void parameters::Likelihood(const VectorXd & eff){
VectorXd loc;
loc.resize(m_proba.rows());
loc=(m_proba.rowwise().sum().array().log());
m_loglikelihood=eff.transpose()*loc;
m_bic=m_loglikelihood - 0.5*m_nbparam*log(eff.sum());
}
double unimcd_in(
const VectorXd& m_resd,
const int& h
){
const int n1=m_resd.size(),len=n1-h+1;
double initmean=0.0,initcov=0.0,sumw=0.0;
int minone;
if(h==n1){
initmean=m_resd.sum()/(double)h;
initcov=(m_resd.array()-initmean).abs2().sum()/(double)(h-1);
return(sqrt(initcov));
}
VectorXd y=m_resd;
VectorXd ay(len);
VectorXd ay2(len);
VectorXd sq(len);
VectorXd y2(n1);
std::sort(y.data(),y.data()+y.size());
ay(0)=y.head(h).sum();
for(int samp=1;samp<len;samp++) ay(samp)=ay(samp-1)-y(samp-1)+y(samp+h-1);
ay2=ay.array().square()/(double)h;
y2=y.array().square();
sq(0)=y2.head(h).sum()-ay2(0);
for(int samp=1;samp<len;samp++) sq(samp)=sq(samp-1)-y2(samp-1)+y2(samp+h-1)-ay2(samp)+ay2(samp-1);
initcov=sq.minCoeff(&minone);
initcov/=(double)(h-1);
initmean=ay(minone)/(double)h;
return(initmean);
}
SpMat make_C(SpMat chol_K_inv,VectorXd h2s, SpMat ZtZ){
SpMat Ki = chol_K_inv.transpose() * chol_K_inv;
SpMat C = ZtZ;
C /= (1.0 - h2s.sum());
C += Ki;
return C;
}
void LoadMatrices(MatrixXd &A, VectorXd &W, VectorXd &p, string weight_type) {
A = MatrixXd::Zero(n_n, n_n);
MatrixXd Apn = MatrixXd::Zero(n_p, n_n);
MatrixXd abs_Apn = MatrixXd::Zero(n_p, n_n);
VectorXd k = VectorXd::Zero(n_n);
p = VectorXd::Zero(n_n);
W = VectorXd::Zero(n_p);
// Topological incidence matrix
for (unsigned int j = 0; j < n_p; j++) {
int idx_n1 = wds->agelemek.at(pipe_idx.at(j))->Get_Cspe_Index();
int idx_n2 = wds->agelemek.at(pipe_idx.at(j))->Get_Cspv_Index();
Apn(j, idx_n1)++;
Apn(j, idx_n2)--;
abs_Apn(j, idx_n1)++;
abs_Apn(j, idx_n2)++;
}
A = Apn.transpose() * Apn;
for (unsigned i = 0; i < n_n; i++) {
A(i, i) = 0;
for (unsigned int j = 0; j < n_n; j++) {
if (A(i, j) != 0) {
A(i, j) = 1.;
// k(i)++;
}
}
}
if (0 == strcmp(weight_type.c_str(), "topology")) {
for (unsigned int i = 0; i < W.size(); i++)
W(i) = 1;
}
if (0 == strcmp(weight_type.c_str(), "dp")) {
double dp, dp_max = -1., weight_min = 0.0001;
for (unsigned int i = 0; i < W.size(); i++) {
// dp = wds->agelemek.at(pipe_idx.at(i))->Get_dprop("mass_flow_rate");
dp = wds->agelemek.at(pipe_idx.at(i))->Get_dprop("headloss");
// dp = wds->agelemek.at(pipe_idx.at(i))->Get_dprop("length");
W(i) = abs(dp);
if (W(i) > dp_max)
dp_max = W(i);
//cout<<endl<<wds->agelemek.at(pipe_idx.at(i))->Get_nev()<<" dp="<<dp;
}
for (unsigned int i = 0; i < W.size(); i++) {
W(i) /= dp_max;
if (W(i) < weight_min)
W(i) = weight_min;
// cout<<endl<<wds->agelemek.at(pipe_idx.at(i))->Get_nev()<<" weight="<<W(i);
}
}
// Final computations
p = abs_Apn.transpose() * W;
sumW = W.sum();
}
double entropy(const VectorXd &values) {
MatrixXd fy = values.array() / values.sum();
double invlog = 1 / std::log(2);
double epsilon = std::numeric_limits<double>::epsilon();
// h = sum(fy * log2(fy+epsilon))
double h = (fy.array() * (fy.array() + epsilon).log().array() * invlog).sum();
return (-1) * h;
}
VectorXd Zscores2Post(VectorXd& Zs){
VectorXd post(Zs.size());
VectorXd Zsq = Zs.array().square();
for(int i = 0; i < Zsq.size(); i ++){
VectorXd Ztemp = (Zsq.array() - Zsq[i])/2;
VectorXd Zexp = Ztemp.array().exp();
post[i] = 1/Zexp.sum();
}
return(post);
}
SpMat make_Sigma(std::vector<SpMat> ZKZts, VectorXd h2s,double tol){
int n = ZKZts[0].rows();
int h = h2s.size();
MatrixXd R(n,n);
R.setZero();
for(int i = 0; i < h; i++){
R += h2s[i] * ZKZts[i];
}
R.diagonal().array() += (1.0-h2s.sum());
return R.sparseView(0,tol);
}
void PF::propagate(VectorXd &particles, VectorXd &weights, int t)
{
for(int i = 0; i < N; i++) {
double p = particles[i];
boost::normal_distribution<> f_rng(p, f_std); // sample from f = q
particles[i] = f_rng(rng);
boost::math::normal g(p, g_std);
weights[i] *= pdf(g, y[t]);
}
weights /= weights.sum();
}
// exponentiates and normalizes a vector
void expAndNormalize(VectorXd& v)
{
if (v.size() == 0) return;
double maxValue = v[0];
for (int i = 1; i < v.size(); i++) {
if (v[i] > maxValue)
maxValue = v[i];
}
v = (v.cwise() - maxValue).cwise().exp();
