function p = mog_P(x,covtype,means,invcovs,priors)%MOG_P Compute the probability density of a Mixture of Gaussians%%       P = MOG_P(X,COVTYPE,MEANS,INVCOVS,PRIORS)%% Calculate the probability density for all objects X for all of the% clusters of a mixture of Gaussians, characterized with the MEANS,% INVCOVS and PRIORS. COVTYPE indicates the shape of the covariance% matrix, and INVCOVS means that the *inverse* of the covariance% matrices is used!  see mogdd.% Note that P is not normalized!%% See also: mog_dd, mog_init, mog_update% Copyright: D.M.J. Tax, D.M.J.Tax@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlands% Get the useful parameters[N,d] = size(x);k = length(priors);p = zeros(N,k);% Depending on the covariance matrix, the p is computed differently:switch covtypecase 'sphr' % Spherical cov. matrices	D = distm(x,means);	sig = repmat(0.5*invcovs',N,1);	Z = (sig/pi).^(d/2);	p = Z.*exp(-D.*sig);case 'diag' % Diagonal cov.matrix with unequal variances	Z = (2*pi).^(-d/2);	sig = prod(sqrt(invcovs),2);	for i=1:k		dif = x - repmat(means(i,:),N,1);		p(:,i) = Z*sig(i)*exp(-0.5*sum(dif.*dif.*repmat(invcovs(i,:),N,1) ,2));	endcase 'full' % Complete covariance matrix	Z = (2*pi).^(-d/2);	for i=1:k		dif = x - repmat(means(i,:),N,1);		c = squeeze(invcovs(i,:,:));		p(:,i) = sqrt(det(c))*Z*exp(-0.5*sum((dif*c).*dif,2));	endotherwise	error('The inverse covariance matrix parameter is not well-defined');end% include the priors:p = p.*repmat(priors',N,1);return