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1 function lam_msg = CPD_to_lambda_msg(CPD, msg_type, n, ps, msg, p)
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2 % CPD_TO_LAMBDA_MSG Compute lambda message (gaussian)
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3 % lam_msg = compute_lambda_msg(CPD, msg_type, n, ps, msg, p)
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4 % Pearl p183 eq 4.52
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5
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6 switch msg_type
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7 case 'd',
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8 error('gaussian_CPD can''t create discrete msgs')
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9 case 'g',
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10 self_size = CPD.sizes(end);
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11 if all(msg{n}.lambda.precision == 0) % no info to send on
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12 lam_msg.precision = zeros(self_size);
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13 lam_msg.info_state = zeros(self_size, 1);
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14 return;
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15 end
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16 cpsizes = CPD.sizes(CPD.cps);
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17 dpval = 1;
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18 Q = CPD.cov(:,:,dpval);
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19 Sigmai = Q;
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20 wmu = zeros(self_size, 1);
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21 for k=1:length(ps)
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22 pk = ps(k);
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23 if pk ~= p
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24 bk = block(k, cpsizes);
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25 Bk = CPD.weights(:, bk, dpval);
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26 m = msg{n}.pi_from_parent{k};
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27 Sigmai = Sigmai + Bk * m.Sigma * Bk';
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28 wmu = wmu + Bk * m.mu; % m.mu = u(k)
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29 end
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30 end
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31 % Sigmai = Q + sum_{k \neq i} B_k Sigma_k B_k'
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32 i = find_equiv_posns(p, ps);
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33 bi = block(i, cpsizes);
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34 Bi = CPD.weights(:,bi, dpval);
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35
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36 if 0
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37 P = msg{n}.lambda.precision;
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38 if isinf(P) % inv(P)=Sigma_lambda=0
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39 precision_temp = inv(Sigmai);
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40 lam_msg.precision = Bi' * precision_temp * Bi;
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41 lam_msg.info_state = precision_temp * (msg{n}.lambda.mu - wmu);
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42 else
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43 A = inv(P + inv(Sigmai));
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44 precision_temp = P + P*A*P;
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45 lam_msg.precision = Bi' * precision_temp * Bi;
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46 self_size = length(P);
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47 C = eye(self_size) + P*A;
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48 z = msg{n}.lambda.info_state;
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49 lam_msg.info_state = C*z - C*P*wmu;
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50 end
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51 end
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52
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53 if isinf(msg{n}.lambda.precision)
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54 Sigma_lambda = zeros(self_size, self_size); % infinite precision => 0 variance
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55 mu_lambda = msg{n}.lambda.mu; % observed_value;
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56 else
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57 Sigma_lambda = inv(msg{n}.lambda.precision);
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58 mu_lambda = Sigma_lambda * msg{n}.lambda.info_state;
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59 end
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60 precision_temp = inv(Sigma_lambda + Sigmai);
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61 lam_msg.precision = Bi' * precision_temp * Bi;
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62 lam_msg.info_state = Bi' * precision_temp * (mu_lambda - wmu);
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63 end
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64
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