wolffd@0: function [muXY, SigmaXY] = condGaussToJoint(muX, SigmaX, muY, SigmaY, WYgivenX)
wolffd@0: 
wolffd@0: % Compute P(X,Y) from P(X) * P(Y|X) where P(X)=N(X;muX,SigmaX) 
wolffd@0: % and P(Y|X) = N(Y; WX + muY, SigmaY)
wolffd@0: 
wolffd@0: % For details on how to compute a Gaussian from a Bayes net
wolffd@0: % - "Gaussian Influence Diagrams", R. Shachter and C. R. Kenley, Management Science, 35(5):527--550, 1989.
wolffd@0: 
wolffd@0: % size(W) = dy x dx
wolffd@0: dx = length(muX);
wolffd@0: dy = length(muY);
wolffd@0: muXY = [muX(:); WYgivenX*muX(:) + muY];
wolffd@0: 
wolffd@0: W = [zeros(dx,dx) WYgivenX';
wolffd@0:      zeros(dy,dx) zeros(dy,dy)];
wolffd@0: D = [SigmaX       zeros(dx,dy);
wolffd@0:      zeros(dy,dx) SigmaY];
wolffd@0: 
wolffd@0: U = inv(eye(size(W)) - W')';
wolffd@0: SigmaXY = U' * D * U;
wolffd@0: 
wolffd@0: