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gtsam/tests/testDoglegOptimizer.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 DoglegOptimizer.h
* @brief Unit tests for DoglegOptimizer
* @author Richard Roberts
*/
#include <CppUnitLite/TestHarness.h>
#include <gtsam/base/numericalDerivative.h>
#include <gtsam/inference/BayesTree-inl.h>
#include <gtsam/linear/JacobianFactor.h>
#include <gtsam/linear/GaussianSequentialSolver.h>
#include <gtsam/nonlinear/DoglegOptimizerImpl.h>
#include <gtsam/slam/pose2SLAM.h>
#include <gtsam/slam/smallExample.h>
#include <boost/bind.hpp>
#include <boost/assign/list_of.hpp> // for 'list_of()'
#include <functional>
using namespace std;
using namespace gtsam;
using boost::shared_ptr;
/* ************************************************************************* */
double computeError(const GaussianBayesNet& gbn, const LieVector& values) {
// Convert Vector to VectorValues
VectorValues vv = *allocateVectorValues(gbn);
vv.vector() = values;
// Convert to factor graph
GaussianFactorGraph gfg(gbn);
return gfg.error(vv);
}
/* ************************************************************************* */
double computeErrorBt(const BayesTree<GaussianConditional>& gbt, const LieVector& values) {
// Convert Vector to VectorValues
VectorValues vv = *allocateVectorValues(gbt);
vv.vector() = values;
// Convert to factor graph
GaussianFactorGraph gfg(gbt);
return gfg.error(vv);
}
/* ************************************************************************* */
TEST(DoglegOptimizer, ComputeSteepestDescentPoint) {
// Create an arbitrary Bayes Net
GaussianBayesNet gbn;
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
0, Vector_(2, 1.0,2.0), Matrix_(2,2, 3.0,4.0,0.0,6.0),
3, Matrix_(2,2, 7.0,8.0,9.0,10.0),
4, Matrix_(2,2, 11.0,12.0,13.0,14.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
1, Vector_(2, 15.0,16.0), Matrix_(2,2, 17.0,18.0,0.0,20.0),
2, Matrix_(2,2, 21.0,22.0,23.0,24.0),
4, Matrix_(2,2, 25.0,26.0,27.0,28.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
2, Vector_(2, 29.0,30.0), Matrix_(2,2, 31.0,32.0,0.0,34.0),
3, Matrix_(2,2, 35.0,36.0,37.0,38.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
3, Vector_(2, 39.0,40.0), Matrix_(2,2, 41.0,42.0,0.0,44.0),
4, Matrix_(2,2, 45.0,46.0,47.0,48.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
4, Vector_(2, 49.0,50.0), Matrix_(2,2, 51.0,52.0,0.0,54.0), ones(2)));
// Compute the Hessian numerically
Matrix hessian = numericalHessian(
boost::function<double(const LieVector&)>(boost::bind(&computeError, gbn, _1)),
LieVector(VectorValues::Zero(*allocateVectorValues(gbn)).vector()));
// Compute the gradient numerically
VectorValues gradientValues = *allocateVectorValues(gbn);
Vector gradient = numericalGradient(
boost::function<double(const LieVector&)>(boost::bind(&computeError, gbn, _1)),
LieVector(VectorValues::Zero(gradientValues).vector()));
gradientValues.vector() = gradient;
// Compute the gradient using dense matrices
Matrix augmentedHessian = GaussianFactorGraph(gbn).denseHessian();
LONGS_EQUAL(11, augmentedHessian.cols());
VectorValues denseMatrixGradient = *allocateVectorValues(gbn);
denseMatrixGradient.vector() = -augmentedHessian.col(10).segment(0,10);
EXPECT(assert_equal(gradientValues, denseMatrixGradient, 1e-5));
// Compute the steepest descent point
double step = -gradient.squaredNorm() / (gradient.transpose() * hessian * gradient)(0);
VectorValues expected = gradientValues; scal(step, expected);
// Compute the steepest descent point with the dogleg function
VectorValues actual = DoglegOptimizerImpl::ComputeSteepestDescentPoint(gbn);
