328 lines
13 KiB
C++
328 lines
13 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file testGaussianISAM.cpp
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* @brief Unit tests for GaussianISAM
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* @author Michael Kaess
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*/
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#include <tests/smallExample.h>
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#include <gtsam/inference/Symbol.h>
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#include <gtsam/linear/GaussianBayesTree.h>
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#include <gtsam/linear/GaussianBayesNet.h>
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#include <gtsam/linear/GaussianConditional.h>
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#include <gtsam/linear/GaussianDensity.h>
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#include <gtsam/linear/HessianFactor.h>
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#include <gtsam/geometry/Rot2.h>
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#include <CppUnitLite/TestHarness.h>
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#include <boost/foreach.hpp>
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#include <boost/assign/std/list.hpp> // for operator +=
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using namespace boost::assign;
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using namespace std;
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using namespace gtsam;
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using namespace example;
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using symbol_shorthand::X;
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using symbol_shorthand::L;
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/* ************************************************************************* */
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// Some numbers that should be consistent among all smoother tests
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static double sigmax1 = 0.786153, /*sigmax2 = 1.0/1.47292,*/ sigmax3 = 0.671512, sigmax4 =
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0.669534 /*, sigmax5 = sigmax3, sigmax6 = sigmax2*/, sigmax7 = sigmax1;
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static const double tol = 1e-4;
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/* ************************************************************************* *
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Bayes tree for smoother with "natural" ordering:
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C1 x6 x7
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C2 x5 : x6
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C3 x4 : x5
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C4 x3 : x4
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C5 x2 : x3
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C6 x1 : x2
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**************************************************************************** */
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TEST( GaussianBayesTree, linear_smoother_shortcuts )
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{
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// Create smoother with 7 nodes
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GaussianFactorGraph smoother = createSmoother(7);
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GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal();
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// Create the Bayes tree
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LONGS_EQUAL(6, (long)bayesTree.size());
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// Check the conditional P(Root|Root)
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GaussianBayesNet empty;
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GaussianBayesTree::sharedClique R = bayesTree.roots().front();
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GaussianBayesNet actual1 = R->shortcut(R);
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EXPECT(assert_equal(empty,actual1,tol));
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// Check the conditional P(C2|Root)
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GaussianBayesTree::sharedClique C2 = bayesTree[X(5)];
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GaussianBayesNet actual2 = C2->shortcut(R);
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EXPECT(assert_equal(empty,actual2,tol));
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// Check the conditional P(C3|Root)
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double sigma3 = 0.61808;
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Matrix A56 = (Matrix(2,2) << -0.382022,0.,0.,-0.382022);
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GaussianBayesNet expected3;
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expected3 += GaussianConditional(X(5), zero(2), eye(2)/sigma3, X(6), A56/sigma3);
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GaussianBayesTree::sharedClique C3 = bayesTree[X(4)];
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GaussianBayesNet actual3 = C3->shortcut(R);
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EXPECT(assert_equal(expected3,actual3,tol));
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// Check the conditional P(C4|Root)
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double sigma4 = 0.661968;
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Matrix A46 = (Matrix(2,2) << -0.146067,0.,0.,-0.146067);
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GaussianBayesNet expected4;
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expected4 += GaussianConditional(X(4), zero(2), eye(2)/sigma4, X(6), A46/sigma4);
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GaussianBayesTree::sharedClique C4 = bayesTree[X(3)];
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GaussianBayesNet actual4 = C4->shortcut(R);
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EXPECT(assert_equal(expected4,actual4,tol));
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}
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/* ************************************************************************* *
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Bayes tree for smoother with "nested dissection" ordering:
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Node[x1] P(x1 | x2)
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Node[x3] P(x3 | x2 x4)
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Node[x5] P(x5 | x4 x6)
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Node[x7] P(x7 | x6)
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Node[x2] P(x2 | x4)
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Node[x6] P(x6 | x4)
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Node[x4] P(x4)
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becomes
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C1 x5 x6 x4
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C2 x3 x2 : x4
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C3 x1 : x2
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C4 x7 : x6
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************************************************************************* */
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TEST( GaussianBayesTree, balanced_smoother_marginals )
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{
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// Create smoother with 7 nodes
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GaussianFactorGraph smoother = createSmoother(7);
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// Create the Bayes tree
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Ordering ordering;
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ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4);
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GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering);
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VectorValues actualSolution = bayesTree.optimize();
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VectorValues expectedSolution = VectorValues::Zero(actualSolution);
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EXPECT(assert_equal(expectedSolution,actualSolution,tol));
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LONGS_EQUAL(4, (long)bayesTree.size());
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double tol=1e-5;
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// Check marginal on x1
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JacobianFactor expected1 = GaussianDensity::FromMeanAndStddev(X(1), zero(2), sigmax1);
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JacobianFactor actual1 = *bayesTree.marginalFactor(X(1));
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Matrix expectedCovarianceX1 = eye(2,2) * (sigmax1 * sigmax1);
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Matrix actualCovarianceX1;
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GaussianFactor::shared_ptr m = bayesTree.marginalFactor(X(1), EliminateCholesky);
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actualCovarianceX1 = bayesTree.marginalFactor(X(1), EliminateCholesky)->information().inverse();
