testNonlinearOptimizer.cpp

Go to the documentation of this file.

/* ----------------------------------------------------------------------------
 
 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
 
 * See LICENSE for the license information
 
 * -------------------------------------------------------------------------- */
 
#include <tests/smallExample.h>
#include <gtsam/slam/BetweenFactor.h>
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include <gtsam/nonlinear/Values.h>
#include <gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h>
#include <gtsam/nonlinear/GaussNewtonOptimizer.h>
#include <gtsam/nonlinear/DoglegOptimizer.h>
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/linear/GaussianFactorGraph.h>
#include <gtsam/linear/NoiseModel.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam/geometry/Pose2.h>
#include <gtsam/base/Matrix.h>
 
#include <CppUnitLite/TestHarness.h>
 
 
#include <iostream>
#include <fstream>
 
using namespace std;
using namespace gtsam;
 
const double tol = 1e-5;
 
using symbol_shorthand::X;
using symbol_shorthand::L;
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, paramsEquals )
{
  // default constructors lead to two identical params
  GaussNewtonParams gnParams1;
  GaussNewtonParams gnParams2;
  CHECK(gnParams1.equals(gnParams2));
 
  // but the params become different if we change something in gnParams2
  gnParams2.setVerbosity("DELTA");
  CHECK(!gnParams1.equals(gnParams2));
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, iterateLM )
{
  // really non-linear factor graph
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  // config far from minimum
  Point2 x0(3,0);
  Values config;
  config.insert(X(1), x0);
 
  // normal iterate
  GaussNewtonParams gnParams;
  GaussNewtonOptimizer gnOptimizer(fg, config, gnParams);
  gnOptimizer.iterate();
 
  // LM iterate with lambda 0 should be the same
  LevenbergMarquardtParams lmParams;
  lmParams.lambdaInitial = 0.0;
  LevenbergMarquardtOptimizer lmOptimizer(fg, config, lmParams);
  lmOptimizer.iterate();
 
  CHECK(assert_equal(gnOptimizer.values(), lmOptimizer.values(), 1e-9));
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, optimize )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  // test error at minimum
  Point2 xstar(0,0);
  Values cstar;
  cstar.insert(X(1), xstar);
  DOUBLES_EQUAL(0.0,fg.error(cstar),0.0);
 
  // test error at initial = [(1-cos(3))^2 + (sin(3))^2]*50 =
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
  DOUBLES_EQUAL(199.0,fg.error(c0),1e-3);
 
  // optimize parameters
  Ordering ord;
  ord.push_back(X(1));
 
  // Gauss-Newton
  GaussNewtonParams gnParams;
  gnParams.ordering = ord;
  Values actual1 = GaussNewtonOptimizer(fg, c0, gnParams).optimize();
  DOUBLES_EQUAL(0,fg.error(actual1),tol);
 
  // Levenberg-Marquardt
  LevenbergMarquardtParams lmParams;
  lmParams.ordering = ord;
  Values actual2 = LevenbergMarquardtOptimizer(fg, c0, lmParams).optimize();
  DOUBLES_EQUAL(0,fg.error(actual2),tol);
 
  // Dogleg
  DoglegParams dlParams;
  dlParams.ordering = ord;
  Values actual3 = DoglegOptimizer(fg, c0, dlParams).optimize();
  DOUBLES_EQUAL(0,fg.error(actual3),tol);
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, SimpleLMOptimizer )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  Values actual = LevenbergMarquardtOptimizer(fg, c0).optimize();
  DOUBLES_EQUAL(0,fg.error(actual),tol);
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, SimpleGNOptimizer )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  Values actual = GaussNewtonOptimizer(fg, c0).optimize();
  DOUBLES_EQUAL(0,fg.error(actual),tol);
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, SimpleDLOptimizer )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  Values actual = DoglegOptimizer(fg, c0).optimize();
  DOUBLES_EQUAL(0,fg.error(actual),tol);
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, optimization_method )
{
  LevenbergMarquardtParams paramsQR;
  paramsQR.linearSolverType = LevenbergMarquardtParams::MULTIFRONTAL_QR;
  LevenbergMarquardtParams paramsChol;
  paramsChol.linearSolverType = LevenbergMarquardtParams::MULTIFRONTAL_CHOLESKY;
 