// Check that points agree
EXPECT(assert_equal(expected, actual, 1e-5));
// Check that point causes a decrease in error
double origError = GaussianFactorGraph(gbn).error(VectorValues::Zero(*allocateVectorValues(gbn)));
double newError = GaussianFactorGraph(gbn).error(actual);
EXPECT(newError < origError);
}
/* ************************************************************************* */
TEST(DoglegOptimizer, BT_BN_equivalency) {
// Create an arbitrary Bayes Tree
BayesTree<GaussianConditional> bt;
bt.insert(BayesTree<GaussianConditional>::sharedClique(new BayesTree<GaussianConditional>::Clique(
GaussianConditional::shared_ptr(new GaussianConditional(
boost::assign::pair_list_of
(2, Matrix_(6,2,
31.0,32.0,
0.0,34.0,
0.0,0.0,
0.0,0.0,
0.0,0.0,
0.0,0.0))
(3, Matrix_(6,2,
35.0,36.0,
37.0,38.0,
41.0,42.0,
0.0,44.0,
0.0,0.0,
0.0,0.0))
(4, Matrix_(6,2,
0.0,0.0,
0.0,0.0,
45.0,46.0,
47.0,48.0,
51.0,52.0,
0.0,54.0)),
3, Vector_(6, 29.0,30.0,39.0,40.0,49.0,50.0), ones(6))))));
bt.insert(BayesTree<GaussianConditional>::sharedClique(new BayesTree<GaussianConditional>::Clique(
GaussianConditional::shared_ptr(new GaussianConditional(
boost::assign::pair_list_of
(0, Matrix_(4,2,
3.0,4.0,
0.0,6.0,
0.0,0.0,
0.0,0.0))
(1, Matrix_(4,2,
0.0,0.0,
0.0,0.0,
17.0,18.0,
0.0,20.0))
(2, Matrix_(4,2,
0.0,0.0,
0.0,0.0,
21.0,22.0,
23.0,24.0))
(3, Matrix_(4,2,
7.0,8.0,
9.0,10.0,
0.0,0.0,
0.0,0.0))
(4, Matrix_(4,2,
11.0,12.0,
13.0,14.0,
25.0,26.0,
27.0,28.0)),
2, Vector_(4, 1.0,2.0,15.0,16.0), ones(4))))));
// Create an arbitrary Bayes Net
GaussianBayesNet gbn;
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
0, Vector_(2, 1.0,2.0), Matrix_(2,2, 3.0,4.0,0.0,6.0),
3, Matrix_(2,2, 7.0,8.0,9.0,10.0),
4, Matrix_(2,2, 11.0,12.0,13.0,14.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
1, Vector_(2, 15.0,16.0), Matrix_(2,2, 17.0,18.0,0.0,20.0),
2, Matrix_(2,2, 21.0,22.0,23.0,24.0),
4, Matrix_(2,2, 25.0,26.0,27.0,28.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
2, Vector_(2, 29.0,30.0), Matrix_(2,2, 31.0,32.0,0.0,34.0),
3, Matrix_(2,2, 35.0,36.0,37.0,38.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
3, Vector_(2, 39.0,40.0), Matrix_(2,2, 41.0,42.0,0.0,44.0),
4, Matrix_(2,2, 45.0,46.0,47.0,48.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
4, Vector_(2, 49.0,50.0), Matrix_(2,2, 51.0,52.0,0.0,54.0), ones(2)));
GaussianFactorGraph expected(gbn);
GaussianFactorGraph actual(bt);
EXPECT(assert_equal(expected.denseJacobian(), actual.denseJacobian()));
}
/* ************************************************************************* */
TEST(DoglegOptimizer, ComputeSteepestDescentPointBT) {
// Create an arbitrary Bayes Tree
BayesTree<GaussianConditional> bt;
bt.insert(BayesTree<GaussianConditional>::sharedClique(new BayesTree<GaussianConditional>::Clique(
GaussianConditional::shared_ptr(new GaussianConditional(
boost::assign::pair_list_of
(2, Matrix_(6,2,
31.0,32.0,
0.0,34.0,
0.0,0.0,
0.0,0.0,
0.0,0.0,
0.0,0.0))
(3, Matrix_(6,2,
35.0,36.0,
37.0,38.0,
41.0,42.0,
0.0,44.0,
0.0,0.0,
0.0,0.0))
(4, Matrix_(6,2,
0.0,0.0,
0.0,0.0,
45.0,46.0,
47.0,48.0,
51.0,52.0,
0.0,54.0)),
3, Vector_(6, 29.0,30.0,39.0,40.0,49.0,50.0), ones(6))))));
bt.insert(BayesTree<GaussianConditional>::sharedClique(new BayesTree<GaussianConditional>::Clique(
GaussianConditional::shared_ptr(new GaussianConditional(
boost::assign::pair_list_of
(0, Matrix_(4,2,
3.0,4.0,
0.0,6.0,
0.0,0.0,
0.0,0.0))
(1, Matrix_(4,2,
0.0,0.0,
0.0,0.0,
17.0,18.0,
0.0,20.0))
(2, Matrix_(4,2,
0.0,0.0,
0.0,0.0,
21.0,22.0,
23.0,24.0))
(3, Matrix_(4,2,
7.0,8.0,
9.0,10.0,
0.0,0.0,