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EXPECT(assert_equal(expectedCovarianceX1, actualCovarianceX1, tol));
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EXPECT(assert_equal(expected1,actual1,tol));
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// Check marginal on x2
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double sigx2 = 0.68712938; // FIXME: this should be corrected analytically
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JacobianFactor expected2 = GaussianDensity::FromMeanAndStddev(X(2), zero(2), sigx2);
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JacobianFactor actual2 = *bayesTree.marginalFactor(X(2));
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EXPECT(assert_equal(expected2,actual2,tol));
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// Check marginal on x3
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JacobianFactor expected3 = GaussianDensity::FromMeanAndStddev(X(3), zero(2), sigmax3);
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JacobianFactor actual3 = *bayesTree.marginalFactor(X(3));
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EXPECT(assert_equal(expected3,actual3,tol));
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// Check marginal on x4
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JacobianFactor expected4 = GaussianDensity::FromMeanAndStddev(X(4), zero(2), sigmax4);
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JacobianFactor actual4 = *bayesTree.marginalFactor(X(4));
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EXPECT(assert_equal(expected4,actual4,tol));
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// Check marginal on x7 (should be equal to x1)
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JacobianFactor expected7 = GaussianDensity::FromMeanAndStddev(X(7), zero(2), sigmax7);
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JacobianFactor actual7 = *bayesTree.marginalFactor(X(7));
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EXPECT(assert_equal(expected7,actual7,tol));
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}
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/* ************************************************************************* */
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TEST( GaussianBayesTree, balanced_smoother_shortcuts )
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{
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// Create smoother with 7 nodes
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GaussianFactorGraph smoother = createSmoother(7);
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// Create the Bayes tree
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Ordering ordering;
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ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4);
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GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering);
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// Check the conditional P(Root|Root)
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GaussianBayesNet empty;
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GaussianBayesTree::sharedClique R = bayesTree.roots().front();
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GaussianBayesNet actual1 = R->shortcut(R);
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EXPECT(assert_equal(empty,actual1,tol));
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// Check the conditional P(C2|Root)
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GaussianBayesTree::sharedClique C2 = bayesTree[X(3)];
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GaussianBayesNet actual2 = C2->shortcut(R);
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EXPECT(assert_equal(empty,actual2,tol));
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// Check the conditional P(C3|Root), which should be equal to P(x2|x4)
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/** TODO: Note for multifrontal conditional:
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* p_x2_x4 is now an element conditional of the multifrontal conditional bayesTree[ordering[X(2)]]->conditional()
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* We don't know yet how to take it out.
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*/
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// GaussianConditional::shared_ptr p_x2_x4 = bayesTree[ordering[X(2)]]->conditional();
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// p_x2_x4->print("Conditional p_x2_x4: ");
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// GaussianBayesNet expected3(p_x2_x4);
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// GaussianISAM::sharedClique C3 = isamTree[ordering[X(1)]];
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// GaussianBayesNet actual3 = GaussianISAM::shortcut(C3,R);
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// EXPECT(assert_equal(expected3,actual3,tol));
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}
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///* ************************************************************************* */
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//TEST( BayesTree, balanced_smoother_clique_marginals )
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//{
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// // Create smoother with 7 nodes
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// Ordering ordering;
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// ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4);
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// GaussianFactorGraph smoother = createSmoother(7, ordering).first;
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//
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// // Create the Bayes tree
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// GaussianBayesNet chordalBayesNet = *GaussianSequentialSolver(smoother).eliminate();
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// GaussianISAM bayesTree(chordalBayesNet);
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//
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// // Check the clique marginal P(C3)
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// double sigmax2_alt = 1/1.45533; // THIS NEEDS TO BE CHECKED!
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// GaussianBayesNet expected = simpleGaussian(ordering[X(2)],zero(2),sigmax2_alt);
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// push_front(expected,ordering[X(1)], zero(2), eye(2)*sqrt(2), ordering[X(2)], -eye(2)*sqrt(2)/2, ones(2));
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// GaussianISAM::sharedClique R = bayesTree.root(), C3 = bayesTree[ordering[X(1)]];
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// GaussianFactorGraph marginal = C3->marginal(R);
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// GaussianVariableIndex varIndex(marginal);
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// Permutation toFront(Permutation::PullToFront(C3->keys(), varIndex.size()));
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// Permutation toFrontInverse(*toFront.inverse());
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// varIndex.permute(toFront);
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// BOOST_FOREACH(const GaussianFactor::shared_ptr& factor, marginal) {
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// factor->permuteWithInverse(toFrontInverse); }
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// GaussianBayesNet actual = *inference::EliminateUntil(marginal, C3->keys().size(), varIndex);
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// actual.permuteWithInverse(toFront);
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// EXPECT(assert_equal(expected,actual,tol));
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//}
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/* ************************************************************************* */
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TEST( GaussianBayesTree, balanced_smoother_joint )
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{
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// Create smoother with 7 nodes
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Ordering ordering;
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ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4);
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GaussianFactorGraph smoother = createSmoother(7);
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// Create the Bayes tree, expected to look like:
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// x5 x6 x4
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// x3 x2 : x4
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// x1 : x2
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// x7 : x6
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GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering);
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// Conditional density elements reused by both tests
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const Matrix I = eye(2), A = -0.00429185*I;
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// Check the joint density P(x1,x7) factored as P(x1|x7)P(x7)
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GaussianBayesNet expected1 = list_of
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// Why does the sign get flipped on the prior?
