394 lines
15 KiB
C++
394 lines
15 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 <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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#include <CppUnitLite/TestHarness.h>
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#define GTSAM_MAGIC_KEY
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#include <gtsam/geometry/Rot2.h>
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#include <gtsam/nonlinear/Ordering.h>
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#include <gtsam/linear/GaussianBayesNet.h>
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#include <gtsam/inference/ISAM-inl.h>
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#include <gtsam/linear/GaussianISAM.h>
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#include <gtsam/linear/GaussianSequentialSolver.h>
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#include <gtsam/linear/GaussianMultifrontalSolver.h>
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#include <gtsam/slam/smallExample.h>
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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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/* ************************************************************************* */
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// Some numbers that should be consistent among all smoother tests
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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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const double tol = 1e-4;
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/* ************************************************************************* */
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TEST( ISAM, iSAM_smoother )
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{
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Ordering ordering;
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for (int t = 1; t <= 7; t++) ordering += Symbol('x', t);
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// Create smoother with 7 nodes
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GaussianFactorGraph smoother = createSmoother(7, ordering).first;
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// run iSAM for every factor
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GaussianISAM actual;
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BOOST_FOREACH(boost::shared_ptr<GaussianFactor> factor, smoother) {
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GaussianFactorGraph factorGraph;
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factorGraph.push_back(factor);
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actual.update(factorGraph);
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}
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// Create expected Bayes Tree by solving smoother with "natural" ordering
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GaussianISAM expected(*GaussianSequentialSolver(smoother).eliminate());
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// Check whether BayesTree is correct
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CHECK(assert_equal(expected, actual));
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// obtain solution
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VectorValues e(vector<size_t>(7,2)); // expected solution
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e.makeZero();
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VectorValues optimized = optimize(actual); // actual solution
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CHECK(assert_equal(e, optimized));
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}
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/* ************************************************************************* */
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// SL-FIX TEST( ISAM, iSAM_smoother2 )
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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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//
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// // Create initial tree from first 4 timestamps in reverse order !
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// Ordering ord; ord += "x4","x3","x2","x1";
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// GaussianFactorGraph factors1;
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// for (int i=0;i<7;i++) factors1.push_back(smoother[i]);
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// GaussianISAM actual(*Inference::Eliminate(factors1));
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//
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// // run iSAM with remaining factors
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// GaussianFactorGraph factors2;
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// for (int i=7;i<13;i++) factors2.push_back(smoother[i]);
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// actual.update(factors2);
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//
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// // Create expected Bayes Tree by solving smoother with "natural" ordering
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// Ordering ordering;
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// for (int t = 1; t <= 7; t++) ordering += symbol('x', t);
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// GaussianISAM expected(smoother.eliminate(ordering));
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//
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// CHECK(assert_equal(expected, actual));
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//}
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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( BayesTree, linear_smoother_shortcuts )
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{
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// Create smoother with 7 nodes
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Ordering ordering;
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GaussianFactorGraph smoother;
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boost::tie(smoother, ordering) = createSmoother(7);
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// eliminate using the "natural" ordering
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GaussianBayesNet chordalBayesNet = *GaussianSequentialSolver(smoother).eliminate();
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// Create the Bayes tree
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GaussianISAM bayesTree(chordalBayesNet);
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LONGS_EQUAL(6,bayesTree.size());
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// Check the conditional P(Root|Root)
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GaussianBayesNet empty;
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GaussianISAM::sharedClique R = bayesTree.root();
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GaussianBayesNet actual1 = R->shortcut(R);
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CHECK(assert_equal(empty,actual1,tol));
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// Check the conditional P(C2|Root)
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GaussianISAM::sharedClique C2 = bayesTree[ordering["x5"]];
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GaussianBayesNet actual2 = C2->shortcut(R);
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CHECK(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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push_front(expected3,ordering["x5"], zero(2), eye(2)/sigma3, ordering["x6"], A56/sigma3, ones(2));
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GaussianISAM::sharedClique C3 = bayesTree[ordering["x4"]];
