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% function [lik, likv]=mfa_cl(X,Lh,Ph,Mu,Pi);
%
% Calculates log likelihoods of a data set under a mixture of factor
% analysis model.
%
% X - data matrix
% Lh - factor loadings
% Ph - diagonal uniquenesses matrix
% Mu - mean vectors
% Pi - priors
%
% lik - log likelihood of X
% likv - vector of log likelihoods
%
% If 0 or 1 output arguments requested, lik is returned. If 2 output
% arguments requested, [lik likv] is returned.
function [lik, likv]=mfa_cl(X,Lh,Ph,Mu,Pi);
N=length(X(:,1));
D=length(X(1,:));
K=length(Lh(1,:));
M=length(Pi);
if (abs(sum(Pi)-1) > 1e-6)
disp('ERROR: Pi should sum to 1');
return;
elseif ((size(Lh) ~= [D*M K]) | (size(Ph) ~= [D 1]) | (size(Mu) ~= [M D]) ...
| (size(Pi) ~= [M 1] & size(Pi) ~= [1 M]))
disp('ERROR in input matrix sizes');
return;
end;
tiny=exp(-744);
const=(2*pi)^(-D/2);
I=eye(K);
Phi=1./Ph;
Phid=diag(Phi);
for k=1:M
Lht=Lh((k-1)*D+1:k*D,:);
LP=Phid*Lht;
MM=Phid-LP*inv(I+Lht'*LP)*LP';
dM=sqrt(det(MM));
Xk=(X-ones(N,1)*Mu(k,:));
XM=Xk*MM;
H(:,k)=const*Pi(k)*dM*exp(-0.5*sum((XM.*Xk)'))';
end;
Hsum=rsum(H);
likv=log(Hsum+(Hsum==0)*tiny);
lik=sum(likv);
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