0.0,0.0))
(4, Matrix_(4,2,
11.0,12.0,
13.0,14.0,
25.0,26.0,
27.0,28.0)),
2, Vector_(4, 1.0,2.0,15.0,16.0), ones(4))))));
// Compute the Hessian numerically
Matrix hessian = numericalHessian(
boost::function<double(const LieVector&)>(boost::bind(&computeErrorBt, bt, _1)),
LieVector(VectorValues::Zero(*allocateVectorValues(bt)).vector()));
// Compute the gradient numerically
VectorValues gradientValues = *allocateVectorValues(bt);
Vector gradient = numericalGradient(
boost::function<double(const LieVector&)>(boost::bind(&computeErrorBt, bt, _1)),
LieVector(VectorValues::Zero(gradientValues).vector()));
gradientValues.vector() = gradient;
// Compute the gradient using dense matrices
Matrix augmentedHessian = GaussianFactorGraph(bt).denseHessian();
LONGS_EQUAL(11, augmentedHessian.cols());
VectorValues denseMatrixGradient = *allocateVectorValues(bt);
denseMatrixGradient.vector() = -augmentedHessian.col(10).segment(0,10);
EXPECT(assert_equal(gradientValues, denseMatrixGradient, 1e-5));
// Compute the steepest descent point
double step = -gradient.squaredNorm() / (gradient.transpose() * hessian * gradient)(0);
VectorValues expected = gradientValues; scal(step, expected);
// Known steepest descent point from Bayes' net version
VectorValues expectedFromBN(5,2);
expectedFromBN[0] = Vector_(2, 0.000129034, 0.000688183);
expectedFromBN[1] = Vector_(2, 0.0109679, 0.0253767);
expectedFromBN[2] = Vector_(2, 0.0680441, 0.114496);
expectedFromBN[3] = Vector_(2, 0.16125, 0.241294);
expectedFromBN[4] = Vector_(2, 0.300134, 0.423233);
// Compute the steepest descent point with the dogleg function
VectorValues actual = DoglegOptimizerImpl::ComputeSteepestDescentPoint(bt);
// Check that points agree
EXPECT(assert_equal(expected, actual, 1e-5));
EXPECT(assert_equal(expectedFromBN, actual, 1e-5));
// Check that point causes a decrease in error
double origError = GaussianFactorGraph(bt).error(VectorValues::Zero(*allocateVectorValues(bt)));
double newError = GaussianFactorGraph(bt).error(actual);
EXPECT(newError < origError);
}
/* ************************************************************************* */
TEST(DoglegOptimizer, ComputeBlend) {
// Create an arbitrary Bayes Net
GaussianBayesNet gbn;
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
0, Vector_(2, 1.0,2.0), Matrix_(2,2, 3.0,4.0,0.0,6.0),
3, Matrix_(2,2, 7.0,8.0,9.0,10.0),
4, Matrix_(2,2, 11.0,12.0,13.0,14.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
1, Vector_(2, 15.0,16.0), Matrix_(2,2, 17.0,18.0,0.0,20.0),
2, Matrix_(2,2, 21.0,22.0,23.0,24.0),
4, Matrix_(2,2, 25.0,26.0,27.0,28.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
2, Vector_(2, 29.0,30.0), Matrix_(2,2, 31.0,32.0,0.0,34.0),
3, Matrix_(2,2, 35.0,36.0,37.0,38.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
3, Vector_(2, 39.0,40.0), Matrix_(2,2, 41.0,42.0,0.0,44.0),
4, Matrix_(2,2, 45.0,46.0,47.0,48.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
4, Vector_(2, 49.0,50.0), Matrix_(2,2, 51.0,52.0,0.0,54.0), ones(2)));
// Compute steepest descent point
VectorValues xu = DoglegOptimizerImpl::ComputeSteepestDescentPoint(gbn);
// Compute Newton's method point
VectorValues xn = optimize(gbn);
// The Newton's method point should be more "adventurous", i.e. larger, than the steepest descent point
EXPECT(xu.vector().norm() < xn.vector().norm());
// Compute blend
double Delta = 1.5;
VectorValues xb = DoglegOptimizerImpl::ComputeBlend(Delta, xu, xn);
DOUBLES_EQUAL(Delta, xb.vector().norm(), 1e-10);
}
/* ************************************************************************* */
