function [mix, options, errlog] = gmmem(mix, x, options)%GMMEM	EM algorithm for Gaussian mixture model.%%	Description%	[MIX, OPTIONS, ERRLOG] = GMMEM(MIX, X, OPTIONS) uses the Expectation%	Maximization algorithm of Dempster et al. to estimate the parameters%	of a Gaussian mixture model defined by a data structure MIX. The%	matrix X represents the data whose expectation is maximized, with%	each row corresponding to a vector.    The optional parameters have%	the following interpretations.%%	OPTIONS(1) is set to 1 to display error values; also logs error%	values in the return argument ERRLOG. If OPTIONS(1) is set to 0, then%	only warning messages are displayed.  If OPTIONS(1) is -1, then%	nothing is displayed.%%	OPTIONS(3) is a measure of the absolute precision required of the%	error function at the solution. If the change in log likelihood%	between two steps of the EM algorithm is less than this value, then%	the function terminates.%%	OPTIONS(5) is set to 1 if a covariance matrix is reset to its%	original value when any of its singular values are too small (less%	than eps).  With the default value of 0 no action is taken.%%	OPTIONS(14) is the maximum number of iterations; default 100.%%	The optional return value OPTIONS contains the final error value%	(i.e. data log likelihood) in OPTIONS(8).%%	See also%	GMM, GMMINIT%%	Copyright (c) Christopher M Bishop, Ian T Nabney (1996, 1997)% Check that inputs are consistenterrstring = consist(mix, 'gmm', x);if ~isempty(errstring)  error(errstring);end[ndata, xdim] = size(x);% Sort out the optionsif (options(14))  niters = options(14);else  niters = 100;enddisplay = options(1);store = 0;if (nargout > 2)  store = 1;	% Store the error values to return them  errlog = zeros(1, niters);endtest = 0;if options(3) > 0.0  test = 1;	% Test log likelihood for terminationendcheck_covars = 0;if options(5) >= 1  disp('check_covars is on');  check_covars = 1;	% Ensure that covariances don't collapse  MIN_COVAR = eps;	% Minimum singular value of covariance matrix  init_covars = mix.covars;end% Main loop of algorithmfor n = 1:niters  % Calculate posteriors based on old parameters  [post, act] = gmmpost(mix, x);    % Calculate error value if needed  if (display | store | test)    prob = act*(mix.priors)';    % Error value is negative log likelihood of data    e = - sum(log(prob));    if store      errlog(n) = e;    end    if display > 0      fprintf(1, 'Cycle %4d  Error %11.6f\n', n, e);    end    if test      if (n > 1 & abs(e - eold) < options(3))	options(8) = e;	return;      else	eold = e;      end    end  end  % Adjust the new estimates for the parameters  new_pr = sum(post, 1);  new_c = post' * x;      % Now move new estimates to old parameter vectors  mix.priors = new_pr ./ ndata;    mix.centres = new_c ./ (new_pr' * ones(1, mix.nin));    switch mix.covar_type    case 'spherical'      n2 = dist2(x, mix.centres);      for j = 1:mix.ncentres        v(j) = (post(:,j)'*n2(:,j));      end      mix.covars = ((v./new_pr))./mix.nin;            if check_covars	% Ensure that no covariance is too small	for j = 1:mix.ncentres	  if mix.covars(j) < MIN_COVAR	    mix.covars(j) = init_covars(j);	  end	end      end    case 'diag'      for j = 1:mix.ncentres	diffs = x - (ones(ndata, 1) * mix.centres(j,:));	mix.covars(j,:) = sum((diffs.*diffs).*(post(:,j)*ones(1, ...	  mix.nin)), 1)./new_pr(j);      end      if check_covars	% Ensure that no covariance is too small	for j = 1:mix.ncentres	  if min(mix.covars(j,:)) < MIN_COVAR	    mix.covars(j,:) = init_covars(j,:);	  end	end      end    case 'full'      for j = 1:mix.ncentres        diffs = x - (ones(ndata, 1) * mix.centres(j,:));        diffs = diffs.*(sqrt(post(:,j))*ones(1, mix.nin));        mix.covars(:,:,j) = (diffs'*diffs)/new_pr(j);      end      if check_covars	% Ensure that no covariance is too small	for j = 1:mix.ncentres	  if min(svd(mix.covars(:,:,j))) < MIN_COVAR	    mix.covars(:,:,j) = init_covars(:,:,j);	  end	end      end  endendoptions(8) = -sum(log(gmmprob(mix, x)));if (display >= 0) % disp('Warning: Maximum number of iterations has been exceeded');end