samer@0: function p=mc_fixpt(Pt)
samer@0: % mc_fixpt - fixed point of Markov chain (stationary state distribution)
samer@0: %
samer@0: % mc_fixpt :: [[K,K]]~'transition matrix'-> [[K]].
samer@0: 
samer@0: 
samer@0: % for ergodic HMM we want to get stationary distribution 
samer@0: % use eigenvalues of transition matrix.
samer@0: [V,D]=eig(Pt);
samer@0: 
samer@0: % one of the eigenvalues should be 1
samer@0: [dummy,k]=max(-abs(diag(D)-1));
samer@0: 
samer@0: % check that it is really close
samer@0: if abs(D(k,k)-1)>0.001
samer@0: 	disp('mc_fixpt: failed to find eigenvalue of 1 in ');
samer@0: 	disp(Pt)
samer@0: 	error('mc_fixpt:noeig','failed to find eigenvalue of 1');
samer@0: end
samer@0: 
samer@0: % get eigenvector and flip it over if all negative
samer@0: v=V(:,k); if sum(v)<0, v=-v; end
samer@0: 
samer@0: if ~isreal(v)
samer@0: 	disp('mc_fixpt: discarding complex parts of eigenvector'); 
samer@0: 	v=real(v);
samer@0: end
samer@0: if any(v<0)
samer@0: 	%fprintf('mc_fixpt: discarding negative parts of eigenvector: %s\n',mat2str(v(v<0))); 
samer@0: 	v=max(0,v);
samer@0: end
samer@0: 
samer@0: % final normalisation
samer@0: p=v/sum(v);