  NonlinearFactorGraph fg = example::createReallyNonlinearFactorGraph();
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  Values actualMFQR = LevenbergMarquardtOptimizer(fg, c0, paramsQR).optimize();
  DOUBLES_EQUAL(0,fg.error(actualMFQR),tol);
 
  Values actualMFChol = LevenbergMarquardtOptimizer(fg, c0, paramsChol).optimize();
  DOUBLES_EQUAL(0,fg.error(actualMFChol),tol);
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, Factorization )
{
  Values config;
  config.insert(X(1), Pose2(0.,0.,0.));
  config.insert(X(2), Pose2(1.5,0.,0.));
 
  NonlinearFactorGraph graph;
  graph.addPrior(X(1), Pose2(0.,0.,0.), noiseModel::Isotropic::Sigma(3, 1e-10));
  graph.emplace_shared<BetweenFactor<Pose2>>(X(1),X(2), Pose2(1.,0.,0.), noiseModel::Isotropic::Sigma(3, 1));
 
  Ordering ordering;
  ordering.push_back(X(1));
  ordering.push_back(X(2));
 
  LevenbergMarquardtParams params;
  LevenbergMarquardtParams::SetLegacyDefaults(&params);
  LevenbergMarquardtOptimizer optimizer(graph, config, ordering, params);
  optimizer.iterate();
 
  Values expected;
  expected.insert(X(1), Pose2(0.,0.,0.));
  expected.insert(X(2), Pose2(1.,0.,0.));
  CHECK(assert_equal(expected, optimizer.values(), 1e-5));
}
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, NullFactor) {
 
  NonlinearFactorGraph fg = example::createReallyNonlinearFactorGraph();
 
  // Add null factor
  fg.push_back(NonlinearFactorGraph::sharedFactor());
 
  // test error at minimum
  Point2 xstar(0,0);
  Values cstar;
  cstar.insert(X(1), xstar);
  DOUBLES_EQUAL(0.0,fg.error(cstar),0.0);
 
  // test error at initial = [(1-cos(3))^2 + (sin(3))^2]*50 =
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
  DOUBLES_EQUAL(199.0,fg.error(c0),1e-3);
 
  // optimize parameters
  Ordering ord;
  ord.push_back(X(1));
 
  // Gauss-Newton
  Values actual1 = GaussNewtonOptimizer(fg, c0, ord).optimize();
  DOUBLES_EQUAL(0,fg.error(actual1),tol);
 
  // Levenberg-Marquardt
  Values actual2 = LevenbergMarquardtOptimizer(fg, c0, ord).optimize();
  DOUBLES_EQUAL(0,fg.error(actual2),tol);
 
  // Dogleg
  Values actual3 = DoglegOptimizer(fg, c0, ord).optimize();
  DOUBLES_EQUAL(0,fg.error(actual3),tol);
}
 
/* ************************************************************************* */
TEST_UNSAFE(NonlinearOptimizer, MoreOptimization) {
 
  NonlinearFactorGraph fg;
  fg.addPrior(0, Pose2(0, 0, 0), noiseModel::Isotropic::Sigma(3, 1));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(1, 0, M_PI / 2),
      noiseModel::Isotropic::Sigma(3, 1));
  fg.emplace_shared<BetweenFactor<Pose2>>(1, 2, Pose2(1, 0, M_PI / 2),
      noiseModel::Isotropic::Sigma(3, 1));
 
  Values init;
  init.insert(0, Pose2(3, 4, -M_PI));
  init.insert(1, Pose2(10, 2, -M_PI));
  init.insert(2, Pose2(11, 7, -M_PI));
 
