wolffd@0: function lam_msg = CPD_to_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence)
wolffd@0: % CPD_TO_LAMBDA_MSG Compute lambda message (gaussian)
wolffd@0: % lam_msg = compute_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence)
wolffd@0: % Pearl p183 eq 4.52
wolffd@0: 
wolffd@0: switch msg_type
wolffd@0:  case 'd',
wolffd@0:   error('gaussian_CPD can''t create discrete msgs')
wolffd@0:  case 'g',
wolffd@0:   cps = ps(CPD.cps);
wolffd@0:   cpsizes = CPD.sizes(CPD.cps);
wolffd@0:   self_size = CPD.sizes(end);
wolffd@0:   i = find_equiv_posns(p, cps); % p is n's i'th cts parent
wolffd@0:   psz = cpsizes(i);
wolffd@0:   if all(msg{n}.lambda.precision == 0) % no info to send on
wolffd@0:     lam_msg.precision = zeros(psz, psz);
wolffd@0:     lam_msg.info_state = zeros(psz, 1);
wolffd@0:     return;
wolffd@0:   end
wolffd@0:   [m, Q, W] = gaussian_CPD_params_given_dps(CPD, [ps n], evidence);
wolffd@0:   Bmu = m;
wolffd@0:   BSigma = Q;
wolffd@0:   for k=1:length(cps) % only get pi msgs from cts parents
wolffd@0:     pk = cps(k);
wolffd@0:     if pk ~= p
wolffd@0:       %bk = block(k, cpsizes);
wolffd@0:       bk = CPD.cps_block_ndx{k};
wolffd@0:       Bk = W(:, bk);
wolffd@0:       m = msg{n}.pi_from_parent{k}; 
wolffd@0:       BSigma = BSigma + Bk * m.Sigma * Bk';
wolffd@0:       Bmu = Bmu + Bk * m.mu;
wolffd@0:     end
wolffd@0:   end
wolffd@0:   % BSigma = Q + sum_{k \neq i} B_k Sigma_k B_k'
wolffd@0:   %bi = block(i, cpsizes);
wolffd@0:   bi = CPD.cps_block_ndx{i};
wolffd@0:   Bi = W(:,bi);
wolffd@0:   P = msg{n}.lambda.precision;
wolffd@0:   if (rcond(P) > 1e-3) | isinf(P)
wolffd@0:     if isinf(P) % Y is observed
wolffd@0:       Sigma_lambda = zeros(self_size, self_size); % infinite precision => 0 variance
wolffd@0:       mu_lambda = msg{n}.lambda.mu; % observed_value;
wolffd@0:     else
wolffd@0:       Sigma_lambda = inv(P);
wolffd@0:       mu_lambda = Sigma_lambda * msg{n}.lambda.info_state;
wolffd@0:     end
wolffd@0:     C = inv(Sigma_lambda + BSigma);
wolffd@0:     lam_msg.precision = Bi' * C * Bi;
wolffd@0:     lam_msg.info_state = Bi' * C * (mu_lambda - Bmu);
wolffd@0:   else
wolffd@0:     % method that uses matrix inversion lemma to avoid inverting P
wolffd@0:     A = inv(P + inv(BSigma));
wolffd@0:     C = P - P*A*P;
wolffd@0:     lam_msg.precision = Bi' * C * Bi;
wolffd@0:     D = eye(self_size) - P*A;
wolffd@0:     z = msg{n}.lambda.info_state;
wolffd@0:     lam_msg.info_state = Bi' * (D*z - D*P*Bmu);
wolffd@0:   end
wolffd@0: end