int main(const int argc, const char *argv[]) {
// Read graph from file
string g2oFile;
if (argc < 2)
g2oFile = findExampleDataFile("noisyToyGraph.txt");
else
g2oFile = argv[1];
NonlinearFactorGraph::shared_ptr graph;
Values::shared_ptr initial;
boost::tie(graph, initial) = readG2o(g2oFile);
// Add prior on the pose having index (key) = 0
NonlinearFactorGraph graphWithPrior = *graph;
noiseModel::Diagonal::shared_ptr priorModel = //
noiseModel::Diagonal::Variances((Vector(3) << 1e-6, 1e-6, 1e-8));
graphWithPrior.add(PriorFactor<Pose2>(0, Pose2(), priorModel));
graphWithPrior.print();
std::cout << "Computing LAGO estimate" << std::endl;
Values estimateLago = lago::initialize(graphWithPrior);
std::cout << "done!" << std::endl;
if (argc < 3) {
estimateLago.print("estimateLago");
} else {
const string outputFile = argv[2];
std::cout << "Writing results to file: " << outputFile << std::endl;
writeG2o(*graph, estimateLago, outputFile);
std::cout << "done! " << std::endl;
}
return 0;
}
int main(int argc, char** argv) {
// 1. Create a factor graph container and add factors to it
NonlinearFactorGraph graph;
// 2a. Add a prior on the first pose, setting it to the origin
// A prior factor consists of a mean and a noise model (covariance matrix)
Pose2 prior(0.0, 0.0, 0.0); // prior at origin
noiseModel::Diagonal::shared_ptr priorNoise = noiseModel::Diagonal::Sigmas(Vector_(3, 0.3, 0.3, 0.1));
graph.add(PriorFactor<Pose2>(1, prior, priorNoise));
// 2b. Add odometry factors
// For simplicity, we will use the same noise model for each odometry factor
noiseModel::Diagonal::shared_ptr odometryNoise = noiseModel::Diagonal::Sigmas(Vector_(3, 0.2, 0.2, 0.1));
// Create odometry (Between) factors between consecutive poses
graph.add(BetweenFactor<Pose2>(1, 2, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
graph.add(BetweenFactor<Pose2>(2, 3, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
graph.add(BetweenFactor<Pose2>(3, 4, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
graph.add(BetweenFactor<Pose2>(4, 5, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
// 2c. Add the loop closure constraint
// This factor encodes the fact that we have returned to the same pose. In real systems,
// these constraints may be identified in many ways, such as appearance-based techniques
// with camera images.
// We will use another Between Factor to enforce this constraint, with the distance set to zero,
noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Sigmas(Vector_(3, 0.2, 0.2, 0.1));
graph.add(BetweenFactor<Pose2>(5, 1, Pose2(0.0, 0.0, 0.0), model));
graph.print("\nFactor Graph:\n"); // print
// 3. Create the data structure to hold the initialEstimate estimate to the solution
// For illustrative purposes, these have been deliberately set to incorrect values
Values initialEstimate;
initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2));
initialEstimate.insert(2, Pose2(2.3, 0.1, 1.1));
initialEstimate.insert(3, Pose2(2.1, 1.9, 2.8));
initialEstimate.insert(4, Pose2(-.3, 2.5, 4.2));
initialEstimate.insert(5, Pose2(0.1,-0.7, 5.8));
initialEstimate.print("\nInitial Estimate:\n"); // print
// 4. Single Step Optimization using Levenberg-Marquardt
LevenbergMarquardtParams parameters;
parameters.verbosity = NonlinearOptimizerParams::ERROR;
parameters.verbosityLM = LevenbergMarquardtParams::LAMBDA;
parameters.linearSolverType = SuccessiveLinearizationParams::CONJUGATE_GRADIENT;
{
parameters.iterativeParams = boost::make_shared<SubgraphSolverParameters>();
LevenbergMarquardtOptimizer optimizer(graph, initialEstimate, parameters);
Values result = optimizer.optimize();
result.print("Final Result:\n");
cout << "subgraph solver final error = " << graph.error(result) << endl;
}
return 0;
}
/* ************************************************************************* */
int main(int argc, char* argv[]) {
// Define the camera calibration parameters
Cal3_S2::shared_ptr K(new Cal3_S2(50.0, 50.0, 0.0, 50.0, 50.0));
// Define the camera observation noise model
noiseModel::Isotropic::shared_ptr measurementNoise = noiseModel::Isotropic::Sigma(2, 1.0); // one pixel in u and v
// Create the set of ground-truth landmarks
vector<Point3> points = createPoints();
// Create the set of ground-truth poses
vector<Pose3> poses = createPoses();
// Create a factor graph
NonlinearFactorGraph graph;
// Add a prior on pose x1. This indirectly specifies where the origin is.
