wolffd@0: function [A,C] = est_transmat(seq)
wolffd@0: % ESTIMATE_TRANSMAT Max likelihood of a Markov chain transition matrix
wolffd@0: % [A,C] = estimate_transmat(seq)
wolffd@0: %
wolffd@0: % seq is a vector of positive integers
wolffd@0: %
wolffd@0: % e.g., seq = [1 2 1 2 3], C(1,2)=2, C(2,1)=1, C(2,3)=1, so
wolffd@0: % A(1,:)=[0 1 0], A(2,:) = [0.5 0 0.5],
wolffd@0: % all other entries are 0
wolffd@0: 
wolffd@0: % Use a trick with sparse matrices to count the number of each transition.
wolffd@0: % From http://www.mathworks.com/company/newsletter/may03/dna.shtml
wolffd@0: 
wolffd@0: C = full(sparse(seq(1:end-1), seq(2:end),1));
wolffd@0: A = mk_stochastic(C);