double Z = v.sum();
v /= Z;
}
int argrand(const VectorXd &v)
{
double cutoff = v.sum() * rand() / (double)RAND_MAX;
double cumSum = 0.0;
for (int i = 0; i < v.size(); i++) {
cumSum += v[i];
if (cumSum >= cutoff) {
return i;
}
}
SVL_LOG(SVL_LOG_FATAL, "bug");
return -1;
}
// If there are two draws and the first has two tiles and the second -- three tiles,
// then sizes = c(2,3) and array = c(m_{1t_1},m_{1t_2},m_{2t_1},m_{2t_2},m_{2t_3})
bool dlmcell(const string &filename, const VectorXd &sizes, const vector<double> &array) {
bool error = false;
if (array.size()!=sizes.sum()) { error = true; return(error); }
ofstream out(filename.c_str(),ofstream::out);
if (!out.is_open()) { error = true; return(error); }
vector<double>::const_iterator it = array.begin();
for ( int i = 0 ; i < sizes.size() ; i++ ) {
for ( int j = 0 ; j < sizes(i) ; j++ ) {
out << fixed << setprecision(6) << *it << " "; it++;
}
out << endl;
}
out.close( );
return(error);
}
/* The Variational Bayes Expectation step for each group.
*
* mutable: Group assignment probabilities, qZj
* returns: The complete-data (X,Z) free energy E[log p(X,Z)/q(Z)] for group j.
* throws: invalid_argument rethrown from other functions.
*/
template <class W, class C> double vbexpectation (
const MatrixXd& Xj, // Observations in group J
const W& weights, // Group Weight parameter distribution
const vector<C>& clusters, // Cluster parameter distributions
MatrixXd& qZj, // Observations to group mixture assignments
const bool sparse // Do sparse updates to groups
)
{
const int K = clusters.size(),
Nj = Xj.rows();
// Get log marginal weight likelihoods
const ArrayXd E_logZ = weights.Elogweight();
// Initialise and set K = 1 defaults for cluster counts
ArrayXi Kful = ArrayXi::Zero(1), Kemp = ArrayXi::Zero(0);
// Find empty clusters if sparse
if ( (sparse == false) && (K > 1) )
Kful = ArrayXi::LinSpaced(Sequential, K, 0, K-1);
else if (sparse == true)
arrfind((weights.getNk() >= ZEROCUTOFF), Kful, Kemp);
const int nKful = Kful.size(),
nKemp = Kemp.size();
// Find Expectations of log joint observation probs -- allow sparse evaluation
MatrixXd logqZj(Nj, nKful);
for (int k = 0; k < nKful; ++k)
logqZj.col(k) = E_logZ(Kful(k)) + clusters[Kful(k)].Eloglike(Xj).array();
// Log normalisation constant of log observation likelihoods
const VectorXd logZzj = logsumexp(logqZj);
// Make sure qZ is the right size, this is a nop if it is
qZj.resize(Nj, K);
// Normalise and Compute Responsibilities -- again allow sparse evaluation
for (int k = 0; k < nKful; ++k)
qZj.col(Kful(k)) = ((logqZj.col(k) - logZzj).array().exp()).matrix();
// Empty Cluster Responsabilities
for (int k = 0; k < nKemp; ++k)
qZj.col(Kemp(k)).setZero();
return -logZzj.sum();
}
GTEST_TEST(TestConvexHull, testRandomConvexCombinations) {
// Generate a set of points, then find a random convex combination of those
// points, and verify that it's correctly reported as being inside the
// convex hull
for (int i = 2; i < 50; ++i) {
for (int j = 0; j < 500; ++j) {
MatrixXd pts = MatrixXd::Random(2, i);
VectorXd weights = VectorXd::Random(i);
if (weights.minCoeff() < 0) {
weights = weights.array() -
weights.minCoeff(); // make sure they're all nonnegative
}
weights = weights.array() / weights.sum();
Vector2d q = pts * weights;
EXPECT_TRUE(inConvexHull(pts, q, 1e-8));
}
}
}
void UpdaterMean::costsToWeights(const VectorXd& costs, string weighting_method, double eliteness, VectorXd& weights) const
{
weights.resize(costs.size());
if (weighting_method.compare("PI-BB")==0)
{
// PI^2 style weighting: continuous, cost exponention
double h = eliteness; // In PI^2, eliteness parameter is known as "h"
double range = costs.maxCoeff()-costs.minCoeff();
if (range==0)
weights.fill(1);
else
weights = (-h*(costs.array()-costs.minCoeff())/range).exp();
}
else if (weighting_method.compare("CMA-ES")==0 || weighting_method.compare("CEM")==0 )
{
// CMA-ES and CEM are rank-based, so we must first sort the costs, and the assign a weight to
// each rank.
VectorXd costs_sorted = costs;
std::sort(costs_sorted.data(), costs_sorted.data()+costs_sorted.size());
// In Python this is more elegant because we have argsort.
// indices = np.argsort(costs)
// It is possible to do this with fancy lambda functions or std::pair in C++ too, but I don't
// mind writing two for loops instead ;-)
weights.fill(0.0);
int mu = eliteness; // In CMA-ES, eliteness parameter is known as "mu"
assert(mu<costs.size());
for (int ii=0; ii<mu; ii++)
{
double cur_cost = costs_sorted[ii];
for (int jj=0; jj<costs.size(); jj++)
{
if (costs[jj] == cur_cost)
{
if (weighting_method.compare("CEM")==0)
weights[jj] = 1.0/mu; // CEM
else
weights[jj] = log(mu+0.5) - log(ii+1); // CMA-ES
break;
}
}
}
// For debugging
//MatrixXd print_mat(3,costs.size());
//print_mat.row(0) = costs_sorted;
//print_mat.row(1) = costs;
//print_mat.row(2) = weights;
//cout << print_mat << endl;
}
else
{
cout << __FILE__ << ":" << __LINE__ << ":WARNING: Unknown weighting method '" << weighting_method << "'. Calling with PI-BB weighting." << endl;
costsToWeights(costs, "PI-BB", eliteness, weights);
return;
}
// Relative standard deviation of total costs
double mean = weights.mean();
double std = sqrt((weights.array()-mean).pow(2).mean());
double rel_std = std/mean;
if (rel_std<1e-10)
{
// Special case: all costs are the same
// Set same weights for all.
weights.fill(1);
}
// Normalize weights
weights = weights/weights.sum();
}
double ave(VectorXd y) {
const double n(y.size());
const double ySum(y.sum());
const double yAve(ySum/n);
return(yAve);
}
double CalcEuclidean(VectorXd &vec1 , VectorXd &vec2){
VectorXd diff = vec1 - vec2;
VectorXd sq = diff.array().square();
return(sq.sum());
}
Matrix3d msac( const Eigen::Matrix2Xd& pointsFrom, const Eigen::Matrix2Xd& pointsTo,
int maxNumTrials, double confidence, double maxDistance ) {
double threshold = maxDistance;
int numPts = pointsFrom.cols();
int idxTrial = 1;
int numTrials = maxNumTrials;
double maxDis = threshold * numPts;
double bestDist = maxDis;
Matrix3d bestT;
bestT << 1, 0, 0, 0, 1, 0, 0, 0, 1;
int index1;
int index2;
// Get two random, different numbers in [0:pointsFrom.cols()-1]
std::uniform_int_distribution<int> distribution1( 0, pointsFrom.cols()-1 );
std::uniform_int_distribution<int> distribution2( 0, pointsFrom.cols()-2 );
while ( idxTrial <= numTrials ) {
// Get two random, different numbers in [0:pointsFrom.cols()-1]
index1 = distribution1( msacGenerator );
index2 = distribution2( msacGenerator );
if ( index2 >= index1 )
index2++;
Vector2d indices( index1, index2 );
/*std::cout << "indices: " << indices.transpose()
<< " pointsFrom.cols: " << pointsFrom.cols()
<< " pointsTo.cols: " << pointsTo.cols() << std::endl;*/
// Get T form Calculated from this set of points
Matrix3d T = computeTform( pointsFrom, pointsTo, indices );
VectorXd dis = evaluateTform( pointsFrom, pointsTo, T, threshold );
double accDis = dis.sum();
if ( accDis < bestDist ) {
bestDist = accDis;
bestT = T;
}
idxTrial++;
}
VectorXd dis = evaluateTform( pointsFrom, pointsTo, bestT, threshold );
threshold *= dis.mean();
int numInliers = 0;
for ( int i = 0; i < dis.rows(); i++ ){
if ( dis(i) < threshold )
numInliers++;
}
VectorXd inliers( numInliers );
int j = 0;
for ( int i = 0; i < dis.rows(); i++ ){
if ( dis(i) < threshold )
inliers(j++) = i;
}
Matrix3d T;
if ( numInliers >= 2 )
T = computeTform( pointsFrom, pointsTo, inliers );
else
T << 1, 0, 0, 0, 1, 0, 0, 0, 1;
return T;
}
double gini(const VectorXd &values) {
double sum = values.sum();
VectorXd fy = values / sum;
double g = 1 - fy.array().square().sum();
return g;
}
int main(int argc, char *argv[])
{
using namespace Eigen;
using namespace std;
// Load a mesh in OFF format
igl::readOFF("../shared/cow.off", V, F);
// Compute Laplace-Beltrami operator: #V by #V
igl::cotmatrix(V,F,L);
// Alternative construction of same Laplacian
SparseMatrix<double> G,K;
// Gradient/Divergence
igl::grad(V,F,G);
// Diagonal per-triangle "mass matrix"
VectorXd dblA;
igl::doublearea(V,F,dblA);
// Place areas along diagonal #dim times
const auto & T = 1.*(dblA.replicate(3,1)*0.5).asDiagonal();
// Laplacian K built as discrete divergence of gradient or equivalently
// discrete Dirichelet energy Hessian
K = -G.transpose() * T * G;
cout<<"|K-L|: "<<(K-L).norm()<<endl;
const auto &key_down = [](igl::Viewer &viewer,unsigned char key,int mod)->bool
{
switch(key)
{
case 'r':
case 'R':
U = V;
break;
case ' ':
{
// Recompute just mass matrix on each step
SparseMatrix<double> M;
igl::massmatrix(U,F,igl::MASSMATRIX_TYPE_BARYCENTRIC,M);
// Solve (M-delta*L) U = M*U
const auto & S = (M - 0.001*L);
Eigen::SimplicialLLT<Eigen::SparseMatrix<double > > solver(S);
assert(solver.info() == Eigen::Success);
U = solver.solve(M*U).eval();
// Compute centroid and subtract (also important for numerics)
VectorXd dblA;
igl::doublearea(U,F,dblA);
double area = 0.5*dblA.sum();
MatrixXd BC;
igl::barycenter(U,F,BC);
RowVector3d centroid(0,0,0);
for(int i = 0;i<BC.rows();i++)
{
centroid += 0.5*dblA(i)/area*BC.row(i);
}
U.rowwise() -= centroid;
// Normalize to unit surface area (important for numerics)
U.array() /= sqrt(area);
break;
}
default:
return false;
}
// Send new positions, update normals, recenter
viewer.data.set_vertices(U);
viewer.data.compute_normals();
viewer.core.align_camera_center(U,F);
return true;
};
// Use original normals as pseudo-colors
MatrixXd N;
igl::per_vertex_normals(V,F,N);
MatrixXd C = N.rowwise().normalized().array()*0.5+0.5;
// Initialize smoothing with base mesh
U = V;
viewer.data.set_mesh(U, F);
viewer.data.set_colors(C);
viewer.callback_key_down = key_down;
cout<<"Press [space] to smooth."<<endl;;
cout<<"Press [r] to reset."<<endl;;
return viewer.launch();
}
void CLBPInference::infer(CGraph &graph,
map<size_t,VectorXd> &nodeBeliefs,
map<size_t,MatrixXd> &edgeBeliefs,
double &logZ)
{
//
// Algorithm workflow:
// 1. Compute the messages passed
// 2. Compute node beliefs
// 3. Compute edge beliefs
// 4. Compute logZ
//
nodeBeliefs.clear();
edgeBeliefs.clear();
const vector<CNodePtr> nodes = graph.getNodes();
const vector<CEdgePtr> edges = graph.getEdges();
multimap<size_t,CEdgePtr> edges_f = graph.getEdgesF();
size_t N_nodes = nodes.size();
size_t N_edges = edges.size();
//
// 1. Compute the messages passed
//
vector<vector<VectorXd> > messages;
bool maximize = false;
messagesLBP( graph, m_options, messages, maximize );
//
// 2. Compute node beliefs
//
for ( size_t nodeIndex = 0; nodeIndex < N_nodes; nodeIndex++ )
{
const CNodePtr nodePtr = graph.getNode( nodeIndex );
size_t nodeID = nodePtr->getID();
VectorXd nodePotPlusIncMsg = nodePtr->getPotentials( m_options.considerNodeFixedValues );
NEIGHBORS_IT neighbors = edges_f.equal_range(nodeID);
//
// Get the messages for all the neighbors, and multiply them with the node potential
//
for ( multimap<size_t,CEdgePtr>::iterator itNeigbhor = neighbors.first;
itNeigbhor != neighbors.second;
itNeigbhor++ )
{
CEdgePtr edgePtr( (*itNeigbhor).second );
size_t edgeIndex = graph.getEdgeIndex( edgePtr->getID() );
if ( !edgePtr->getNodePosition( nodeID ) ) // nodeID is the first node in the edge
nodePotPlusIncMsg = nodePotPlusIncMsg.cwiseProduct(messages[ edgeIndex ][ 1 ]);
else // nodeID is the second node in the dege
nodePotPlusIncMsg = nodePotPlusIncMsg.cwiseProduct(messages[ edgeIndex ][ 0 ]);
}
// Normalize
nodePotPlusIncMsg = nodePotPlusIncMsg / nodePotPlusIncMsg.sum();
nodeBeliefs[ nodeID ] = nodePotPlusIncMsg;
//cout << "Beliefs of node " << nodeIndex << endl << nodePotPlusIncMsg << endl;
}
//
// 3. Compute edge beliefs
//
for ( size_t edgeIndex = 0; edgeIndex < N_edges; edgeIndex++ )
{
CEdgePtr edgePtr = edges[edgeIndex];
size_t edgeID = edgePtr->getID();
size_t ID1, ID2;
edgePtr->getNodesID( ID1, ID2 );
MatrixXd edgePotentials = edgePtr->getPotentials();
MatrixXd edgeBelief = edgePotentials;
VectorXd &message1To2 = messages[edgeIndex][0];
VectorXd &message2To1 = messages[edgeIndex][1];
//cout << "----------------------" << endl;
//cout << nodeBeliefs[ ID1 ] << endl;
//cout << "----------------------" << endl;
//cout << message2To1 << endl;
VectorXd node1Belief = nodeBeliefs[ ID1 ].cwiseQuotient( message2To1 );
VectorXd node2Belief = nodeBeliefs[ ID2 ].cwiseQuotient( message1To2 );
//cout << "----------------------" << endl;
MatrixXd node1BeliefMatrix ( edgePotentials.rows(), edgePotentials.cols() );
for ( size_t row = 0; row < edgePotentials.rows(); row++ )
for ( size_t col = 0; col < edgePotentials.cols(); col++ )
node1BeliefMatrix(row,col) = node1Belief(row);
//cout << "Node 1 belief matrix: " << endl << node1BeliefMatrix << endl;
edgeBelief = edgeBelief.cwiseProduct( node1BeliefMatrix );
MatrixXd node2BeliefMatrix ( edgePotentials.rows(), edgePotentials.cols() );
for ( size_t row = 0; row < edgePotentials.rows(); row++ )
for ( size_t col = 0; col < edgePotentials.cols(); col++ )
node2BeliefMatrix(row,col) = node2Belief(col);
//cout << "Node 2 belief matrix: " << endl << node2BeliefMatrix << endl;
edgeBelief = edgeBelief.cwiseProduct( node2BeliefMatrix );
//cout << "Edge potentials" << endl << edgePotentials << endl;
//cout << "Edge beliefs" << endl << edgeBelief << endl;
// Normalize
edgeBelief = edgeBelief / edgeBelief.sum();
edgeBeliefs[ edgeID ] = edgeBelief;
}
//
// 4. Compute logZ
//
double energyNodes = 0;
double energyEdges = 0;
double entropyNodes = 0;
double entropyEdges = 0;
// Compute energy and entropy from nodes
for ( size_t nodeIndex = 0; nodeIndex < nodes.size(); nodeIndex++ )
{
CNodePtr nodePtr = nodes[ nodeIndex ];
size_t nodeID = nodePtr->getID();
size_t N_Neighbors = graph.getNumberOfNodeNeighbors( nodeID );
// Useful computations and shorcuts
VectorXd &nodeBelief = nodeBeliefs[nodeID];
VectorXd logNodeBelief = nodeBeliefs[nodeID].array().log();
VectorXd nodePotentials = nodePtr->getPotentials( m_options.considerNodeFixedValues );
VectorXd logNodePotentials = nodePotentials.array().log();
