/*
 * @file testSQP.cpp
 * @brief demos of SQP using existing gtsam components
 * @author Alex Cunningham
 */

#include <iostream>
#include <cmath>
#include <boost/assign/std/list.hpp> // for operator +=
#include <boost/assign/std/map.hpp> // for insert
#include <boost/foreach.hpp>
#include <boost/shared_ptr.hpp>
#include <CppUnitLite/TestHarness.h>

// TODO: DANGEROUS, create shared pointers
#define GTSAM_DANGEROUS_GAUSSIAN 2
#define GTSAM_MAGIC_KEY

#include <Pose3.h>
#include <GaussianFactorGraph.h>
#include <NonlinearOptimizer.h>
#include <SQPOptimizer.h>
#include <simulated2D.h>
#include <Ordering.h>
#include <visualSLAM.h>

// templated implementations
#include <NonlinearFactorGraph-inl.h>
#include <NonlinearConstraint-inl.h>
#include <NonlinearOptimizer-inl.h>
#include <SQPOptimizer-inl.h>

using namespace std;
using namespace gtsam;
using namespace boost;
using namespace boost::assign;

// Models to use
SharedDiagonal probModel1 = sharedSigma(1,1.0);
SharedDiagonal probModel2 = sharedSigma(2,1.0);
SharedDiagonal constraintModel1 = noiseModel::Constrained::All(1);

// trick from some reading group
#define FOREACH_PAIR( KEY, VAL, COL) BOOST_FOREACH (boost::tie(KEY,VAL),COL)

///* *********************************************************************
// * This example uses a nonlinear objective function and
// * nonlinear equality constraint.  The formulation is actually
// * the Cholesky form that creates the full Hessian explicitly,
// * which should really be avoided with our QR-based machinery.
// *
// * Note: the update equation used here has a fixed step size
// * and gain that is rather arbitrarily chosen, and as such,
// * will take a silly number of iterations.
// */
//TEST (SQP, problem1_cholesky ) {
//	bool verbose = false;
//	// use a nonlinear function of f(x) = x^2+y^2
//	// nonlinear equality constraint: g(x) = x^2-5-y=0
//	// Lagrangian: f(x) + \lambda*g(x)
//
//	// state structure: [x y \lambda]
//	VectorConfig init, state;
//	init.insert("x", Vector_(1, 1.0));
//	init.insert("y", Vector_(1, 1.0));
//	init.insert("L", Vector_(1, 1.0));
//	state = init;
//
//	if (verbose) init.print("Initial State");
//
//	// loop until convergence
//	int maxIt = 10;
//	for (int i = 0; i<maxIt; ++i) {
//		if (verbose) cout << "\n******************************\nIteration: " << i+1 << endl;
//
//		// extract the states
//		double x, y, lambda;
//		x = state["x"](0);
//		y = state["y"](0);
//		lambda = state["L"](0);
//
//		// calculate the components
//		Matrix H1, H2, gradG;
//		Vector gradL, gx;
//
//		// hessian of lagrangian function, in two columns:
//		H1 = Matrix_(2,1,
//				2.0+2.0*lambda,
//				0.0);
//		H2 = Matrix_(2,1,
//				0.0,
//				2.0);
//
//		// deriviative of lagrangian function
//		gradL = Vector_(2,
//				2.0*x*(1+lambda),
//				2.0*y-lambda);
//
//		// constraint derivatives
//		gradG = Matrix_(2,1,
//				2.0*x,
//				0.0);
//
//		// constraint value
//		gx = Vector_(1,
//				x*x-5-y);
//
//		// create a factor for the states
//		GaussianFactor::shared_ptr f1(new
//				GaussianFactor("x", H1, "y", H2, "L", gradG, gradL, probModel2));
//
//		// create a factor for the lagrange multiplier
//		GaussianFactor::shared_ptr f2(new
//				GaussianFactor("x", -sub(gradG, 0, 1, 0, 1),
//							   "y", -sub(gradG, 1, 2, 0, 1), -gx, constraintModel1));
//
//		// construct graph
//		GaussianFactorGraph fg;
//		fg.push_back(f1);
//		fg.push_back(f2);
//		if (verbose) fg.print("Graph");
//
//		// solve
//		Ordering ord;
//		ord += "x", "y", "L";
//		VectorConfig delta = fg.optimize(ord).scale(-1.0);
//		if (verbose) delta.print("Delta");
//
//		// update initial estimate
//		VectorConfig newState = expmap(state, delta);
//		state = newState;
//
//		if (verbose) state.print("Updated State");
//	}
//
//	// verify that it converges to the nearest optimal point
//	VectorConfig expected;
//	expected.insert("L", Vector_(1, -1.0));
//	expected.insert("x", Vector_(1, 2.12));
//	expected.insert("y", Vector_(1, -0.5));
//	CHECK(assert_equal(expected,state, 1e-2));
//}
//
///* *********************************************************************
// * This example uses a nonlinear objective function and
// * nonlinear equality constraint.  This formulation splits
// * the constraint into a factor and a linear constraint.