  Values expected;
  expected.insert(0, Pose2(0, 0, 0));
  expected.insert(1, Pose2(1, 0, M_PI / 2));
  expected.insert(2, Pose2(1, 1, M_PI));
 
  VectorValues expectedGradient;
  expectedGradient.insert(0,Z_3x1);
  expectedGradient.insert(1,Z_3x1);
  expectedGradient.insert(2,Z_3x1);
 
  // Try LM and Dogleg
  LevenbergMarquardtParams params = LevenbergMarquardtParams::LegacyDefaults();
  {
    LevenbergMarquardtOptimizer optimizer(fg, init, params);
 
    // test convergence
    Values actual = optimizer.optimize();
    EXPECT(assert_equal(expected, actual));
 
    // Check that the gradient is zero
    GaussianFactorGraph::shared_ptr linear = optimizer.linearize();
    EXPECT(assert_equal(expectedGradient,linear->gradientAtZero()));
  }
  EXPECT(assert_equal(expected, DoglegOptimizer(fg, init).optimize()));
 
//  cout << "===================================================================================" << endl;
 
  // Try LM with diagonal damping
  Values initBetter;
    initBetter.insert(0, Pose2(3,4,0));
    initBetter.insert(1, Pose2(10,2,M_PI/3));
    initBetter.insert(2, Pose2(11,7,M_PI/2));
 
  {
    params.diagonalDamping = true;
    LevenbergMarquardtOptimizer optimizer(fg, initBetter, params);
 
    // test the diagonal
    GaussianFactorGraph::shared_ptr linear = optimizer.linearize();
    VectorValues d = linear->hessianDiagonal();
    VectorValues sqrtHessianDiagonal = d;
    for (auto& [key, value] : sqrtHessianDiagonal) {
      value = value.cwiseSqrt();
    }
    GaussianFactorGraph damped = optimizer.buildDampedSystem(*linear, sqrtHessianDiagonal);
    VectorValues  expectedDiagonal = d + params.lambdaInitial * d;
    EXPECT(assert_equal(expectedDiagonal, damped.hessianDiagonal()));
 
    // test convergence (does not!)
    Values actual = optimizer.optimize();
    EXPECT(assert_equal(expected, actual));
 
    // Check that the gradient is zero (it is not!)
    linear = optimizer.linearize();
    EXPECT(assert_equal(expectedGradient,linear->gradientAtZero()));
 
    // Check that the gradient is zero for damped system (it is not!)
    damped = optimizer.buildDampedSystem(*linear, sqrtHessianDiagonal);
    VectorValues actualGradient = damped.gradientAtZero();
    EXPECT(assert_equal(expectedGradient,actualGradient));
 
    /* This block was made to test the original initial guess "init"
    // Check errors at convergence and errors in direction of gradient (decreases!)
    EXPECT_DOUBLES_EQUAL(46.02558,fg.error(actual),1e-5);
    EXPECT_DOUBLES_EQUAL(44.742237,fg.error(actual.retract(-0.01*actualGradient)),1e-5);
 
    // Check that solve yields gradient (it's not equal to gradient, as predicted)
    VectorValues delta = damped.optimize();
    double factor = actualGradient[0][0]/delta[0][0];
    EXPECT(assert_equal(actualGradient,factor*delta));
 
    // Still pointing downhill wrt actual gradient !
    EXPECT_DOUBLES_EQUAL( 0.1056157,dot(-1*actualGradient,delta),1e-3);
 
    // delta.print("This is the delta value computed by LM with diagonal damping");
 
    // Still pointing downhill wrt expected gradient (IT DOES NOT! actually they are perpendicular)
    EXPECT_DOUBLES_EQUAL( 0.0,dot(-1*expectedGradient,delta),1e-5);
 
    // Check errors at convergence and errors in direction of solution (does not decrease!)
    EXPECT_DOUBLES_EQUAL(46.0254859,fg.error(actual.retract(delta)),1e-5);
 
    // Check errors at convergence and errors at a small step in direction of solution (does not decrease!)
    EXPECT_DOUBLES_EQUAL(46.0255,fg.error(actual.retract(0.01*delta)),1e-3);
    */
  }
}
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, Pose2OptimizationWithHuberNoOutlier) {
 
