function theta = dirichlet_sample(alpha, N)% SAMPLE_DIRICHLET Sample N vectors from Dir(alpha(1), ..., alpha(k))% theta = sample_dirichlet(alpha, N)% theta(i,j) = i'th sample of theta_j, where theta ~ Dir% We use the method from p. 482 of "Bayesian Data Analysis", Gelman et al.assert(alpha > 0);k = length(alpha);theta = zeros(N, k);scale = 1; % arbitraryfor i=1:k  %theta(:,i) = gamrnd(alpha(i), scale, N, 1);  theta(:,i) = gamma_sample(alpha(i), scale, N, 1);end%theta = mk_stochastic(theta);S = sum(theta,2); theta = theta ./ repmat(S, 1, k);