noiseModel::Diagonal::shared_ptr poseNoise = noiseModel::Diagonal::Sigmas((Vector(6) << Vector3::Constant(0.3), Vector3::Constant(0.1))); // 30cm std on x,y,z 0.1 rad on roll,pitch,yaw
graph.push_back(PriorFactor<Pose3>(Symbol('x', 0), poses[0], poseNoise)); // add directly to graph
// Simulated measurements from each camera pose, adding them to the factor graph
for (size_t i = 0; i < poses.size(); ++i) {
for (size_t j = 0; j < points.size(); ++j) {
SimpleCamera camera(poses[i], *K);
Point2 measurement = camera.project(points[j]);
graph.push_back(GenericProjectionFactor<Pose3, Point3, Cal3_S2>(measurement, measurementNoise, Symbol('x', i), Symbol('l', j), K));
}
}
// Because the structure-from-motion problem has a scale ambiguity, the problem is still under-constrained
// Here we add a prior on the position of the first landmark. This fixes the scale by indicating the distance
// between the first camera and the first landmark. All other landmark positions are interpreted using this scale.
noiseModel::Isotropic::shared_ptr pointNoise = noiseModel::Isotropic::Sigma(3, 0.1);
graph.push_back(PriorFactor<Point3>(Symbol('l', 0), points[0], pointNoise)); // add directly to graph
graph.print("Factor Graph:\n");
// Create the data structure to hold the initial estimate to the solution
// Intentionally initialize the variables off from the ground truth
Values initialEstimate;
for (size_t i = 0; i < poses.size(); ++i)
initialEstimate.insert(Symbol('x', i), poses[i].compose(Pose3(Rot3::rodriguez(-0.1, 0.2, 0.25), Point3(0.05, -0.10, 0.20))));
for (size_t j = 0; j < points.size(); ++j)
initialEstimate.insert(Symbol('l', j), points[j].compose(Point3(-0.25, 0.20, 0.15)));
initialEstimate.print("Initial Estimates:\n");
/* Optimize the graph and print results */
Values result = DoglegOptimizer(graph, initialEstimate).optimize();
result.print("Final results:\n");
return 0;
}
int main(int argc, char** argv) {
// 1. Create a factor graph container and add factors to it
NonlinearFactorGraph graph;
// 2a. Add a prior on the first pose, setting it to the origin
Pose2 prior(0.0, 0.0, 0.0); // prior at origin
noiseModel::Diagonal::shared_ptr priorNoise = noiseModel::Diagonal::Sigmas(Vector3(0.3, 0.3, 0.1));
graph.push_back(PriorFactor<Pose2>(1, prior, priorNoise));
// 2b. Add odometry factors
noiseModel::Diagonal::shared_ptr odometryNoise = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
graph.push_back(BetweenFactor<Pose2>(1, 2, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
graph.push_back(BetweenFactor<Pose2>(2, 3, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
graph.push_back(BetweenFactor<Pose2>(3, 4, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
graph.push_back(BetweenFactor<Pose2>(4, 5, Pose2(2.0, 0.0, M_PI_2), odometryNoise));
// 2c. Add the loop closure constraint
noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
graph.push_back(BetweenFactor<Pose2>(5, 1, Pose2(0.0, 0.0, 0.0), model));
graph.print("\nFactor Graph:\n"); // print
// 3. Create the data structure to hold the initialEstimate estimate to the solution
Values initialEstimate;
initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2));
initialEstimate.insert(2, Pose2(2.3, 0.1, 1.1));
initialEstimate.insert(3, Pose2(2.1, 1.9, 2.8));
initialEstimate.insert(4, Pose2(-.3, 2.5, 4.2));
initialEstimate.insert(5, Pose2(0.1,-0.7, 5.8));
initialEstimate.print("\nInitial Estimate:\n"); // print
// 4. Single Step Optimization using Levenberg-Marquardt
LevenbergMarquardtParams parameters;
parameters.verbosity = NonlinearOptimizerParams::ERROR;
parameters.verbosityLM = LevenbergMarquardtParams::LAMBDA;
// LM is still the outer optimization loop, but by specifying "Iterative" below
// We indicate that an iterative linear solver should be used.
