function [obs, hidden] = sample_mhmm(T, numex, initial_prob, transmat, mu, Sigma, mixmat)% SAMPLE_MHMM Generate random sequences from an HMM with (mixtures of) Gaussian output.% [obs, hidden] = sample_mhmm(T, numex, initial_prob, transmat, mu, Sigma, mixmat)%% Inputs:% T - length of each sequence% numex - num. sequences% init_state_prob(i) = Pr(Q(1) = i)% transmat(i,j) = Pr(Q(t+1)=j | Q(t)=i)% mu(:,j,k) = mean of Y(t) given Q(t)=j, M(t)=k% Sigma(:,:,j,k) = cov. of Y(t) given Q(t)=j, M(t)=k% mixmat(j,k) = Pr(M(t)=k | Q(t)=j) where M(t) is the mixture component at time t%% Output:% obs(:,t,l) = observation vector at time t for sequence l% hidden(t,l) = the hidden state at time t for sequence lO = size(mu,1);hidden = zeros(T, numex);obs = zeros(O, T, numex);hidden = sample_mc(initial_prob, transmat, T, numex)';for i=1:numex  for t=1:T    q = hidden(t,i);    m = sample_discrete(mixmat(q,:), 1, 1);    obs(:,t,i) =  gsamp(mu(:,q,m), Sigma(:,:,q,m), 1);  endend