TEST(DoglegOptimizer, ComputeDoglegPoint) {
// Create an arbitrary Bayes Net
GaussianBayesNet gbn;
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
0, Vector_(2, 1.0,2.0), Matrix_(2,2, 3.0,4.0,0.0,6.0),
3, Matrix_(2,2, 7.0,8.0,9.0,10.0),
4, Matrix_(2,2, 11.0,12.0,13.0,14.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
1, Vector_(2, 15.0,16.0), Matrix_(2,2, 17.0,18.0,0.0,20.0),
2, Matrix_(2,2, 21.0,22.0,23.0,24.0),
4, Matrix_(2,2, 25.0,26.0,27.0,28.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
2, Vector_(2, 29.0,30.0), Matrix_(2,2, 31.0,32.0,0.0,34.0),
3, Matrix_(2,2, 35.0,36.0,37.0,38.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
3, Vector_(2, 39.0,40.0), Matrix_(2,2, 41.0,42.0,0.0,44.0),
4, Matrix_(2,2, 45.0,46.0,47.0,48.0), ones(2)));
gbn += GaussianConditional::shared_ptr(new GaussianConditional(
4, Vector_(2, 49.0,50.0), Matrix_(2,2, 51.0,52.0,0.0,54.0), ones(2)));
// Compute dogleg point for different deltas
double Delta1 = 0.5; // Less than steepest descent
VectorValues actual1 = DoglegOptimizerImpl::ComputeDoglegPoint(Delta1, DoglegOptimizerImpl::ComputeSteepestDescentPoint(gbn), optimize(gbn));
DOUBLES_EQUAL(Delta1, actual1.vector().norm(), 1e-5);
double Delta2 = 1.5; // Between steepest descent and Newton's method
VectorValues expected2 = DoglegOptimizerImpl::ComputeBlend(Delta2, DoglegOptimizerImpl::ComputeSteepestDescentPoint(gbn), optimize(gbn));
VectorValues actual2 = DoglegOptimizerImpl::ComputeDoglegPoint(Delta2, DoglegOptimizerImpl::ComputeSteepestDescentPoint(gbn), optimize(gbn));
DOUBLES_EQUAL(Delta2, actual2.vector().norm(), 1e-5);
EXPECT(assert_equal(expected2, actual2));
double Delta3 = 5.0; // Larger than Newton's method point
VectorValues expected3 = optimize(gbn);
VectorValues actual3 = DoglegOptimizerImpl::ComputeDoglegPoint(Delta3, DoglegOptimizerImpl::ComputeSteepestDescentPoint(gbn), optimize(gbn));
EXPECT(assert_equal(expected3, actual3));
}
/* ************************************************************************* */
TEST(DoglegOptimizer, Iterate) {
// really non-linear factor graph
shared_ptr<example::Graph> fg(new example::Graph(
example::createReallyNonlinearFactorGraph()));
// config far from minimum
Point2 x0(3,0);
boost::shared_ptr<Values> config(new Values);
config->insert(simulated2D::PoseKey(1), x0);
// ordering
shared_ptr<Ordering> ord(new Ordering());
ord->push_back(simulated2D::PoseKey(1));
double Delta = 1.0;
for(size_t it=0; it<10; ++it) {
GaussianSequentialSolver solver(*fg->linearize(*config, *ord));
GaussianBayesNet gbn = *solver.eliminate();
// Iterate assumes that linear error = nonlinear error at the linearization point, and this should be true
double nonlinearError = fg->error(*config);
double linearError = GaussianFactorGraph(gbn).error(VectorValues::Zero(*allocateVectorValues(gbn)));
DOUBLES_EQUAL(nonlinearError, linearError, 1e-5);
// cout << "it " << it << ", Delta = " << Delta << ", error = " << fg->error(*config) << endl;
DoglegOptimizerImpl::IterationResult result = DoglegOptimizerImpl::Iterate(Delta, DoglegOptimizerImpl::SEARCH_EACH_ITERATION, gbn, *fg, *config, *ord, fg->error(*config));
Delta = result.Delta;
EXPECT(result.f_error < fg->error(*config)); // Check that error decreases
Values newConfig(config->retract(result.dx_d, *ord));
(*config) = newConfig;
DOUBLES_EQUAL(fg->error(*config), result.f_error, 1e-5); // Check that error is correctly filled in
}
}
/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
/* ************************************************************************* */
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