// m_ij(x_j) = sum_xi {phi(i)*phi(i,j)*prod_{u \in N(i)\j} {m_uj(xi)}}
// m_ij(x_j) = max_xi {phi(i)*phi(i,j)*prod_{u \in N(i)\j} {m_uj(xi)}}
void InferenceEngineBP::sendMessage(BPNode* xi, BPNode* xj, dVector* phi_i, dMatrix** phi_ij, dVector** msg)
{
// potential(i) -> Vi
dVector Vi(phi_i[xi->id]);
// potential(i,j) -> Mij
dMatrix Mij;
if( xi->id < xj->id )
Mij.set( phi_ij[xi->id][xj->id] );
else {
Mij.set( phi_ij[xj->id][xi->id] );
Mij.transpose();
}
// prod_{u \in N(i)\j} {m_ui(xi)} -> Vi
std::list<BPNode*>::iterator it;
for(it=xi->neighbors.begin(); it!=xi->neighbors.end(); it++) {
if( xj->equal(*it) ) continue;
Vi.add( msg[(*it)->id][xi->id] );
}
if( isSumProduct )
logMultiply( Vi, Mij, msg[xi->id][xj->id] );
else
logMultiplyMaxProd( Vi, Mij, msg[xi->id][xj->id] );
}
// m_ij(x_j) = sum_xi {potential(i)*potential(i,j)*prod_{u \in N(i)\j} {m_ui(xi)}}
void InferenceEngineLoopyBP::sendMessage(int xi, int xj, int nbNodes, const Beliefs potentials,
std::vector<dVector>& messages, iMatrix adjMat, int adjMatMax, bool bMaxProd)
{
int max_hi=-1; // for Viterbi decoding
// potential(i)
dVector Vi(potentials.belStates[xi]);
// potential(i,j)
dMatrix Mij(potentials.belEdges[adjMat(xi,xj)-1]);
if( xi>xj ) Mij.transpose();
// prod_{u \in N(i)\j} {m_ui(xi)}}
int msg_idx;
for( int xu=0; xu<nbNodes; xu++ ) {
if( !adjMat(xu,xi) || xu==xj ) continue;
msg_idx = (xu>xi) ? adjMatMax+adjMat(xu,xi)-1 : adjMat(xu,xi)-1;
Vi.add(messages[msg_idx]);
}
// m_ij(xj) = Vi \dot Mij
msg_idx = (xi>xj) ? adjMatMax+adjMat(xi,xj)-1 : adjMat(xi,xj)-1;
if( bMaxProd )
max_hi = logMultiplyMaxProd(Vi, Mij, messages[msg_idx]);
else
logMultiply(Vi, Mij, messages[msg_idx]);
// Normalize messages to avoid numerical over/under-flow
// Make \sum_{xj} m_ij(xj)=1. Other methods could also be used.
double min = messages[msg_idx].min();
if( min < 0 ) messages[msg_idx].add(-min);
messages[msg_idx].multiply(1/messages[msg_idx].sum());
}