// In addition, the *type* of the iterativeParams decides on the type of
// iterative solver, in this case the SPCG (subgraph PCG)
parameters.linearSolverType = NonlinearOptimizerParams::Iterative;
parameters.iterativeParams = boost::make_shared<SubgraphSolverParameters>();
LevenbergMarquardtOptimizer optimizer(graph, initialEstimate, parameters);
Values result = optimizer.optimize();
result.print("Final Result:\n");
cout << "subgraph solver final error = " << graph.error(result) << endl;
return 0;
}
int main(int argc, char** argv) {
// 1. Create a factor graph container and add factors to it
NonlinearFactorGraph graph;
// 2a. Add odometry factors
// For simplicity, we will use the same noise model for each odometry factor
noiseModel::Diagonal::shared_ptr odometryNoise = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
// Create odometry (Between) factors between consecutive poses
graph.add(BetweenFactor<Pose2>(1, 2, Pose2(2.0, 0.0, 0.0), odometryNoise));
graph.add(BetweenFactor<Pose2>(2, 3, Pose2(2.0, 0.0, 0.0), odometryNoise));
// 2b. Add "GPS-like" measurements
// We will use our custom UnaryFactor for this.
noiseModel::Diagonal::shared_ptr unaryNoise = noiseModel::Diagonal::Sigmas(Vector2(0.1, 0.1)); // 10cm std on x,y
graph.add(boost::make_shared<UnaryFactor>(1, 0.0, 0.0, unaryNoise));
graph.add(boost::make_shared<UnaryFactor>(2, 2.0, 0.0, unaryNoise));
graph.add(boost::make_shared<UnaryFactor>(3, 4.0, 0.0, unaryNoise));
graph.print("\nFactor Graph:\n"); // print
// 3. Create the data structure to hold the initialEstimate estimate to the solution
// For illustrative purposes, these have been deliberately set to incorrect values
Values initialEstimate;
initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2));
initialEstimate.insert(2, Pose2(2.3, 0.1, -0.2));
initialEstimate.insert(3, Pose2(4.1, 0.1, 0.1));
initialEstimate.print("\nInitial Estimate:\n"); // print
// 4. Optimize using Levenberg-Marquardt optimization. The optimizer
// accepts an optional set of configuration parameters, controlling
// things like convergence criteria, the type of linear system solver
// to use, and the amount of information displayed during optimization.
// Here we will use the default set of parameters. See the
// documentation for the full set of parameters.
LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
Values result = optimizer.optimize();
result.print("Final Result:\n");
// 5. Calculate and print marginal covariances for all variables
Marginals marginals(graph, result);
cout << "x1 covariance:\n" << marginals.marginalCovariance(1) << endl;
cout << "x2 covariance:\n" << marginals.marginalCovariance(2) << endl;
cout << "x3 covariance:\n" << marginals.marginalCovariance(3) << endl;
return 0;
}
int main(int argc, char** argv) {
// Create an empty nonlinear factor graph
NonlinearFactorGraph graph;
// Add a prior on the first pose, setting it to the origin
// A prior factor consists of a mean and a noise model (covariance matrix)
Pose2 priorMean(0.0, 0.0, 0.0); // prior at origin
noiseModel::Diagonal::shared_ptr priorNoise = noiseModel::Diagonal::Sigmas(Vector3(0.3, 0.3, 0.1));
graph.add(PriorFactor<Pose2>(1, priorMean, priorNoise));
// Add odometry factors
Pose2 odometry(2.0, 0.0, 0.0);
// For simplicity, we will use the same noise model for each odometry factor
noiseModel::Diagonal::shared_ptr odometryNoise = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
// Create odometry (Between) factors between consecutive poses
graph.add(BetweenFactor<Pose2>(1, 2, odometry, odometryNoise));
graph.add(BetweenFactor<Pose2>(2, 3, odometry, odometryNoise));
graph.print("\nFactor Graph:\n"); // print
// Create the data structure to hold the initialEstimate estimate to the solution
// For illustrative purposes, these have been deliberately set to incorrect values
Values initial;
initial.insert(1, Pose2(0.5, 0.0, 0.2));
initial.insert(2, Pose2(2.3, 0.1, -0.2));
initial.insert(3, Pose2(4.1, 0.1, 0.1));
initial.print("\nInitial Estimate:\n"); // print
// optimize using Levenberg-Marquardt optimization
Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
result.print("Final Result:\n");
// Calculate and print marginal covariances for all variables
cout.precision(2);
Marginals marginals(graph, result);
cout << "x1 covariance:\n" << marginals.marginalCovariance(1) << endl;
cout << "x2 covariance:\n" << marginals.marginalCovariance(2) << endl;
cout << "x3 covariance:\n" << marginals.marginalCovariance(3) << endl;
return 0;
}
int main() {
/**
* Step 1: Create a factor to express a unary constraint
* The "prior" in this case is the measurement from a sensor,
* with a model of the noise on the measurement.
*
* The "Key" created here is a label used to associate parts of the
* state (stored in "RotValues") with particular factors. They require
* an index to allow for lookup, and should be unique.
*
* In general, creating a factor requires:
* - A key or set of keys labeling the variables that are acted upon
* - A measurement value
* - A measurement model with the correct dimensionality for the factor
*/
Rot2 prior = Rot2::fromAngle(30 * degree);
prior.print("goal angle");
noiseModel::Isotropic::shared_ptr model = noiseModel::Isotropic::Sigma(1, 1 * degree);
Symbol key('x',1);
PriorFactor<Rot2> factor(key, prior, model);
/**
* Step 2: Create a graph container and add the factor to it
* Before optimizing, all factors need to be added to a Graph container,
* which provides the necessary top-level functionality for defining a
* system of constraints.
*
* In this case, there is only one factor, but in a practical scenario,
* many more factors would be added.
*/
NonlinearFactorGraph graph;
graph.add(factor);
graph.print("full graph");
/**
* Step 3: Create an initial estimate
* An initial estimate of the solution for the system is necessary to
* start optimization. This system state is the "RotValues" structure,
* which is similar in structure to a STL map, in that it maps
* keys (the label created in step 1) to specific values.
*
* The initial estimate provided to optimization will be used as
* a linearization point for optimization, so it is important that
* all of the variables in the graph have a corresponding value in
* this structure.
*
* The interface to all RotValues types is the same, it only depends
* on the type of key used to find the appropriate value map if there
* are multiple types of variables.
*/
Values initial;
initial.insert(key, Rot2::fromAngle(20 * degree));
initial.print("initial estimate");
/**
* Step 4: Optimize
* After formulating the problem with a graph of constraints
* and an initial estimate, executing optimization is as simple
* as calling a general optimization function with the graph and
* initial estimate. This will yield a new RotValues structure
* with the final state of the optimization.
*/
Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
result.print("final result");
return 0;
}
/* ************************************************************************* */
int main(int argc, char* argv[]) {
// Define the camera calibration parameters
Cal3_S2::shared_ptr K(new Cal3_S2(50.0, 50.0, 0.0, 50.0, 50.0));
// Define the camera observation noise model
noiseModel::Isotropic::shared_ptr measurementNoise =
noiseModel::Isotropic::Sigma(2, 1.0); // one pixel in u and v
// Create the set of ground-truth landmarks and poses
vector<Point3> points = createPoints();
vector<Pose3> poses = createPoses();
// Create a factor graph
NonlinearFactorGraph graph;
// Simulated measurements from each camera pose, adding them to the factor graph
for (size_t j = 0; j < points.size(); ++j) {
// every landmark represent a single landmark, we use shared pointer to init the factor, and then insert measurements.
SmartFactor::shared_ptr smartfactor(new SmartFactor(measurementNoise, K));
for (size_t i = 0; i < poses.size(); ++i) {
// generate the 2D measurement
Camera camera(poses[i], K);
Point2 measurement = camera.project(points[j]);
// call add() function to add measurement into a single factor, here we need to add:
// 1. the 2D measurement
// 2. the corresponding camera's key
// 3. camera noise model
// 4. camera calibration
smartfactor->add(measurement, i);
}
// insert the smart factor in the graph
graph.push_back(smartfactor);
}
// Add a prior on pose x0. This indirectly specifies where the origin is.