  NonlinearFactorGraph fg;
  fg.addPrior(0, Pose2(0,0,0), noiseModel::Isotropic::Sigma(3,1));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(1,1.1,M_PI/4),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(2.0),
                                                         noiseModel::Isotropic::Sigma(3,1)));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(1,0.9,M_PI/2),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(3.0),
                                                         noiseModel::Isotropic::Sigma(3,1)));
 
  Values init;
  init.insert(0, Pose2(0,0,0));
  init.insert(1, Pose2(0.961187, 0.99965, 1.1781));
 
  Values expected;
  expected.insert(0, Pose2(0,0,0));
  expected.insert(1, Pose2(0.961187, 0.99965, 1.1781));
 
  LevenbergMarquardtParams lm_params;
 
  auto gn_result = GaussNewtonOptimizer(fg, init).optimize();
  auto lm_result = LevenbergMarquardtOptimizer(fg, init, lm_params).optimize();
  auto dl_result = DoglegOptimizer(fg, init).optimize();
 
  EXPECT(assert_equal(expected, gn_result, 3e-2));
  EXPECT(assert_equal(expected, lm_result, 3e-2));
  EXPECT(assert_equal(expected, dl_result, 3e-2));
}
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, Point2LinearOptimizationWithHuber) {
 
  NonlinearFactorGraph fg;
  fg.addPrior(0, Point2(0,0), noiseModel::Isotropic::Sigma(2,0.01));
  fg.emplace_shared<BetweenFactor<Point2>>(0, 1, Point2(1,1.8),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(1.0),
                                                         noiseModel::Isotropic::Sigma(2,1)));
  fg.emplace_shared<BetweenFactor<Point2>>(0, 1, Point2(1,0.9),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(1.0),
                                                         noiseModel::Isotropic::Sigma(2,1)));
  fg.emplace_shared<BetweenFactor<Point2>>(0, 1, Point2(1,90),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(1.0),
                                                         noiseModel::Isotropic::Sigma(2,1)));
 
  Values init;
  init.insert(0, Point2(1,1));
  init.insert(1, Point2(1,0));
 
  Values expected;
  expected.insert(0, Point2(0,0));
  expected.insert(1, Point2(1,1.85));
 
  LevenbergMarquardtParams params;
 
  auto gn_result = GaussNewtonOptimizer(fg, init).optimize();
  auto lm_result = LevenbergMarquardtOptimizer(fg, init, params).optimize();
  auto dl_result = DoglegOptimizer(fg, init).optimize();
 
  EXPECT(assert_equal(expected, gn_result, 1e-4));
  EXPECT(assert_equal(expected, lm_result, 1e-4));
  EXPECT(assert_equal(expected, dl_result, 1e-4));
}
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, Pose2OptimizationWithHuber) {
 
  NonlinearFactorGraph fg;
  fg.addPrior(0, Pose2(0,0, 0), noiseModel::Isotropic::Sigma(3,0.1));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(0,9, M_PI/2),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(0.2),
                                                         noiseModel::Isotropic::Sigma(3,1)));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(0, 11, M_PI/2),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(0.2),
                                                         noiseModel::Isotropic::Sigma(3,1)));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(0, 10, M_PI/2),
                             noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(0.2),
                                                        noiseModel::Isotropic::Sigma(3,1)));
  fg.emplace_shared<BetweenFactor<Pose2>>(0, 1, Pose2(0,9, 0),
                              noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(0.2),
                                                         noiseModel::Isotropic::Sigma(3,1)));
 
  Values init;
  init.insert(0, Pose2(0, 0, 0));
  init.insert(1, Pose2(0, 10, M_PI/4));
 
  Values expected;
  expected.insert(0, Pose2(0, 0, 0));
  expected.insert(1, Pose2(0, 10, 1.45212));
 
  LevenbergMarquardtParams params;
 
  auto gn_result = GaussNewtonOptimizer(fg, init).optimize();
  auto lm_result = LevenbergMarquardtOptimizer(fg, init, params).optimize();
  auto dl_result = DoglegOptimizer(fg, init).optimize();
 
  EXPECT(assert_equal(expected, gn_result, 1e-1));
  EXPECT(assert_equal(expected, lm_result, 1e-1));
  EXPECT(assert_equal(expected, dl_result, 1e-1));
}
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, RobustMeanCalculation) {
 
  NonlinearFactorGraph fg;
 
  Values init;
 
  Values expected;
 
  auto huber = noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(20),
                                          noiseModel::Isotropic::Sigma(1, 1));
 
  vector<double> pts{-10,-3,-1,1,3,10,1000};
  for(auto pt : pts) {
    fg.addPrior(0, pt, huber);
  }
 
  init.insert(0, 100.0);
  expected.insert(0, 3.33333333);
 
  DoglegParams params_dl;
  params_dl.setRelativeErrorTol(1e-10);
 
  auto gn_result = GaussNewtonOptimizer(fg, init).optimize();
  auto lm_result = LevenbergMarquardtOptimizer(fg, init).optimize();
  auto dl_result = DoglegOptimizer(fg, init, params_dl).optimize();
 
  EXPECT(assert_equal(expected, gn_result, tol));
  EXPECT(assert_equal(expected, lm_result, tol));
  EXPECT(assert_equal(expected, dl_result, tol));
}
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, disconnected_graph) {
  Values expected;
  expected.insert(X(1), Pose2(0.,0.,0.));
  expected.insert(X(2), Pose2(1.5,0.,0.));
  expected.insert(X(3), Pose2(3.0,0.,0.));
 
  Values init;
  init.insert(X(1), Pose2(0.,0.,0.));
  init.insert(X(2), Pose2(0.,0.,0.));
  init.insert(X(3), Pose2(0.,0.,0.));
 
  NonlinearFactorGraph graph;
  graph.addPrior(X(1), Pose2(0.,0.,0.), noiseModel::Isotropic::Sigma(3,1));
  graph.emplace_shared<BetweenFactor<Pose2>>(X(1),X(2), Pose2(1.5,0.,0.), noiseModel::Isotropic::Sigma(3,1));
  graph.addPrior(X(3), Pose2(3.,0.,0.), noiseModel::Isotropic::Sigma(3,1));
 
  EXPECT(assert_equal(expected, LevenbergMarquardtOptimizer(graph, init).optimize()));
}
 
/* ************************************************************************* */
#include <gtsam/linear/iterative.h>
 
class IterativeLM : public LevenbergMarquardtOptimizer {
  ConjugateGradientParameters cgParams_;
  Values initial_;
 
 public:
  IterativeLM(const NonlinearFactorGraph& graph, const Values& initialValues,
              const ConjugateGradientParameters& p,
              const LevenbergMarquardtParams& params =
                  LevenbergMarquardtParams::LegacyDefaults())
      : LevenbergMarquardtOptimizer(graph, initialValues, params),
        cgParams_(p),
        initial_(initialValues) {}
 
  VectorValues solve(const GaussianFactorGraph& gfg,
                             const NonlinearOptimizerParams& params) const override {
    VectorValues zeros = initial_.zeroVectors();
    return conjugateGradientDescent(gfg, zeros, cgParams_);
  }
};
 
/* ************************************************************************* */
TEST(NonlinearOptimizer, subclass_solver) {
  Values expected;
  expected.insert(X(1), Pose2(0., 0., 0.));
  expected.insert(X(2), Pose2(1.5, 0., 0.));
  expected.insert(X(3), Pose2(3.0, 0., 0.));
 
  Values init;
  init.insert(X(1), Pose2(0., 0., 0.));
  init.insert(X(2), Pose2(0., 0., 0.));
  init.insert(X(3), Pose2(0., 0., 0.));
 
