The following code snippet is copied from the MATLAB Topic Modeling Toolbox by Mark Steyvers and Tom Griffiths:

function r = drchrnd(a,n)
% take a sample from a dirichlet distribution
p = length(a);
r = gamrnd(repmat(a,n,1),1,n,p);
r = r ./ repmat(sum(r,2),1,p);

The following is an example that generates three discrete distributions from a symmetric Dirichlet distribution Dir( \theta ; [ 1 1 1 1 ] ):

>> A = drchrnd([1 1 1 1], 3)

A =

    0.3889    0.1738    0.0866    0.3507
    0.0130    0.0874    0.6416    0.2579
    0.0251    0.0105    0.2716    0.6928

>> sum(A, 2)

ans =

     1
     1
     1