function [converged, decrease] = em_converged(loglik, previous_loglik, threshold, check_increased)
% EM_CONVERGED Has EM converged?
% [converged, decrease] = em_converged(loglik, previous_loglik, threshold)
%
% We have converged if the slope of the log-likelihood function falls below 'threshold', 
% i.e., |f(t) - f(t-1)| / avg < threshold,
% where avg = (|f(t)| + |f(t-1)|)/2 and f(t) is log lik at iteration t.
% 'threshold' defaults to 1e-4.
%
% This stopping criterion is from Numerical Recipes in C p423
%
% If we are doing MAP estimation (using priors), the likelihood can decrase,
% even though the mode of the posterior is increasing.

if nargin < 3, threshold = 1e-4; end
if nargin < 4, check_increased = 1; end

converged = 0;
decrease = 0;

if check_increased
  if loglik - previous_loglik < -1e-3 % allow for a little imprecision
    fprintf(1, '******likelihood decreased from %6.4f to %6.4f!\n', previous_loglik, loglik);
    decrease = 1;
converged = 0;
return;
  end
end

delta_loglik = abs(loglik - previous_loglik);
avg_loglik = (abs(loglik) + abs(previous_loglik) + eps)/2;
if (delta_loglik / avg_loglik) < threshold, converged = 1; end