  NonlinearFactorGraph graph;
  graph.addPrior(X(1), Pose2(0., 0., 0.), noiseModel::Isotropic::Sigma(3, 1));
  graph.emplace_shared<BetweenFactor<Pose2>>(X(1), X(2), Pose2(1.5, 0., 0.),
                                noiseModel::Isotropic::Sigma(3, 1));
  graph.addPrior(X(3), Pose2(3., 0., 0.), noiseModel::Isotropic::Sigma(3, 1));
 
  ConjugateGradientParameters p;
  Values actual = IterativeLM(graph, init, p).optimize();
  EXPECT(assert_equal(expected, actual, 1e-4));
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, logfile )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  // Levenberg-Marquardt
  LevenbergMarquardtParams lmParams;
  static const string filename("testNonlinearOptimizer.log");
  lmParams.logFile = filename;
  LevenbergMarquardtOptimizer(fg, c0, lmParams).optimize();
 
//  stringstream expected,actual;
//  ifstream ifs(("../../gtsam/tests/" + filename).c_str());
//  if(!ifs) throw std::runtime_error(filename);
//  expected << ifs.rdbuf();
//  ifs.close();
//  ifstream ifs2(filename.c_str());
//  if(!ifs2) throw std::runtime_error(filename);
//  actual << ifs2.rdbuf();
//  EXPECT(actual.str()==expected.str());
}
 
/* ************************************************************************* */
TEST( NonlinearOptimizer, iterationHook_LM )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  // Levenberg-Marquardt
  LevenbergMarquardtParams lmParams;
  size_t lastIterCalled = 0;
  lmParams.iterationHook = [&](size_t iteration, double oldError, double newError)
  {
    // Tests:
    lastIterCalled = iteration;
    EXPECT(newError<oldError);
    
    // Example of evolution printout:
    //std::cout << "iter: " << iteration << " error: " << oldError << " => " << newError <<"\n";
  };
  LevenbergMarquardtOptimizer(fg, c0, lmParams).optimize();
  
  EXPECT(lastIterCalled>5);
}
/* ************************************************************************* */
TEST( NonlinearOptimizer, iterationHook_CG )
{
  NonlinearFactorGraph fg(example::createReallyNonlinearFactorGraph());
 
  Point2 x0(3,3);
  Values c0;
  c0.insert(X(1), x0);
 
  // Levenberg-Marquardt
  NonlinearConjugateGradientOptimizer::Parameters cgParams;
  size_t lastIterCalled = 0;
  cgParams.iterationHook = [&](size_t iteration, double oldError, double newError)
  {
    // Tests:
    lastIterCalled = iteration;
    EXPECT(newError<oldError);
    
    // Example of evolution printout:
    //std::cout << "iter: " << iteration << " error: " << oldError << " => " << newError <<"\n";
  };
  NonlinearConjugateGradientOptimizer(fg, c0, cgParams).optimize();
  
  EXPECT(lastIterCalled>5);
}
 
 
/* ************************************************************************* */
struct MyType : public Vector3 {
  using Vector3::Vector3;
};
 
namespace gtsam {
template <>
struct traits<MyType> {
  static bool Equals(const MyType& a, const MyType& b, double tol) {
    return (a - b).array().abs().maxCoeff() < tol;
  }
  static void Print(const MyType&, const string&) {}
  static int GetDimension(const MyType&) { return 3; }
  static MyType Retract(const MyType& a, const Vector3& b) { return a + b; }
  static Vector3 Local(const MyType& a, const MyType& b) { return b - a; }
};
}
 
TEST(NonlinearOptimizer, Traits) {
  NonlinearFactorGraph fg;
  fg.addPrior(0, MyType(0, 0, 0), noiseModel::Isotropic::Sigma(3, 1));
 
  Values init;
  init.insert(0, MyType(0,0,0));
 
  LevenbergMarquardtOptimizer optimizer(fg, init);
  Values actual = optimizer.optimize();
  EXPECT(assert_equal(init, actual));
}
 
/* ************************************************************************* */
int main() {
  TestResult tr;
  return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */