wolffd@0: function [engine,engine2] = test_ho_inf_enginge(order,T)
wolffd@0: 
wolffd@0: assert(order >= 1)
wolffd@0: % Model a SISO system, i. e. all node are one-dimensional
wolffd@0: % The nodes are numbered as follows
wolffd@0: % u(t) = 1 input
wolffd@0: % y(t) = 2 model output
wolffd@0: % z(t) = 3 noise
wolffd@0: % q(t) = 4 observed output = noise + model output
wolffd@0: 
wolffd@0: ns = [1 1 1 1];
wolffd@0: 
wolffd@0: % Model a linear system, i.e. there are no discrete nodes
wolffd@0: dn = [];
wolffd@0: 
wolffd@0: % Modeling of connections within a time slice
wolffd@0: intra = zeros(4);
wolffd@0: intra(2,4) = 1; % Connection y(t) -> q(t)
wolffd@0: intra(3,4) = 1; % Connection z(t) -> q(t)
wolffd@0: 
wolffd@0: % Connections to the next time slice
wolffd@0: inter = zeros(4,4,order);
wolffd@0: inter(1,2,1) = 1; % u(t) -> y(t+1);
wolffd@0: inter(2,2,1) = 1; %y(t) -> y(t+1);
wolffd@0: inter(3,3,1) = 1; %z(t) -> z(t+1);
wolffd@0: 
wolffd@0: if order >= 2
wolffd@0:     inter(1,2,2) = 1; % u(t) -> y(t+2);
wolffd@0:     inter(2,2,2) = 1; % y(t) -> y(t+2);
wolffd@0: end
wolffd@0: 
wolffd@0: for i = 3: order
wolffd@0:     inter(:,:,i) = inter(:,:,i-1); %u(t) -> y(t+i) y(t) -> y(t) +i
wolffd@0: end;
wolffd@0: 
wolffd@0: 
wolffd@0: % Compution of a higer order Markov Model
wolffd@0: bnet = mk_higher_order_dbn(intra,inter,ns,'discrete',dn);
wolffd@0: bnet2 = mk_dbn(intra,inter(:,:,1),ns,'discrete',dn)
wolffd@0: 
wolffd@0: 
wolffd@0: %Calculation of the number of nodes with different parameters
wolffd@0: %There is one input and one output nodes  2
wolffd@0: %There are two different disturbance node 2
wolffd@0: %There are order +1 nodes for y           1 + order
wolffd@0: numOfNodes = 5 + order; 
wolffd@0: 
wolffd@0: % First input node
wolffd@0: bnet.CPD{1} = gaussian_CPD(bnet,1,'mean',0);
wolffd@0: bnet2.CPD{1} = gaussian_CPD(bnet,1,'mean',0);
wolffd@0: % Modeled output
wolffd@0: bnet.CPD{2} = gaussian_CPD(bnet,2,'mean',0);
wolffd@0: bnet2.CPD{2} = gaussian_CPD(bnet,2,'mean',0);
wolffd@0: %Disturbance
wolffd@0: bnet.CPD{3} = gaussian_CPD(bnet,3,'mean',0);
wolffd@0: bnet2.CPD{3} = gaussian_CPD(bnet,3,'mean',0);
wolffd@0: 
wolffd@0: %Qutput
wolffd@0: bnet.CPD{4} = gaussian_CPD(bnet,4,'mean',0);
wolffd@0: bnet2.CPD{4} = gaussian_CPD(bnet,4,'mean',0);
wolffd@0: 
wolffd@0: 
wolffd@0: %Output node in the second time-slice
wolffd@0: %Remember that node number 6 is an example for 
wolffd@0: %the fifth equivalence class
wolffd@0: bnet.CPD{5} = gaussian_CPD(bnet,6,'mean',0);
wolffd@0: bnet2.CPD{5} = gaussian_CPD(bnet,6,'mean',0);
wolffd@0: 
wolffd@0: %Disturbance node in the second time slice
wolffd@0: bnet.CPD{6} = gaussian_CPD(bnet,7,'mean',0);
wolffd@0: bnet2.CPD{6} = gaussian_CPD(bnet,7,'mean',0);
wolffd@0: 
wolffd@0: % Modeling of the remaining nodes for y
wolffd@0: for i = 7:numOfNodes
wolffd@0:     bnet.CPD{i} = gaussian_CPD(bnet,(i - 6)*4 + 7,'mean',0);
wolffd@0: end
wolffd@0: 
wolffd@0: % Generation of the inference engine
wolffd@0: engine = dv_unrolled_dbn_inf_engine(bnet,T);
wolffd@0: engine2 = jtree_unrolled_dbn_inf_engine(bnet,T);
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: