/**
* Calculate covariances for both points and poses up to the given time step.
*/
void covariances(unsigned int step, list<MatrixXd>& point_marginals,
list<MatrixXd>& pose_marginals) {
// make sure return arguments are empty
point_marginals.clear();
pose_marginals.clear();
// combining everything into one call is faster,
// as it avoids recalculating commonly needed entries
Covariances::node_lists_t node_lists;
for (unsigned int i = 0; i < step; i++) {
list<Node*> entry;
entry.push_back(loader->pose_nodes()[i]);
node_lists.push_back(entry);
}
for (unsigned int i = 0; i < loader->num_points(step); i++) {
list<Node*> entry;
entry.push_back(loader->point_nodes()[i]);
node_lists.push_back(entry);
}
pose_marginals = slam.covariances().marginal(node_lists);
// split into points and poses
if (pose_marginals.size() > 0) {
list<MatrixXd>::iterator center = pose_marginals.begin();
for (unsigned int i = 0; i < step; i++, center++)
;
point_marginals.splice(point_marginals.begin(), pose_marginals, center,
pose_marginals.end());
}
}
int main(int argc, const char* argv[]) {
Pose2d origin;
Noise noise = SqrtInformation(10. * eye(3));
Pose2d_Node* pose_node_1 = new Pose2d_Node(); // create node
slam.add_node(pose_node_1); // add it to the Slam graph
Pose2d_Factor* prior = new Pose2d_Factor(pose_node_1, origin, noise); // create prior measurement, an factor
slam.add_factor(prior); // add it to the Slam graph
Pose2d_Node* pose_node_2 = new Pose2d_Node(); // create node
slam.add_node(pose_node_2); // add it to the Slam graph
Pose2d delta(1., 0., 0.);
Pose2d_Pose2d_Factor* odo = new Pose2d_Pose2d_Factor(pose_node_1, pose_node_2, delta, noise);
slam.add_factor(odo);
slam.batch_optimization();
#if 0
const Covariances& covariances = slam.covariances();
#else
// operate on a copy (just an example, cloning is useful for running
// covariance recovery in a separate thread)
const Covariances& covariances = slam.covariances().clone();
#endif
// recovering the full covariance matrix
cout << "Full covariance matrix:" << endl;
MatrixXd cov_full = covariances.marginal(slam.get_nodes());
cout << cov_full << endl << endl;
// sanity checking by inverting the information matrix, not using R
SparseSystem Js = slam.jacobian();
MatrixXd J(Js.num_cols(), Js.num_cols());
for (int r=0; r<Js.num_cols(); r++) {
for (int c=0; c<Js.num_cols(); c++) {
J(r,c) = Js(r,c);
}
}
MatrixXd H = J.transpose() * J;
MatrixXd cov_full2 = H.inverse();
cout << cov_full2 << endl;
// recovering the block-diagonals only of the full covariance matrix
cout << "Block-diagonals only:" << endl;
Covariances::node_lists_t node_lists;
list<Node*> nodes;
nodes.push_back(pose_node_1);
node_lists.push_back(nodes);
nodes.clear();
nodes.push_back(pose_node_2);
node_lists.push_back(nodes);
list<MatrixXd> cov_blocks = covariances.marginal(node_lists);
int i = 1;
for (list<MatrixXd>::iterator it = cov_blocks.begin(); it!=cov_blocks.end(); it++, i++) {
cout << "block " << i << endl;
cout << *it << endl;
}
// recovering individual entries, here the right block column
cout << "Right block column:" << endl;
Covariances::node_pair_list_t node_pair_list;
node_pair_list.push_back(make_pair(pose_node_1, pose_node_2));
node_pair_list.push_back(make_pair(pose_node_2, pose_node_2));
list<MatrixXd> cov_entries = covariances.access(node_pair_list);
for (list<MatrixXd>::iterator it = cov_entries.begin(); it!=cov_entries.end(); it++) {
cout << *it << endl;
}
}
int main() {
// setup a simple graph
// known poses
Pose2d x0 (0, 0, M_PI/9.0);
Pose2d x1 (10, 10, 0.0 );
Pose2d x2 (20, 20, M_PI/6.0);
Pose2d x3 (30, 30, -M_PI/4.0);
Pose2d x4 (40, 40, -M_PI/8.0);
// known landmarks
Point2d la (100, 100);
// mesurements
Pose2d z0 = x0;
Pose2d z01 = x1.ominus(x0);
Pose2d z12 = x2.ominus(x1);
Pose2d z23 = x3.ominus(x2);
Pose2d z34 = x4.ominus(x3);