// 30cm std on x,y,z 0.1 rad on roll,pitch,yaw
noiseModel::Diagonal::shared_ptr noise = noiseModel::Diagonal::Sigmas(
(Vector(6) << Vector3::Constant(0.3), Vector3::Constant(0.1)).finished());
graph.push_back(PriorFactor<Pose3>(0, poses[0], noise));
// Because the structure-from-motion problem has a scale ambiguity, the problem is
// still under-constrained. Here we add a prior on the second pose x1, so this will
// fix the scale by indicating the distance between x0 and x1.
// Because these two are fixed, the rest of the poses will be also be fixed.
graph.push_back(PriorFactor<Pose3>(1, poses[1], noise)); // add directly to graph
graph.print("Factor Graph:\n");
// Create the initial estimate to the solution
// Intentionally initialize the variables off from the ground truth
Values initialEstimate;
Pose3 delta(Rot3::Rodrigues(-0.1, 0.2, 0.25), Point3(0.05, -0.10, 0.20));
for (size_t i = 0; i < poses.size(); ++i)
initialEstimate.insert(i, poses[i].compose(delta));
initialEstimate.print("Initial Estimates:\n");
// Optimize the graph and print results
LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
Values result = optimizer.optimize();
result.print("Final results:\n");
// A smart factor represent the 3D point inside the factor, not as a variable.
// The 3D position of the landmark is not explicitly calculated by the optimizer.
// To obtain the landmark's 3D position, we use the "point" method of the smart factor.
Values landmark_result;
for (size_t j = 0; j < points.size(); ++j) {
// The graph stores Factor shared_ptrs, so we cast back to a SmartFactor first
SmartFactor::shared_ptr smart = boost::dynamic_pointer_cast<SmartFactor>(graph[j]);
if (smart) {
// The output of point() is in boost::optional<Point3>, as sometimes
// the triangulation operation inside smart factor will encounter degeneracy.
boost::optional<Point3> point = smart->point(result);
if (point) // ignore if boost::optional return NULL
landmark_result.insert(j, *point);
}
}
landmark_result.print("Landmark results:\n");
cout << "final error: " << graph.error(result) << endl;
cout << "number of iterations: " << optimizer.iterations() << endl;
return 0;
}
int main(int argc, char** argv) {
// 1. Create a factor graph container and add factors to it
NonlinearFactorGraph graph;
// 2a. Add a prior on the first pose, setting it to the origin
// A prior factor consists of a mean and a noise model (covariance matrix)
noiseModel::Diagonal::shared_ptr priorNoise = noiseModel::Diagonal::Sigmas(Vector_(3, 0.3, 0.3, 0.1));
graph.add(PriorFactor<Pose2>(1, Pose2(0, 0, 0), priorNoise));
// For simplicity, we will use the same noise model for odometry and loop closures
noiseModel::Diagonal::shared_ptr model = noiseModel::Diagonal::Sigmas(Vector_(3, 0.2, 0.2, 0.1));
// 2b. Add odometry factors
// Create odometry (Between) factors between consecutive poses
graph.add(BetweenFactor<Pose2>(1, 2, Pose2(2, 0, 0 ), model));
graph.add(BetweenFactor<Pose2>(2, 3, Pose2(2, 0, M_PI_2), model));
graph.add(BetweenFactor<Pose2>(3, 4, Pose2(2, 0, M_PI_2), model));
graph.add(BetweenFactor<Pose2>(4, 5, Pose2(2, 0, M_PI_2), model));
// 2c. Add the loop closure constraint
// This factor encodes the fact that we have returned to the same pose. In real systems,
// these constraints may be identified in many ways, such as appearance-based techniques
// with camera images. We will use another Between Factor to enforce this constraint:
graph.add(BetweenFactor<Pose2>(5, 2, Pose2(2, 0, M_PI_2), model));
graph.print("\nFactor Graph:\n"); // print
// 3. Create the data structure to hold the initialEstimate estimate to the solution
// For illustrative purposes, these have been deliberately set to incorrect values
Values initialEstimate;
initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2 ));
initialEstimate.insert(2, Pose2(2.3, 0.1, -0.2 ));
initialEstimate.insert(3, Pose2(4.1, 0.1, M_PI_2));
initialEstimate.insert(4, Pose2(4.0, 2.0, M_PI ));
initialEstimate.insert(5, Pose2(2.1, 2.1, -M_PI_2));
initialEstimate.print("\nInitial Estimate:\n"); // print
// 4. Optimize the initial values using a Gauss-Newton nonlinear optimizer
// The optimizer accepts an optional set of configuration parameters,
// controlling things like convergence criteria, the type of linear
// system solver to use, and the amount of information displayed during
// optimization. We will set a few parameters as a demonstration.
