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gtsam/tests/testNonlinearOptimizer.cpp

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/* ----------------------------------------------------------------------------
* 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
* -------------------------------------------------------------------------- */
/**
* @file testNonlinearOptimizer.cpp
* @brief Unit tests for NonlinearOptimizer class
* @author Frank Dellaert
*/
#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 <boost/range/adaptor/map.hpp>
#include <boost/shared_ptr.hpp>
#include <boost/assign/std/list.hpp> // for operator +=
using namespace boost::assign;
using boost::adaptors::map_values;
#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, 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 += 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 += BetweenFactor<Pose2>(0, 1, Pose2(1, 0, M_PI / 2),
noiseModel::Isotropic::Sigma(3, 1));
fg += 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 (Vector& v : sqrtHessianDiagonal | map_values) v = v.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 += 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 += 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 += BetweenFactor<Point2>(0, 1, Point2(1,1.8),
noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(1.0),
noiseModel::Isotropic::Sigma(2,1)));
fg += BetweenFactor<Point2>(0, 1, Point2(1,0.9),
noiseModel::Robust::Create(noiseModel::mEstimator::Huber::Create(1.0),
noiseModel::Isotropic::Sigma(2,1)));
fg += 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 += 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 += 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 += 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 += 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 += 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 {
/// Solver specific parameters
ConjugateGradientParameters cgParams_;
Values initial_;
public:
/// Constructor
IterativeLM(const NonlinearFactorGraph& graph, const Values& initialValues,
const ConjugateGradientParameters& p,
const LevenbergMarquardtParams& params =
LevenbergMarquardtParams::LegacyDefaults())
: LevenbergMarquardtOptimizer(graph, initialValues, params),
cgParams_(p),
initial_(initialValues) {}
/// Solve that uses conjugate gradient
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 += 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));
}
/* ************************************************************************* */
#include <wrap/utilities.h>
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());
}
/* ************************************************************************* */
//// Minimal traits example
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);
}
/* ************************************************************************* */
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