// *
// * This example uses the same silly number of iterations as the
// * previous example.
// */
//TEST (SQP, problem1_sqp ) {
//	bool verbose = false;
//	// use a nonlinear function of f(x) = x^2+y^2
//	// nonlinear equality constraint: g(x) = x^2-5-y=0
//	// Lagrangian: f(x) + \lambda*g(x)
//
//	// state structure: [x y \lambda]
//	VectorConfig init, state;
//	init.insert("x", Vector_(1, 1.0));
//	init.insert("y", Vector_(1, 1.0));
//	init.insert("L", Vector_(1, 1.0));
//	state = init;
//
//	if (verbose) init.print("Initial State");
//
//	// loop until convergence
//	int maxIt = 5;
//	for (int i = 0; i<maxIt; ++i) {
//		if (verbose) cout << "\n******************************\nIteration: " << i+1 << endl;
//
//		// extract the states
//		double x, y, lambda;
//		x = state["x"](0);
//		y = state["y"](0);
//		lambda = state["L"](0);
//
//		/** create the linear factor
//		 * ||h(x)-z||^2 => ||Ax-b||^2
//		 *  where:
//		 *		h(x) simply returns the inputs
//		 *		z    zeros(2)
//		 *		A 	 identity
//		 *		b	 linearization point
//		 */
//		Matrix A = eye(2);
//		Vector b = Vector_(2, x, y);
//		GaussianFactor::shared_ptr f1(
//						new GaussianFactor("x", sub(A, 0,2, 0,1), // A(:,1)
//										   "y", sub(A, 0,2, 1,2), // A(:,2)
//										   b,                     // rhs of f(x)
//										   probModel2));          // arbitrary sigma
//
//		/** create the constraint-linear factor
//		 * Provides a mechanism to use variable gain to force the constraint
//		 * \lambda*gradG*dx + d\lambda = zero
//		 * formulated in matrix form as:
//		 * [\lambda*gradG eye(1)] [dx; d\lambda] = zero
//		 */
//		Matrix gradG = Matrix_(1, 2,2*x, -1.0);
//		GaussianFactor::shared_ptr f2(
//				new GaussianFactor("x", lambda*sub(gradG, 0,1, 0,1), // scaled gradG(:,1)
//								   "y", lambda*sub(gradG, 0,1, 1,2), // scaled gradG(:,2)
//								   "L", eye(1),                      // dlambda term
//								   Vector_(1, 0.0),                  // rhs is zero
//								   probModel1));                     // arbitrary sigma
//
//		// create the actual constraint
//		// [gradG] [x; y] - g = 0
//		Vector g = Vector_(1,x*x-y-5);
//		GaussianFactor::shared_ptr c1(
//				new GaussianFactor("x", sub(gradG, 0,1, 0,1),   // slice first part of gradG
//								   "y", sub(gradG, 0,1, 1,2),   // slice second part of gradG
//								   g,                           // value of constraint function
//								   constraintModel1));          // force to constraint
//
//		// construct graph
//		GaussianFactorGraph fg;
//		fg.push_back(f1);
//		fg.push_back(f2);
//		fg.push_back(c1);
//		if (verbose) fg.print("Graph");
//
//		// solve
//		Ordering ord;
//		ord += "x", "y", "L";
//		VectorConfig delta = fg.optimize(ord);
//		if (verbose) delta.print("Delta");
//
//		// update initial estimate
//		VectorConfig newState = expmap(state, delta.scale(-1.0));
//
//		// set the state to the updated state
//		state = newState;
//
//		if (verbose) state.print("Updated State");
//	}
//
//	// verify that it converges to the nearest optimal point
//	VectorConfig expected;
//	expected.insert("x", Vector_(1, 2.12));
//	expected.insert("y", Vector_(1, -0.5));
//	CHECK(assert_equal(state["x"], expected["x"], 1e-2));
//	CHECK(assert_equal(state["y"], expected["y"], 1e-2));
//}
//
///* ********************************************************************* */
//
//typedef simulated2D::Config Config2D;
//typedef NonlinearFactorGraph<Config2D> NLGraph;
//typedef NonlinearEquality<Config2D, simulated2D::PoseKey, Point2> NLE;
//typedef boost::shared_ptr<simulated2D::Measurement > shared;
//typedef NonlinearOptimizer<NLGraph, Config2D> Optimizer;
//
//typedef TypedSymbol<Vector, 'L'> LamKey;
//
///*
// * Determining a ground truth linear system
// * with two poses seeing one landmark, with each pose
// * constrained to a particular value
// */
//TEST (SQP, two_pose_truth ) {
//	bool verbose = false;
//
//	// create a graph
//	shared_ptr<NLGraph> graph(new NLGraph);
//
//	// add the constraints on the ends
//	// position (1, 1) constraint for x1
//	// position (5, 6) constraint for x2
//	simulated2D::PoseKey x1(1), x2(2);
//	simulated2D::PointKey l1(1);
//	Point2 pt_x1(1.0, 1.0),
//		   pt_x2(5.0, 6.0);
//	shared_ptr<NLE> ef1(new NLE(x1, pt_x1)),
//			        ef2(new NLE(x2, pt_x2));
//	graph->push_back(ef1);
//	graph->push_back(ef2);
//
//	// measurement from x1 to l1
//	Point2 z1(0.0, 5.0);
//	SharedGaussian sigma(noiseModel::Isotropic::Sigma(2, 0.1));
//	shared f1(new simulated2D::Measurement(z1, sigma, x1,l1));
//	graph->push_back(f1);
//
//	// measurement from x2 to l1
//	Point2 z2(-4.0, 0.0);
//	shared f2(new simulated2D::Measurement(z2, sigma, x2,l1));
//	graph->push_back(f2);
//
//	// create an initial estimate
//	Point2 pt_l1(
//			1.0, 6.0 // ground truth
//		  //1.2, 5.6 // small error
//			);
//	shared_ptr<Config2D> initialEstimate(new Config2D);
//	initialEstimate->insert(l1, pt_l1);
//	initialEstimate->insert(x1, pt_x1);
//	initialEstimate->insert(x2, pt_x2);
//
//	// optimize the graph
//	shared_ptr<Ordering> ordering(new Ordering());
//	*ordering += "x1", "x2", "l1";
//	Optimizer::shared_solver solver(new Optimizer::solver(ordering));
//	Optimizer optimizer(graph, initialEstimate, solver);
//
//	// display solution
//	double relativeThreshold = 1e-5;
//	double absoluteThreshold = 1e-5;
//	Optimizer act_opt = optimizer.gaussNewton(relativeThreshold, absoluteThreshold);
//	boost::shared_ptr<const Config2D> actual = act_opt.config();
//	if (verbose) actual->print("Configuration after optimization");
//
//	// verify
//	Config2D expected;
//	expected.insert(x1, pt_x1);
//	expected.insert(x2, pt_x2);
//	expected.insert(l1, Point2(1.0, 6.0));
//	CHECK(assert_equal(expected, *actual, 1e-5));
//}
//
///* ********************************************************************* */
//namespace sqp_test1 {
//
//	// binary constraint between landmarks
//	/** g(x) = x-y = 0 */
//	Vector g(const Config2D& config, const list<Symbol>& keys) {
//		Point2 pt1, pt2;
//		pt1 = config[simulated2D::PointKey(keys.front().index())];
//		pt2 = config[simulated2D::PointKey(keys.back().index())];
//		return Vector_(2, pt1.x() - pt2.x(), pt1.y() - pt2.y());
//	}
//
//	/** jacobian at l1 */
//	Matrix G1(const Config2D& config, const list<Symbol>& keys) {
//		return eye(2);
//	}
//
//	/** jacobian at l2 */
//	Matrix G2(const Config2D& config, const list<Symbol>& keys) {
//		return -1 * eye(2);
//	}
//
//} // \namespace sqp_test1
//
////namespace sqp_test2 {
////
////	// Unary Constraint on x1
////	/** g(x) = x -[1;1] = 0 */
////	Vector g(const Config2D& config, const list<Symbol>& keys) {
////		return config[keys.front()] - Vector_(2, 1.0, 1.0);
////	}
////
////	/** jacobian at x1 */
////	Matrix G(const Config2D& config, const list<Symbol>& keys) {
////		return eye(2);
////	}
////
////} // \namespace sqp_test2
//
//
//typedef NonlinearConstraint2<
//	Config2D, simulated2D::PointKey, Point2, simulated2D::PointKey, Point2> NLC2;
//
///* *********************************************************************
// *  Version that actually uses nonlinear equality constraints
// *  to to perform optimization.  Same as above, but no
// *  equality constraint on x2, and two landmarks that
// *  should be the same. Note that this is a linear system,
// *  so it will converge in one step.
// */
//TEST (SQP, two_pose ) {
//	bool verbose = false;
//
//	// create the graph
//	shared_ptr<NLGraph> graph(new NLGraph);
//
//	// add the constraints on the ends
//	// position (1, 1) constraint for x1
//	// position (5, 6) constraint for x2
//	simulated2D::PoseKey x1(1), x2(2);
//	simulated2D::PointKey l1(1), l2(2);
//	Point2 pt_x1(1.0, 1.0),
//		   pt_x2(5.0, 6.0);
//	shared_ptr<NLE> ef1(new NLE(x1, pt_x1));
//	graph->push_back(ef1);
//
//	// measurement from x1 to l1
//	Point2 z1(0.0, 5.0);
//	SharedGaussian sigma(noiseModel::Isotropic::Sigma(2, 0.1));
//	shared f1(new simulated2D::Measurement(z1, sigma, x1,l1));
//	graph->push_back(f1);
//
//	// measurement from x2 to l2
//	Point2 z2(-4.0, 0.0);
//	shared f2(new simulated2D::Measurement(z2, sigma, x2,l2));
//	graph->push_back(f2);
//
//	// equality constraint between l1 and l2
//	list<Symbol> keys2; keys2 += "l1", "l2";
//	boost::shared_ptr<NLC2 > c2(new NLC2(
//					boost::bind(sqp_test1::g, _1, keys2),
//					l1, boost::bind(sqp_test1::G1, _1, keys2),
//					l2, boost::bind(sqp_test1::G2, _1, keys2),
//					2, "L1"));
//	graph->push_back(c2);
//
//	// create an initial estimate
//	shared_ptr<Config2D> initialEstimate(new Config2D);
//	initialEstimate->insert(x1, pt_x1);
//	initialEstimate->insert(x2, Point2());
//	initialEstimate->insert(l1, Point2(1.0, 6.0)); // ground truth
//	initialEstimate->insert(l2, Point2(-4.0, 0.0)); // starting with a separate reference frame
//
//	// create an initial estimate for the lagrange multiplier
//	shared_ptr<VectorConfig> initLagrange(new VectorConfig);
//	initLagrange->insert(LamKey(1), Vector_(2, 1.0, 1.0)); // connect the landmarks
//
//	// create state config variables and initialize them
//	Config2D state(*initialEstimate);
//	VectorConfig state_lambda(*initLagrange);
//
//	// optimization loop
//	int maxIt = 1;
//	for (int i = 0; i<maxIt; ++i) {
//
// 		// linearize the graph
//		GaussianFactorGraph fg;
//		typedef FactorGraph<NonlinearFactor<Config2D> >::const_iterator const_iterator;
//		// iterate over all factors
//		for (const_iterator factor = graph->begin(); factor < graph->end(); factor++) {
//			const shared_ptr<NLC2> constraint = boost::shared_dynamic_cast<NLC2>(*factor);
//			if (constraint == NULL) {
//				// if a regular factor, linearize using the default linearization
//				GaussianFactor::shared_ptr f = (*factor)->linearize(state);
//				fg.push_back(f);
//			} else {
//				// if a constraint, linearize using the constraint method (2 configs)
//				GaussianFactor::shared_ptr f, c;
//				boost::tie(f,c) = constraint->linearize(state, state_lambda);
//				fg.push_back(f);
//				fg.push_back(c);
//			}
//		}
//
//		if (verbose) fg.print("Linearized graph");
//
//		// create an ordering
//		Ordering ordering;
//		ordering += "x1", "x2", "l1", "l2", "L1";
//
//		// optimize linear graph to get full delta config
//		VectorConfig delta = fg.optimize(ordering);
//		if (verbose) delta.print("Delta Config");
//
//		// update both state variables
//		state = expmap(state, delta);
//		if (verbose) state.print("newState");
//		state_lambda = expmap(state_lambda, delta);
//		if (verbose) state_lambda.print("newStateLam");
//	}
//
//	// verify
//	Config2D expected;
//	expected.insert(x1, pt_x1);
//	expected.insert(l1, Point2(1.0, 6.0));
//	expected.insert(l2, Point2(1.0, 6.0));
//	expected.insert(x2, Point2(5.0, 6.0));
//	CHECK(assert_equal(expected, state, 1e-5));
//}
//
///* ********************************************************************* */
//// VSLAM Examples
///* ********************************************************************* */
//// make a realistic calibration matrix
//double fov = 60; // degrees
//size_t w=640,h=480;
//Cal3_S2 K(fov,w,h);
//boost::shared_ptr<Cal3_S2> shK(new Cal3_S2(K));
//
//using namespace gtsam::visualSLAM;
//using namespace boost;
//
//// typedefs for visual SLAM example
//typedef visualSLAM::Config VConfig;
//typedef visualSLAM::Graph VGraph;
//typedef boost::shared_ptr<ProjectionFactor> shared_vf;
//typedef NonlinearOptimizer<VGraph,VConfig> VOptimizer;
//typedef SQPOptimizer<VGraph, VConfig> VSOptimizer;
//typedef NonlinearConstraint2<
//	VConfig, visualSLAM::PointKey, Pose3, visualSLAM::PointKey, Pose3> VNLC2;
//
//
///**
// * Ground truth for a visual SLAM example with stereo vision
// */
//TEST (SQP, stereo_truth ) {
//	bool verbose = false;
//
//	// create initial estimates
//	Rot3 faceDownY(Matrix_(3,3,
//				1.0, 0.0, 0.0,
//				0.0, 0.0, 1.0,
//				0.0, 1.0, 0.0));
//	Pose3 pose1(faceDownY, Point3()); // origin, left camera
//	SimpleCamera camera1(K, pose1);
//	Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
//	SimpleCamera camera2(K, pose2);
//	Point3 landmark(1.0, 5.0, 0.0); //centered between the cameras, 5 units away
//	Point3 landmarkNoisy(1.0, 6.0, 0.0);
//
//	// create truth config
//	boost::shared_ptr<VConfig> truthConfig(new Config);
//	truthConfig->insert(1, camera1.pose());
//	truthConfig->insert(2, camera2.pose());
//	truthConfig->insert(1, landmark);
//
//	// create graph
//	shared_ptr<VGraph> graph(new VGraph());
//
//	// create equality constraints for poses
//	graph->push_back(shared_ptr<PoseConstraint>(new PoseConstraint(1, camera1.pose())));
//	graph->push_back(shared_ptr<PoseConstraint>(new PoseConstraint(2, camera2.pose())));
//
//	// create VSLAM factors
//	Point2 z1 = camera1.project(landmark);
//	if (verbose) z1.print("z1");
//	shared_vf vf1(new ProjectionFactor(z1, 1.0, 1, 1, shK));
//	graph->push_back(vf1);
//	Point2 z2 = camera2.project(landmark);
//	if (verbose) z2.print("z2");
//	shared_vf vf2(new ProjectionFactor(z2, 1.0, 2, 1, shK));
//	graph->push_back(vf2);
//
//	if (verbose) graph->print("Graph after construction");
//
//	// create ordering
//	shared_ptr<Ordering> ord(new Ordering());
//	*ord += "x1", "x2", "l1";
//
//	// create optimizer
//	VOptimizer::shared_solver solver(new VOptimizer::solver(ord));
//	VOptimizer optimizer(graph, truthConfig, solver);
//
//	// optimize
//	VOptimizer afterOneIteration = optimizer.iterate();
//
//	// verify
//	DOUBLES_EQUAL(0.0, optimizer.error(), 1e-9);
//
//	// check if correct
//	if (verbose) afterOneIteration.config()->print("After iteration");
//	CHECK(assert_equal(*truthConfig,*(afterOneIteration.config())));
//}
//
//
///* *********************************************************************
// * Ground truth for a visual SLAM example with stereo vision
// * with some noise injected into the initial config
// */
//TEST (SQP, stereo_truth_noisy ) {
//	bool verbose = false;
//
//	// setting to determine how far away the noisy landmark is,
//	// given that the ground truth is 5m in front of the cameras
//	double noisyDist = 7.6;
//
//	// create initial estimates
//	Rot3 faceDownY(Matrix_(3,3,
//			1.0, 0.0, 0.0,
//			0.0, 0.0, 1.0,
//			0.0, 1.0, 0.0));
//	Pose3 pose1(faceDownY, Point3()); // origin, left camera
//	SimpleCamera camera1(K, pose1);
//	Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
//	SimpleCamera camera2(K, pose2);
//	Point3 landmark(1.0, 5.0, 0.0); //centered between the cameras, 5 units away
//	Point3 landmarkNoisy(1.0, noisyDist, 0.0); // initial point is too far out
//
//	// create truth config
//	boost::shared_ptr<Config> truthConfig(new Config);
//	truthConfig->insert(1, camera1.pose());
//	truthConfig->insert(2, camera2.pose());
//	truthConfig->insert(1, landmark);
//
//	// create config
//	boost::shared_ptr<Config> noisyConfig(new Config);
//	noisyConfig->insert(1, camera1.pose());
//	noisyConfig->insert(2, camera2.pose());
//	noisyConfig->insert(1, landmarkNoisy);
//
//	// create graph
//	shared_ptr<Graph> graph(new Graph());
//
//	// create equality constraints for poses
//	graph->push_back(shared_ptr<PoseConstraint>(new PoseConstraint(1, camera1.pose())));
//	graph->push_back(shared_ptr<PoseConstraint>(new PoseConstraint(2, camera2.pose())));
//
//	// create VSLAM factors
//	Point2 z1 = camera1.project(landmark);
//	if (verbose) z1.print("z1");
//	shared_vf vf1(new ProjectionFactor(z1, 1.0, 1, 1, shK));
//	graph->push_back(vf1);
//	Point2 z2 = camera2.project(landmark);
//	if (verbose) z2.print("z2");
//	shared_vf vf2(new ProjectionFactor(z2, 1.0, 2, 1, shK));
//	graph->push_back(vf2);
//
//	if (verbose)  {
//		graph->print("Graph after construction");
//		noisyConfig->print("Initial config");
//	}
//
//	// create ordering
//	shared_ptr<Ordering> ord(new Ordering());
//	*ord += "x1", "x2", "l1";
//
//	// create optimizer
//	VOptimizer::shared_solver solver(new VOptimizer::solver(ord));
//	VOptimizer optimizer0(graph, noisyConfig, solver);
//
//	if (verbose)
//		cout << "Initial Error: " << optimizer0.error() << endl;
//
//	// use Levenberg-Marquardt optimization
//	double relThresh = 1e-5, absThresh = 1e-5;
//	VOptimizer optimizer(optimizer0.levenbergMarquardt(relThresh, absThresh, VOptimizer::SILENT));
//
//	// verify
//	DOUBLES_EQUAL(0.0, optimizer.error(), 1e-9);
//
//	// check if correct
//	if (verbose) {
//		optimizer.config()->print("After iteration");
//		cout << "Final error: " << optimizer.error() << endl;
//	}
//	CHECK(assert_equal(*truthConfig,*(optimizer.config())));
//}
//
///* ********************************************************************* */
//namespace sqp_stereo {
//
//	// binary constraint between landmarks
//	/** g(x) = x-y = 0 */
//	Vector g(const Config& config, const list<Symbol>& keys) {
//		return config[PointKey(keys.front().index())].vector()
//				- config[PointKey(keys.back().index())].vector();
//	}
//
//	/** jacobian at l1 */
//	Matrix G1(const Config& config, const list<Symbol>& keys) {
//		return eye(3);
//	}
//
//	/** jacobian at l2 */
//	Matrix G2(const Config& config, const list<Symbol>& keys) {
//		return -1.0 * eye(3);
//	}
//
//} // \namespace sqp_stereo
//
///* ********************************************************************* */
//VGraph stereoExampleGraph() {
//	// create initial estimates
//	Rot3 faceDownY(Matrix_(3,3,
//			1.0, 0.0, 0.0,
//			0.0, 0.0, 1.0,
//			0.0, 1.0, 0.0));
//	Pose3 pose1(faceDownY, Point3()); // origin, left camera
//	SimpleCamera camera1(K, pose1);
//	Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
//	SimpleCamera camera2(K, pose2);
//	Point3 landmark1(1.0, 5.0, 0.0); //centered between the cameras, 5 units away
//	Point3 landmark2(1.0, 5.0, 0.0);
//
//	// create graph
//	VGraph graph;
//
//	// create equality constraints for poses
//	graph.push_back(shared_ptr<PoseConstraint>(new PoseConstraint(1, camera1.pose())));
//	graph.push_back(shared_ptr<PoseConstraint>(new PoseConstraint(2, camera2.pose())));
//
//	// create  factors
//	Point2 z1 = camera1.project(landmark1);
//	shared_vf vf1(new ProjectionFactor(z1, 1.0, 1, 1, shK));
//	graph.push_back(vf1);
//	Point2 z2 = camera2.project(landmark2);
//	shared_vf vf2(new ProjectionFactor(z2, 1.0, 2, 2, shK));
//	graph.push_back(vf2);
//
//	// create the binary equality constraint between the landmarks
//	// NOTE: this is really just a linear constraint that is exactly the same
//	// as the previous examples
//	list<Symbol> keys; keys += "l1", "l2";
//	visualSLAM::PointKey l1(1), l2(2);
//	shared_ptr<VNLC2> c2(
//			new VNLC2(boost::bind(sqp_stereo::g, _1, keys),
//					 l1, boost::bind(sqp_stereo::G1, _1, keys),
//					 l2, boost::bind(sqp_stereo::G2, _1, keys),
//					 3, "L12"));
//	graph.push_back(c2);
//
//	return graph;
//}
//
///* ********************************************************************* */
//boost::shared_ptr<VConfig> stereoExampleTruthConfig() {
//	// create initial estimates
//	Rot3 faceDownY(Matrix_(3,3,
//				1.0, 0.0, 0.0,
//				0.0, 0.0, 1.0,
//				0.0, 1.0, 0.0));
//	Pose3 pose1(faceDownY, Point3()); // origin, left camera
//	SimpleCamera camera1(K, pose1);
//	Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
//	SimpleCamera camera2(K, pose2);
//	Point3 landmark1(1.0, 5.0, 0.0); //centered between the cameras, 5 units away
//	Point3 landmark2(1.0, 5.0, 0.0);
//
//	// create config
//	boost::shared_ptr<Config> truthConfig(new Config);
//	truthConfig->insert(1, camera1.pose());
//	truthConfig->insert(2, camera2.pose());
//	truthConfig->insert(1, landmark1);
//	truthConfig->insert(2, landmark2); // create two landmarks in same place
//
//	return truthConfig;
//}
//
///* *********************************************************************
// * SQP version of the above stereo example,
// * with the initial case as the ground truth
// */
//TEST (SQP, stereo_sqp ) {
//	bool verbose = false;
//
//	// get a graph
//	VGraph graph = stereoExampleGraph();
//	if (verbose) graph.print("Graph after construction");
//
//	// get the truth config
//	boost::shared_ptr<VConfig> truthConfig = stereoExampleTruthConfig();
//
//	// create ordering
//	Ordering ord;
//	ord += "x1", "x2", "l1", "l2";
//
//	// create optimizer
//	VSOptimizer optimizer(graph, ord, truthConfig);
//
//	// optimize
//	VSOptimizer afterOneIteration = optimizer.iterate();
//
//	// check if correct
//	CHECK(assert_equal(*truthConfig,*(afterOneIteration.config())));
//}
//
///* *********************************************************************
// * SQP version of the above stereo example,
// * with noise in the initial estimate
// */
//TEST (SQP, stereo_sqp_noisy ) {
//	bool verbose = false;
//
//	// get a graph
//	Graph graph = stereoExampleGraph();
//
//	// create initial data
//	Rot3 faceDownY(Matrix_(3,3,
//			1.0, 0.0, 0.0,
//			0.0, 0.0, 1.0,
//			0.0, 1.0, 0.0));
//	Pose3 pose1(faceDownY, Point3()); // origin, left camera
//	Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
//	Point3 landmark1(0.5, 5.0, 0.0); //centered between the cameras, 5 units away
//	Point3 landmark2(1.5, 5.0, 0.0);
//
//	// noisy config
//	boost::shared_ptr<Config> initConfig(new Config);
//	initConfig->insert(1, pose1);
//	initConfig->insert(2, pose2);
//	initConfig->insert(1, landmark1);
//	initConfig->insert(2, landmark2); // create two landmarks in same place
//
//	// create ordering
//	Ordering ord;
//	ord += "x1", "x2", "l1", "l2";
//
//	// create optimizer
//	VSOptimizer optimizer(graph, ord, initConfig);
//
//	// optimize
//	double start_error = optimizer.error();
//	int maxIt = 2;
//	for (int i=0; i<maxIt; ++i) {
//		if (verbose) cout << "\n ************************** \n"
//						  << " Iteration: " << i << endl;
//		//if (verbose) optimizer.graph()->print();
//		if (verbose) optimizer.config()->print();
//		if (verbose)
//			optimizer = optimizer.iterate(VSOptimizer::FULL);
//		else
//			optimizer = optimizer.iterate(VSOptimizer::SILENT);
//	}
//
//	if (verbose) cout << "Initial Error: " << start_error << "\n"
//					  << "Final Error:   " << optimizer.error() << endl;
//
//	// get the truth config
//	boost::shared_ptr<Config> truthConfig = stereoExampleTruthConfig();
//
//	if (verbose) {
//		initConfig->print("Initial Config");
//		truthConfig->print("Truth Config");
//		optimizer.config()->print("After optimization");
//	}
//
//	// check if correct
//	CHECK(assert_equal(*truthConfig,*(optimizer.config())));
//}
//
///* *********************************************************************
// * SQP version of the above stereo example,
// * with noise in the initial estimate and manually specified
// * lagrange multipliers
// */
//TEST (SQP, stereo_sqp_noisy_manualLagrange ) {
//	bool verbose = false;
//
//	// get a graph
//	Graph graph = stereoExampleGraph();
//
//	// create initial data
//	Rot3 faceDownY(Matrix_(3,3,
//			1.0, 0.0, 0.0,
//			0.0, 0.0, 1.0,
//			0.0, 1.0, 0.0));
//	Pose3 pose1(faceDownY, Point3()); // origin, left camera
//	Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
//	Point3 landmark1(0.5, 5.0, 0.0); //centered between the cameras, 5 units away
//	Point3 landmark2(1.5, 5.0, 0.0);
//
//	// noisy config
//	boost::shared_ptr<Config> initConfig(new Config);
//	initConfig->insert(1, pose1);
//	initConfig->insert(2, pose2);
//	initConfig->insert(1, landmark1);
//	initConfig->insert(2, landmark2); // create two landmarks in same place
//
//	// create ordering with lagrange multiplier included
//	Ordering ord;
//	ord += "x1", "x2", "l1", "l2", "L12";
//
//	// create lagrange multipliers
//	VSOptimizer::shared_vconfig initLagrangeConfig(new VectorConfig);
//	initLagrangeConfig->insert("L12", Vector_(3, 0.0, 0.0, 0.0));
//
//	// create optimizer
//	VSOptimizer optimizer(graph, ord, initConfig, initLagrangeConfig);
//
//	// optimize
//	double start_error = optimizer.error();
//	int maxIt = 5;
//	for (int i=0; i<maxIt; ++i) {
//		if (verbose) {
//			cout << "\n ************************** \n"
//				 << " Iteration: " << i << endl;
//			optimizer.config()->print("Config Before Iteration");
//			optimizer.configLagrange()->print("Lagrange Before Iteration");
//			optimizer = optimizer.iterate(VSOptimizer::FULL);
//		}
//		else
//			optimizer = optimizer.iterate(VSOptimizer::SILENT);
//	}
//
//	if (verbose) cout << "Initial Error: " << start_error << "\n"
//					  << "Final Error:   " << optimizer.error() << endl;
//
//	// get the truth config
//	boost::shared_ptr<Config> truthConfig = stereoExampleTruthConfig();
//
//	if (verbose) {
//		initConfig->print("Initial Config");
//		truthConfig->print("Truth Config");
//		optimizer.config()->print("After optimization");
//	}
//
//	// check if correct
//	CHECK(assert_equal(*truthConfig,*(optimizer.config())));
//}

/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
/* ************************************************************************* */