixTemp)

if you want the entire matrix to have only one decimal place :

c=5;
k=3;
while true
matrixTemp=rand(c,k);
matrixTemp=matrixTemp./sum(matrixTemp);
matrixTemp=round(matrixTemp*10)/10;
if prod(prod(matrixTemp))~=0
    break;
end
end
disp(matrixTemp)

[Jesus Montiel]

Thanks a lot, the first example works fine and faster.

Answer 2

[Praveen Iyyappan Valsala]

If you want to list all possible partitions. Not suitable for large k.

randoms = 0.1:0.1:0.9;
%Index of all permutations with repetitions
[k1,k2,k3] = ndgrid(1:length(randoms)) ; %manually type all k;)
allperm = [k1(:) k2(:) k3(:)] ; 
% use the idex to set up permutation matrix of random
random_allperm=randoms(allperm); 
%Pick the permuations with sum==1
AllPartitions=randoms(allperm((sum(random_allperm,2)==1),:));
%% pick c number of partitions according to your needs
c=5; 
disp(AllPartitions(randperm(length(AllPartitions),c),:))