// Entropy from the node
energyNodes += N_Neighbors*( nodeBelief.cwiseProduct( logNodeBelief ).sum() );
// Energy from the node
entropyNodes += N_Neighbors*( nodeBelief.cwiseProduct( logNodePotentials ).sum() );
}
// Compute energy and entropy from nodes
for ( size_t edgeIndex = 0; edgeIndex < N_edges; edgeIndex++ )
{
CEdgePtr edgePtr = edges[ edgeIndex ];
size_t edgeID = edgePtr->getID();
// Useful computations and shorcuts
MatrixXd &edgeBelief = edgeBeliefs[ edgeID ];
MatrixXd logEdgeBelief = edgeBelief.array().log();
MatrixXd &edgePotentials = edgePtr->getPotentials();
MatrixXd logEdgePotentials = edgePotentials.array().log();
// Entropy from the edge
energyEdges += edgeBelief.cwiseProduct( logEdgeBelief ).sum();
// Energy from the edge
entropyEdges += edgeBelief.cwiseProduct( logEdgePotentials ).sum();
}
// Final Bethe free energy
double BethefreeEnergy = ( energyNodes - energyEdges ) - ( entropyNodes - entropyEdges );
// Compute logZ
logZ = - BethefreeEnergy;
}
size_t UPGMpp::messagesLBP(CGraph &graph,
TInferenceOptions &options,
vector<vector<VectorXd> > &messages ,
bool maximize,
const vector<size_t> &tree)
{
const vector<CNodePtr> nodes = graph.getNodes();
const vector<CEdgePtr> edges = graph.getEdges();
multimap<size_t,CEdgePtr> edges_f = graph.getEdgesF();
size_t N_nodes = nodes.size();
size_t N_edges = edges.size();
bool is_tree = (tree.size()>0) ? true : false;
//graph.computePotentials();
//
// Build the messages structure
//
double totalSumOfMsgs = 0;
if ( !messages.size() )
messages.resize( N_edges);
for ( size_t i = 0; i < N_edges; i++ )
{
if ( !messages[i].size() )
{
messages[i].resize(2);
size_t ID1, ID2;
edges[i]->getNodesID(ID1,ID2);
// Messages from first node of the edge to the second one, so the size of
// the message has to be the same as the number of classes of the second node.
double N_classes = graph.getNodeWithID( ID2 )->getPotentials( options.considerNodeFixedValues ).rows();
messages[i][0].resize( N_classes );
messages[i][0].fill(1.0/N_classes);
// Just the opposite as before.
N_classes = graph.getNodeWithID( ID1 )->getPotentials( options.considerNodeFixedValues ).rows();
messages[i][1].resize( N_classes );
messages[i][1].fill(1.0/N_classes);
}
totalSumOfMsgs += messages[i][0].rows() + messages[i][1].rows();
}
// cout << "Initial Messages:" << endl;
// for ( size_t i=0; i < messages.size(); i++)
// for ( size_t j=0; j < messages[i].size(); j++)
// for ( size_t k=0; k < messages[i][j].size(); k++ )
// cout << messages[i][j][k] << " ";
vector<vector<VectorXd> > previousMessages;
if ( options.particularS["order"] == "RBP" )
{
previousMessages = messages;
for ( size_t i = 0; i < previousMessages.size(); i++ )
{
previousMessages[i][0].fill(0);
previousMessages[i][1].fill(0);
}
}
//
// Iterate until convergence or a certain maximum number of iterations is reached
//
size_t iteration;
// cout << endl;
for ( iteration = 0; iteration < options.maxIterations; iteration++ )
{
// cout << "Messages " << iteration << ":" << endl;
// for ( size_t i=0; i < messages.size(); i++)
// for ( size_t j=0; j < messages[i].size(); j++)
// for ( size_t k=0; k < messages[i][j].size(); k++ )
// cout << messages[i][j][k] << " ";
// cout << endl;
// Variables used by Residual Belief Propagation
int edgeWithMaxDiffIndex = -1;
VectorXd associatedMessage;
bool from1to2;
double maxDifference = -1;
//
// Iterate over all the nodes
//
for ( size_t nodeIndex = 0; nodeIndex < N_nodes; nodeIndex++ )
{
const CNodePtr nodePtr = graph.getNode( nodeIndex );
size_t nodeID = nodePtr->getID();
// Check if we are calibrating a tree, and so if the node is not member of the tree,
// so we dont have to update its messages
if ( is_tree && ( std::find(tree.begin(), tree.end(), nodeID ) == tree.end() ) )
continue;
NEIGHBORS_IT neighbors;
neighbors = edges_f.equal_range(nodeID);
//cout << " Sending messages ... " << endl;
//
// Send a message to each neighbor
//
for ( multimap<size_t,CEdgePtr>::iterator itNeigbhor = neighbors.first;
itNeigbhor != neighbors.second;
itNeigbhor++ )
{
// cout << "sending msg to neighbor..." << endl;
VectorXd nodePotPlusIncMsg = nodePtr->getPotentials( options.considerNodeFixedValues );
// cout << "nodePotPlusIncMsg Orig: " << nodePotPlusIncMsg.transpose() << endl;
size_t neighborID;
size_t ID1, ID2;
CEdgePtr edgePtr( (*itNeigbhor).second );
edgePtr->getNodesID(ID1,ID2);
( ID1 == nodeID ) ? neighborID = ID2 : neighborID = ID1;
// cout << "all ready" << endl;
// Check if we are calibrating a tree, and so if the neighbor node
// is not member of the tree, so we dont have to update its messages
if ( is_tree && ( std::find(tree.begin(), tree.end(), neighborID ) == tree.end() ))
continue;
//
// Compute the message from current node as a product of all the
// incoming messages less the one from the current neighbor
// plus the node potential of the current node.
//
for ( multimap<size_t,CEdgePtr>::iterator itNeigbhor2 = neighbors.first;
itNeigbhor2 != neighbors.second;
itNeigbhor2++ )
{
size_t ID11, ID12;
CEdgePtr edgePtr2( (*itNeigbhor2).second );
edgePtr2->getNodesID(ID11,ID12);
size_t edgeIndex = graph.getEdgeIndex( edgePtr2->getID() );
// cout << "Edge index: " << edgeIndex << endl << "node pot" << nodePotPlusIncMsg << endl;
// cout << "Node ID: " << nodeID << " node11 " << ID11 << " node12 " << ID12 << endl;
CNodePtr n1,n2;
edgePtr2->getNodes(n1,n2);
// cout << "Node 1 type: " << n1->getType()->getID() << " label " << n1->getType()->getLabel() << endl;
// cout << "Node 2 type: " << n2->getType()->getID() << " label " << n2->getType()->getLabel() << endl;
// Check if the current neighbor appears in the edge
if ( ( neighborID != ID11 ) && ( neighborID != ID12 ) )
{
if ( nodeID == ID11 )
{
// cout << "nodePotPlusIncMsg Prod: " << messages[ edgeIndex ][ 1 ].transpose() << endl;
// cout << "nodePotPlusIncMsg Bis : " << messages[ edgeIndex ][ 0 ].transpose() << endl;
nodePotPlusIncMsg =
nodePotPlusIncMsg.cwiseProduct(messages[ edgeIndex ][ 1 ]);
// cout << "nodePotPlusIncMsg Prod2: " << nodePotPlusIncMsg.transpose() << endl;
}
else // nodeID == ID2
{
// cout << "nodePotPlusIncMsg Prod: " << messages[ edgeIndex ][ 0 ].transpose() << endl;
// cout << "nodePotPlusIncMsg Bis : " << messages[ edgeIndex ][ 1 ].transpose() << endl;
nodePotPlusIncMsg =
nodePotPlusIncMsg.cwiseProduct(messages[ edgeIndex ][ 0 ]);
// cout << "nodePotPlusIncMsg Prod2: " << nodePotPlusIncMsg.transpose() << endl;
}
}
}
// cout << "Node pot" << endl;
//cout << "Node pot" << nodePotPlusIncMsg << endl;
//
// Take also the potential between the two nodes
//
MatrixXd edgePotentials;
if ( nodeID != ID1 )
edgePotentials = edgePtr->getPotentials();
else
edgePotentials = edgePtr->getPotentials().transpose();
VectorXd newMessage;
size_t edgeIndex = graph.getEdgeIndex( edgePtr->getID() );
// cout << "get new message" << endl;
if ( !maximize )
{
// Multiply both, and update the potential
// cout << "Edge potentials:" << edgePotentials.transpose() << endl;
// cout << "nodePotPlusIncMsg:" << nodePotPlusIncMsg.transpose() << endl;
newMessage = edgePotentials * nodePotPlusIncMsg;
// Normalize new message
if (newMessage.sum())
newMessage = newMessage / newMessage.sum();
//cout << "New message 3:" << newMessage.transpose() << endl;
}
else
{
if ( nodeID == ID1 )
newMessage.resize(messages[ edgeIndex ][0].rows());
else
newMessage.resize(messages[ edgeIndex ][1].rows());
for ( size_t row = 0; row < edgePotentials.rows(); row++ )
{
double maxRowValue = std::numeric_limits<double>::min();
for ( size_t col = 0; col < edgePotentials.cols(); col++ )
{
double value = edgePotentials(row,col)*nodePotPlusIncMsg(col);
if ( value > maxRowValue )
maxRowValue = value;
}
newMessage(row) = maxRowValue;
}
// Normalize new message
if (newMessage.sum())
newMessage = newMessage / newMessage.sum();
//cout << "New message: " << endl << newMessage << endl;
}
//
// Set the message!
//
VectorXd smoothedOldMessage(newMessage.rows());
smoothedOldMessage.setZero();
double smoothing = options.particularD["smoothing"];
if ( smoothing != 0 )
if ( nodeID == ID1 )
newMessage = newMessage + (1-smoothing) * messages[ edgeIndex ][0];
else
newMessage = newMessage + (1-smoothing) * messages[ edgeIndex ][1];
//cout << "New message:" << endl << newMessage << endl << "Smoothed" << endl << smoothedOldMessage << endl;
// If residual belief propagation is activated, just check if the
// newMessage is the one with the higest residual till the
// moment. Otherwise, set the new message as the current one
if ( options.particularS["order"] == "RBP" )
{
if ( nodeID == ID1 )
{
VectorXd differences = messages[edgeIndex][0] - newMessage;
double difference = differences.cwiseAbs().sum();
if ( difference > maxDifference )
{
from1to2 = true;
edgeWithMaxDiffIndex = edgeIndex;
maxDifference = difference;
associatedMessage = newMessage;
}
}
else
{
VectorXd differences = messages[edgeIndex][1] - newMessage;
double difference = differences.cwiseAbs().sum();
if ( difference > maxDifference )
{
from1to2 = false;
edgeWithMaxDiffIndex = edgeIndex;
maxDifference = difference;
associatedMessage = newMessage;
}
}
}
else
{
// cout << newMessage.cols() << " " << newMessage.rows() << endl;
// cout << "edgeIndex" << edgeIndex << endl;
if ( nodeID == ID1 )
{
// cout << messages[ edgeIndex ][0].cols() << " " << messages[ edgeIndex ][0].rows() << endl;
messages[ edgeIndex ][0] = newMessage;
}
else
{
// cout << messages[ edgeIndex ][1].cols() << " " << messages[ edgeIndex ][1].rows() << endl;
messages[ edgeIndex ][1] = newMessage;
}
// cout << "Wop " << endl;
}
}
} // Nodes
if ( options.particularS["order"] == "RBP" && ( edgeWithMaxDiffIndex =! -1 ))
{
if ( from1to2 )
messages[ edgeWithMaxDiffIndex ][0] = associatedMessage;
else
messages[ edgeWithMaxDiffIndex ][1] = associatedMessage;
}
//
// Check convergency!!
//
double newTotalSumOfMsgs = 0;
for ( size_t i = 0; i < N_edges; i++ )
{
newTotalSumOfMsgs += messages[i][0].sum() + messages[i][1].sum();
}
//printf("%4.10f\n",std::abs( totalSumOfMsgs - newTotalSumOfMsgs ));
if ( std::abs( totalSumOfMsgs - newTotalSumOfMsgs ) <
options.convergency )
break;
totalSumOfMsgs = newTotalSumOfMsgs;
// Show messages
/*cout << "Iteration:" << iteration << endl;
for ( size_t i = 0; i < messages.size(); i++ )
{
cout << messages[i][0] << " " << messages[i][1] << endl;
}*/
} // Iterations
return 1;
}
double Sampler::fullIntegrate( const VectorXd &distribution, double delta)
{
return distribution.sum()*delta;
}
void CTRPBPInference::infer(CGraph &graph,
map<size_t,VectorXd> &nodeBeliefs,
map<size_t,MatrixXd> &edgeBeliefs,
double &logZ)
{
//
// Algorithm workflow:
// 1. Compute the messages passed
// 2. Compute node beliefs
// 3. Compute edge beliefs
// 4. Compute logZ
//
nodeBeliefs.clear();
edgeBeliefs.clear();
const vector<CNodePtr> nodes = graph.getNodes();
const vector<CEdgePtr> edges = graph.getEdges();
multimap<size_t,CEdgePtr> edges_f = graph.getEdgesF();
size_t N_nodes = nodes.size();
size_t N_edges = edges.size();
//
// 1. Create spanning trees
//
bool allNodesAdded = false;
vector<vector<size_t > > v_trees;
vector<bool> v_addedNodes(N_nodes,false);
map<size_t,size_t> addedNodesMap;
for (size_t i = 0; i < N_nodes; i++)
addedNodesMap[ nodes[i]->getID() ] = i;
while (!allNodesAdded)
{
allNodesAdded = true;
vector<size_t> tree;
getSpanningTree( graph, tree );
// Check that the tree is not empty
if ( tree.size() )
v_trees.push_back( tree );
cout << "Tree: ";
for ( size_t i_node = 0; i_node < tree.size(); i_node++ )
{
v_addedNodes[ addedNodesMap[tree[i_node]] ] = true;
cout << tree[i_node] << " ";
}
cout << endl;
for ( size_t i_node = 0; i_node < N_nodes; i_node++ )
if ( !v_addedNodes[i_node] )
{
allNodesAdded = false;
break;
}
}
//
// 1. Compute messages passed in each tree until convergence
//
vector<vector<VectorXd> > messages;
bool maximize = false;
double totalSumOfMsgs = std::numeric_limits<double>::max();
size_t iteration;
for ( iteration = 0; iteration < m_options.maxIterations; iteration++ )
{
for ( size_t i_tree=0; i_tree < v_trees.size(); i_tree++ )
messagesLBP( graph, m_options, messages, maximize, v_trees[i_tree] );
double newTotalSumOfMsgs = 0;
for ( size_t i = 0; i < N_edges; i++ )
{
newTotalSumOfMsgs += messages[i][0].sum() + messages[i][1].sum();
}
if ( std::abs( totalSumOfMsgs - newTotalSumOfMsgs ) <
m_options.convergency )
break;
totalSumOfMsgs = newTotalSumOfMsgs;
}
//