Pose2d z13 = x3.ominus(x1);
// landmark measurement
Point2d z1a = x1.transform_to(la);
// add noise to measurements
double sigma = 0.01;
MatrixXd Q = sigma*sigma*eye(3);
Noise Qsqinf = Information(Q.inverse());
MatrixXd Q2 = sigma*sigma*eye(2);
Noise Q2sqinf = Information(Q2.inverse());
z0 = add_noise(z0, sigma);
z01 = add_noise(z01, sigma);
z12 = add_noise(z12, sigma);
z23 = add_noise(z23, sigma);
z34 = add_noise(z34, sigma);
z13 = add_noise(z13, sigma);
z1a = add_noise(z1a, sigma);
// nodes
Pose2d_Node* n0 = new Pose2d_Node();
Pose2d_Node* n1 = new Pose2d_Node();
Pose2d_Node* n2 = new Pose2d_Node();
Pose2d_Node* n3 = new Pose2d_Node();
Pose2d_Node* n4 = new Pose2d_Node();
Point2d_Node* na = new Point2d_Node();
// make graph
Slam slam;
Properties prop;
prop.verbose = true; prop.quiet = false; prop.method = GAUSS_NEWTON;
slam.set_properties(prop);
// add nodes to graph
slam.add_node(n0);
slam.add_node(n1);
slam.add_node(n2),
slam.add_node(n3);
slam.add_node(n4);
slam.add_node(na);
// create factors and add them to the graph
Pose2d_Factor* z0f = new Pose2d_Factor(n0, z0, Qsqinf);
slam.add_factor(z0f);
Pose2d_Pose2d_Factor* z01f = new Pose2d_Pose2d_Factor(n0, n1, z01, Qsqinf);
slam.add_factor(z01f);
Pose2d_Pose2d_Factor* z12f = new Pose2d_Pose2d_Factor(n1, n2, z12, Qsqinf);
slam.add_factor(z12f);
Pose2d_Pose2d_Factor* z23f = new Pose2d_Pose2d_Factor(n2, n3, z23, Qsqinf);
slam.add_factor(z23f);
Pose2d_Pose2d_Factor* z34f = new Pose2d_Pose2d_Factor(n3, n4, z34, Qsqinf);
slam.add_factor(z34f);
Pose2d_Pose2d_Factor* z13f = new Pose2d_Pose2d_Factor(n1, n3, z13, Qsqinf);
slam.add_factor(z13f);
Pose2d_Point2d_Factor* z1af = new Pose2d_Point2d_Factor(n1, na, z1a, Q2sqinf);
slam.add_factor(z1af);
slam.batch_optimization();
slam.print_stats();
ofstream f; f.open ("before.graph"); slam.write(f); f.close();
//slam.print_graph();
//print_all(slam);
// get true marginal distribution over p(x0, x2, x3, x4)
list<Node*> nodes_subset;
nodes_subset.push_back(n0);
nodes_subset.push_back(n2);
nodes_subset.push_back(n3);
nodes_subset.push_back(n4);
MatrixXd P_true = slam.covariances().marginal(nodes_subset);
//MatrixXd L_true = get_info (&slam);
VectorXd mu_true(12);
mu_true.segment<3>(0) = n0->value().vector();
mu_true.segment<3>(3) = n2->value().vector();
mu_true.segment<3>(6) = n3->value().vector();
mu_true.segment<3>(9) = n4->value().vector();
// remove node 1 using GLC ========================================
bool sparse = true; // sparse approximate or dense exact
vector<Factor*> felim = glc_elim_factors (n1); //usefull for local managment of factors
//vector<Factor*> fnew = glc_remove_node (slam, n1, sparse); // not root shifted
GLC_RootShift rs;
vector<Factor*> fnew = glc_remove_node (slam, n1, sparse, &rs); // root shifted
// ================================================================
cout << felim.size() << " factor(s) removed." << endl;
cout << fnew.size() << " new GLC factor(s) added." << endl;
slam.batch_optimization();
slam.print_stats();
f.open ("after.graph"); slam.write(f); f.close();
// get glc marginal distribution over p(x0, x2, x3, x4)
MatrixXd P_glc = slam.covariances().marginal(nodes_subset);
//MatrixXd L_glc = get_info (&slam);
VectorXd mu_glc(12);
mu_glc.segment<3>(0) = n0->value().vector();
mu_glc.segment<3>(3) = n2->value().vector();
mu_glc.segment<3>(6) = n3->value().vector();
mu_glc.segment<3>(9) = n4->value().vector();
// calcualte the KLD
int n = mu_glc.size();
double A = (P_glc.inverse() * P_true).trace();
VectorXd du = mu_glc - mu_true;
// deal with difference in angles
for(int i=0; i<du.size(); i++) {
if(i % 3 == 2)
du(i) = standardRad(du(i));
}
double B = du.transpose() * P_glc.inverse() * du;
double C = log(P_true.determinant()) - log(P_glc.determinant());
double kld = 0.5*(A + B - C - n);
cout << "KLD: " << kld << endl;
return 0;
}