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(GaussianConditional(X(1), zero(2), I/sigmax7, X(7), A/sigmax7))
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(GaussianConditional(X(7), zero(2), -1*I/sigmax7));
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GaussianBayesNet actual1 = *bayesTree.jointBayesNet(X(1),X(7));
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EXPECT(assert_equal(expected1, actual1, tol));
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// // Check the joint density P(x7,x1) factored as P(x7|x1)P(x1)
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// GaussianBayesNet expected2;
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// GaussianConditional::shared_ptr
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// parent2(new GaussianConditional(X(1), zero(2), -1*I/sigmax1, ones(2)));
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// expected2.push_front(parent2);
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// push_front(expected2,X(7), zero(2), I/sigmax1, X(1), A/sigmax1, sigma);
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// GaussianBayesNet actual2 = *bayesTree.jointBayesNet(X(7),X(1));
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// EXPECT(assert_equal(expected2,actual2,tol));
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// Check the joint density P(x1,x4), i.e. with a root variable
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double sig14 = 0.784465;
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Matrix A14 = -0.0769231*I;
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GaussianBayesNet expected3 = list_of
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(GaussianConditional(X(1), zero(2), I/sig14, X(4), A14/sig14))
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(GaussianConditional(X(4), zero(2), I/sigmax4));
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GaussianBayesNet actual3 = *bayesTree.jointBayesNet(X(1),X(4));
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EXPECT(assert_equal(expected3,actual3,tol));
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// // Check the joint density P(x4,x1), i.e. with a root variable, factored the other way
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// GaussianBayesNet expected4;
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// GaussianConditional::shared_ptr
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// parent4(new GaussianConditional(X(1), zero(2), -1.0*I/sigmax1, ones(2)));
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// expected4.push_front(parent4);
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// double sig41 = 0.668096;
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// Matrix A41 = -0.055794*I;
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// push_front(expected4,X(4), zero(2), I/sig41, X(1), A41/sig41, sigma);
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// GaussianBayesNet actual4 = *bayesTree.jointBayesNet(X(4),X(1));
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// EXPECT(assert_equal(expected4,actual4,tol));
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}
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/* ************************************************************************* */
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TEST(GaussianBayesTree, shortcut_overlapping_separator)
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{
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// Test computing shortcuts when the separator overlaps. This previously
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// would have highlighted a problem where information was duplicated.
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// Create factor graph:
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// f(1,2,5)
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// f(3,4,5)
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// f(5,6)
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// f(6,7)
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GaussianFactorGraph fg;
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noiseModel::Diagonal::shared_ptr model = noiseModel::Unit::Create(1);
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fg.add(1, (Matrix(1, 1) << 1.0), 3, (Matrix(1, 1) << 2.0), 5, (Matrix(1, 1) << 3.0), (Vector(1) << 4.0), model);
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fg.add(1, (Matrix(1, 1) << 5.0), (Vector(1) << 6.0), model);
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fg.add(2, (Matrix(1, 1) << 7.0), 4, (Matrix(1, 1) << 8.0), 5, (Matrix(1, 1) << 9.0), (Vector(1) << 10.0), model);
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fg.add(2, (Matrix(1, 1) << 11.0), (Vector(1) << 12.0), model);
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fg.add(5, (Matrix(1, 1) << 13.0), 6, (Matrix(1, 1) << 14.0), (Vector(1) << 15.0), model);
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fg.add(6, (Matrix(1, 1) << 17.0), 7, (Matrix(1, 1) << 18.0), (Vector(1) << 19.0), model);
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fg.add(7, (Matrix(1, 1) << 20.0), (Vector(1) << 21.0), model);
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// Eliminate into BayesTree
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// c(6,7)
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// c(5|6)
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// c(1,2|5)
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// c(3,4|5)
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GaussianBayesTree bt = *fg.eliminateMultifrontal(Ordering(fg.keys())); // eliminate in increasing key order, fg.keys() is sorted.
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GaussianFactorGraph joint = *bt.joint(1,2, EliminateQR);
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Matrix expectedJointJ = (Matrix(2,3) <<
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5, 0, 6,
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0, -11, -12
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).finished();
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Matrix actualJointJ = joint.augmentedJacobian();
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EXPECT(assert_equal(expectedJointJ, actualJointJ));
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}
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/* ************************************************************************* */
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int main() { TestResult tr; return TestRegistry::runAllTests(tr);}
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/* ************************************************************************* */
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