forward_viterbi.m

function [total,argmax,valmax] = forward_viterbi(obs,states,start_p,trans_p,emit_p)
    %Translated from Python code available at:
    %  http://en.wikipedia.org/wiki/Viterbi_algorithm
    
    class(obs)
    class(states)
    class(start_p)
      class(trans_p)
    size(trans_p)
    class(emit_p)
    size(emit_p)
    
    T = {};
    for state = 1:length(states)
        %%          prob.           V. path  V. prob.
        T{state} = {start_p(state),states(state),start_p(state)};
    end
    for output = 1:length(obs)
        U = {};
        for next_state = 1:length(states)
            total = 0;
            argmax = [];
            valmax = 0;
            for source_state = 1:length(states)
                Ti = T{source_state};
                prob = Ti{1}; v_path = Ti{2}; v_prob = Ti{3};
                p = emit_p(source_state,obs(output)) * trans_p(source_state,next_state);
                prob = prob*p;
                v_prob = v_prob*p;
                total = total + prob;
                if v_prob > valmax
                    argmax = [v_path, states(next_state)];
                    valmax = v_prob;
                end
            end
            U{next_state} = {total,argmax,valmax};
        end
        T = U;
    end
    %% apply sum/max to the final states:
    total = 0;
    argmax = [];
    valmax = 0;
    for state = 1:length(states)
        Ti = T{state};
        prob = Ti{1}; v_path = Ti{2}; v_prob = Ti{3};
        total = total + prob;
        if v_prob > valmax
            argmax = v_path;
            valmax = v_prob;
        end
    end
end