www.pudn.com > HMM1.zip > condGaussToJoint.m

function [muXY, SigmaXY] = condGaussToJoint(muX, SigmaX, muY, SigmaY, WYgivenX) 
 
% Compute P(X,Y) from P(X) * P(Y|X) where P(X)=N(X;muX,SigmaX)  
% and P(Y|X) = N(Y; WX + muY, SigmaY) 
 
% For details on how to compute a Gaussian from a Bayes net 
% - "Gaussian Influence Diagrams", R. Shachter and C. R. Kenley, Management Science, 35(5):527--550, 1989. 
 
% size(W) = dy x dx 
dx = length(muX); 
dy = length(muY); 
muXY = [muX(:); WYgivenX*muX(:) + muY]; 
 
W = [zeros(dx,dx) WYgivenX'; 
     zeros(dy,dx) zeros(dy,dy)]; 
D = [SigmaX       zeros(dx,dy); 
     zeros(dy,dx) SigmaY]; 
 
U = inv(eye(size(W)) - W')'; 
SigmaXY = U' * D * U;