// 2. Compute node beliefs
//
for ( size_t nodeIndex = 0; nodeIndex < N_nodes; nodeIndex++ )
{
const CNodePtr nodePtr = graph.getNode( nodeIndex );
size_t nodeID = nodePtr->getID();
VectorXd nodePotPlusIncMsg = nodePtr->getPotentials( m_options.considerNodeFixedValues );
NEIGHBORS_IT neighbors = edges_f.equal_range(nodeID);
//
// Get the messages for all the neighbors, and multiply them with the node potential
//
for ( multimap<size_t,CEdgePtr>::iterator itNeigbhor = neighbors.first;
itNeigbhor != neighbors.second;
itNeigbhor++ )
{
CEdgePtr edgePtr( (*itNeigbhor).second );
size_t edgeIndex = graph.getEdgeIndex( edgePtr->getID() );
if ( !edgePtr->getNodePosition( nodeID ) ) // nodeID is the first node in the edge
nodePotPlusIncMsg = nodePotPlusIncMsg.cwiseProduct(messages[ edgeIndex ][ 1 ]);
else // nodeID is the second node in the dege
nodePotPlusIncMsg = nodePotPlusIncMsg.cwiseProduct(messages[ edgeIndex ][ 0 ]);
}
// Normalize
nodePotPlusIncMsg = nodePotPlusIncMsg / nodePotPlusIncMsg.sum();
nodeBeliefs[ nodeID ] = nodePotPlusIncMsg;
//cout << "Beliefs of node " << nodeIndex << endl << nodePotPlusIncMsg << endl;
}
//
// 3. Compute edge beliefs
//
for ( size_t edgeIndex = 0; edgeIndex < N_edges; edgeIndex++ )
{
CEdgePtr edgePtr = edges[edgeIndex];
size_t edgeID = edgePtr->getID();
size_t ID1, ID2;
edgePtr->getNodesID( ID1, ID2 );
MatrixXd edgePotentials = edgePtr->getPotentials();
MatrixXd edgeBelief = edgePotentials;
VectorXd &message1To2 = messages[edgeIndex][0];
VectorXd &message2To1 = messages[edgeIndex][1];
//cout << "----------------------" << endl;
//cout << nodeBeliefs[ ID1 ] << endl;
//cout << "----------------------" << endl;
//cout << message2To1 << endl;
VectorXd node1Belief = nodeBeliefs[ ID1 ].cwiseQuotient( message2To1 );
VectorXd node2Belief = nodeBeliefs[ ID2 ].cwiseQuotient( message1To2 );
//cout << "----------------------" << endl;
MatrixXd node1BeliefMatrix ( edgePotentials.rows(), edgePotentials.cols() );
for ( size_t row = 0; row < edgePotentials.rows(); row++ )
for ( size_t col = 0; col < edgePotentials.cols(); col++ )
node1BeliefMatrix(row,col) = node1Belief(row);
//cout << "Node 1 belief matrix: " << endl << node1BeliefMatrix << endl;
edgeBelief = edgeBelief.cwiseProduct( node1BeliefMatrix );
MatrixXd node2BeliefMatrix ( edgePotentials.rows(), edgePotentials.cols() );
for ( size_t row = 0; row < edgePotentials.rows(); row++ )
for ( size_t col = 0; col < edgePotentials.cols(); col++ )
node2BeliefMatrix(row,col) = node2Belief(col);
//cout << "Node 2 belief matrix: " << endl << node2BeliefMatrix << endl;
edgeBelief = edgeBelief.cwiseProduct( node2BeliefMatrix );
//cout << "Edge potentials" << endl << edgePotentials << endl;
//cout << "Edge beliefs" << endl << edgeBelief << endl;
// Normalize
edgeBelief = edgeBelief / edgeBelief.sum();
edgeBeliefs[ edgeID ] = edgeBelief;
}
//
// 4. Compute logZ
//
double energyNodes = 0;
double energyEdges = 0;
double entropyNodes = 0;
double entropyEdges = 0;
// Compute energy and entropy from nodes
for ( size_t nodeIndex = 0; nodeIndex < nodes.size(); nodeIndex++ )
{
CNodePtr nodePtr = nodes[ nodeIndex ];
size_t nodeID = nodePtr->getID();
size_t N_Neighbors = graph.getNumberOfNodeNeighbors( nodeID );
// Useful computations and shorcuts
VectorXd &nodeBelief = nodeBeliefs[nodeID];
VectorXd logNodeBelief = nodeBeliefs[nodeID].array().log();
VectorXd nodePotentials = nodePtr->getPotentials( m_options.considerNodeFixedValues );
VectorXd logNodePotentials = nodePotentials.array().log();
// Entropy from the node
energyNodes += N_Neighbors*( nodeBelief.cwiseProduct( logNodeBelief ).sum() );
// Energy from the node
entropyNodes += N_Neighbors*( nodeBelief.cwiseProduct( logNodePotentials ).sum() );
}
// Compute energy and entropy from nodes
for ( size_t edgeIndex = 0; edgeIndex < N_edges; edgeIndex++ )
{
CEdgePtr edgePtr = edges[ edgeIndex ];
size_t edgeID = edgePtr->getID();
// Useful computations and shorcuts
MatrixXd &edgeBelief = edgeBeliefs[ edgeID ];
MatrixXd logEdgeBelief = edgeBelief.array().log();
MatrixXd &edgePotentials = edgePtr->getPotentials();
MatrixXd logEdgePotentials = edgePotentials.array().log();
// Entropy from the edge
energyEdges += edgeBelief.cwiseProduct( logEdgeBelief ).sum();
// Energy from the edge
entropyEdges += edgeBelief.cwiseProduct( logEdgePotentials ).sum();
}
// Final Bethe free energy
double BethefreeEnergy = ( energyNodes - energyEdges ) - ( entropyNodes - entropyEdges );
// Compute logZ
logZ = - BethefreeEnergy;
}