GaussNewtonParams parameters;
// Stop iterating once the change in error between steps is less than this value
parameters.relativeErrorTol = 1e-5;
// Do not perform more than N iteration steps
parameters.maxIterations = 100;
// Create the optimizer ...
GaussNewtonOptimizer optimizer(graph, initialEstimate, parameters);
// ... and optimize
Values result = optimizer.optimize();
result.print("Final Result:\n");
// 5. Calculate and print marginal covariances for all variables
cout.precision(3);
Marginals marginals(graph, result);
cout << "x1 covariance:\n" << marginals.marginalCovariance(1) << endl;
cout << "x2 covariance:\n" << marginals.marginalCovariance(2) << endl;
cout << "x3 covariance:\n" << marginals.marginalCovariance(3) << endl;
cout << "x4 covariance:\n" << marginals.marginalCovariance(4) << endl;
cout << "x5 covariance:\n" << marginals.marginalCovariance(5) << endl;
return 0;
}
int main(int argc, char** argv) {
// Create a factor graph container
NonlinearFactorGraph graph;
// first state prior noise model (covariance matrix)
noiseModel::Diagonal::shared_ptr priorModel = noiseModel::Diagonal::Sigmas(Vector2(0.2, 0.2));
// add prior factor on first state (at origin)
graph.add(PriorFactor<Point2c>(Symbol('x', 1), Point2c(0, 0), priorModel));
// odometry measurement noise model (covariance matrix)
noiseModel::Diagonal::shared_ptr odomModel = noiseModel::Diagonal::Sigmas(Vector2(0.5, 0.5));
// Add odometry factors
// Create odometry (Between) factors between consecutive point2c
graph.add(BetweenFactor<Point2c>(Symbol('x', 1), Symbol('x', 2), Point2c(2, 0), odomModel));
graph.add(BetweenFactor<Point2c>(Symbol('x', 2), Symbol('x', 3), Point2c(2, 0), odomModel));
graph.add(BetweenFactor<Point2c>(Symbol('x', 3), Symbol('x', 4), Point2c(2, 0), odomModel));
graph.add(BetweenFactor<Point2c>(Symbol('x', 4), Symbol('x', 5), Point2c(2, 0), odomModel));
// print factor graph
graph.print("\nFactor Graph:\n");
// initial varible values for the optimization
// add random noise from ground truth values
Values initials;
initials.insert(Symbol('x', 1), Point2c(0.2, -0.3));
initials.insert(Symbol('x', 2), Point2c(2.1, 0.3));
initials.insert(Symbol('x', 3), Point2c(3.9, -0.1));
initials.insert(Symbol('x', 4), Point2c(5.9, -0.3));
initials.insert(Symbol('x', 5), Point2c(8.2, 0.1));
// print initial values
initials.print("\nInitial Values:\n");
// Use Gauss-Newton method optimizes the initial values
GaussNewtonParams parameters;
// print per iteration
parameters.setVerbosity("ERROR");
// optimize!
GaussNewtonOptimizer optimizer(graph, initials, parameters);
Values results = optimizer.optimize();
// print final values
results.print("Final Result:\n");
// Calculate marginal covariances for all poses
Marginals marginals(graph, results);
// print marginal covariances
cout << "x1 covariance:\n" << marginals.marginalCovariance(Symbol('x', 1)) << endl;
cout << "x2 covariance:\n" << marginals.marginalCovariance(Symbol('x', 2)) << endl;
cout << "x3 covariance:\n" << marginals.marginalCovariance(Symbol('x', 3)) << endl;
cout << "x4 covariance:\n" << marginals.marginalCovariance(Symbol('x', 4)) << endl;
cout << "x5 covariance:\n" << marginals.marginalCovariance(Symbol('x', 5)) << endl;
return 0;
}