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GaussianBayesNet actual3 = C3->shortcut(R);
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CHECK(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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push_front(expected4, ordering["x4"], zero(2), eye(2)/sigma4, ordering["x6"], A46/sigma4, ones(2));
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GaussianISAM::sharedClique C4 = bayesTree[ordering["x3"]];
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GaussianBayesNet actual4 = C4->shortcut(R);
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CHECK(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( BayesTree, balanced_smoother_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 += "x1","x3","x5","x7","x2","x6","x4";
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GaussianFactorGraph smoother = createSmoother(7, ordering).first;
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// Create the Bayes tree
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GaussianBayesNet chordalBayesNet = *GaussianSequentialSolver(smoother).eliminate();
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VectorValues expectedSolution(7, 2);
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expectedSolution.makeZero();
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VectorValues actualSolution = optimize(chordalBayesNet);
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CHECK(assert_equal(expectedSolution,actualSolution,tol));
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// Create the Bayes tree
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GaussianISAM bayesTree(chordalBayesNet);
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LONGS_EQUAL(4,bayesTree.size());
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double tol=1e-5;
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// Check marginal on x1
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GaussianBayesNet expected1 = simpleGaussian(ordering["x1"], zero(2), sigmax1);
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GaussianBayesNet actual1 = *bayesTree.marginalBayesNet(ordering["x1"]);
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Matrix expectedCovarianceX1 = eye(2,2) * (sigmax1 * sigmax1);
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Vector expectedMeanX1 = zero(2);
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Matrix actualCovarianceX1; Vector actualMeanX1;
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boost::tie(actualMeanX1, actualCovarianceX1) = bayesTree.marginal(ordering["x1"]);
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EXPECT(assert_equal(expectedCovarianceX1, actualCovarianceX1, tol));
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EXPECT(assert_equal(expectedMeanX1, actualMeanX1, 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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GaussianBayesNet expected2 = simpleGaussian(ordering["x2"], zero(2), sigx2);
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GaussianBayesNet actual2 = *bayesTree.marginalBayesNet(ordering["x2"]);
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Matrix expectedCovarianceX2 = eye(2,2) * (sigx2 * sigx2);
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Vector expectedMeanX2 = zero(2);
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Matrix actualCovarianceX2; Vector actualMeanX2;
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boost::tie(actualMeanX2, actualCovarianceX2) = bayesTree.marginal(ordering["x2"]);
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EXPECT(assert_equal(expectedCovarianceX2, actualCovarianceX2, tol));
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EXPECT(assert_equal(expectedMeanX2, actualMeanX2, tol));
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EXPECT(assert_equal(expected2,actual2,tol));
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// Check marginal on x3
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GaussianBayesNet expected3 = simpleGaussian(ordering["x3"], zero(2), sigmax3);
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GaussianBayesNet actual3 = *bayesTree.marginalBayesNet(ordering["x3"]);
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Matrix expectedCovarianceX3 = eye(2,2) * (sigmax3 * sigmax3);
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Vector expectedMeanX3 = zero(2);
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Matrix actualCovarianceX3; Vector actualMeanX3;
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boost::tie(actualMeanX3, actualCovarianceX3) = bayesTree.marginal(ordering["x3"]);
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EXPECT(assert_equal(expectedCovarianceX3, actualCovarianceX3, tol));
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EXPECT(assert_equal(expectedMeanX3, actualMeanX3, tol));
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EXPECT(assert_equal(expected3,actual3,tol));
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// Check marginal on x4
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GaussianBayesNet expected4 = simpleGaussian(ordering["x4"], zero(2), sigmax4);
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GaussianBayesNet actual4 = *bayesTree.marginalBayesNet(ordering["x4"]);
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Matrix expectedCovarianceX4 = eye(2,2) * (sigmax4 * sigmax4);
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Vector expectedMeanX4 = zero(2);
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Matrix actualCovarianceX4; Vector actualMeanX4;
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boost::tie(actualMeanX4, actualCovarianceX4) = bayesTree.marginal(ordering["x4"]);
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EXPECT(assert_equal(expectedCovarianceX4, actualCovarianceX4, tol));
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EXPECT(assert_equal(expectedMeanX4, actualMeanX4, tol));
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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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GaussianBayesNet expected7 = simpleGaussian(ordering["x7"], zero(2), sigmax7);
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GaussianBayesNet actual7 = *bayesTree.marginalBayesNet(ordering["x7"]);
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Matrix expectedCovarianceX7 = eye(2,2) * (sigmax7 * sigmax7);
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Vector expectedMeanX7 = zero(2);
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Matrix actualCovarianceX7; Vector actualMeanX7;
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boost::tie(actualMeanX7, actualCovarianceX7) = bayesTree.marginal(ordering["x7"]);
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EXPECT(assert_equal(expectedCovarianceX7, actualCovarianceX7, tol));
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EXPECT(assert_equal(expectedMeanX7, actualMeanX7, tol));
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EXPECT(assert_equal(expected7,actual7,tol));
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}
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/* ************************************************************************* */
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TEST( BayesTree, balanced_smoother_shortcuts )
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{
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// Create smoother with 7 nodes
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Ordering ordering;
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ordering += "x1","x3","x5","x7","x2","x6","x4";
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GaussianFactorGraph smoother = createSmoother(7, ordering).first;
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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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// Check the conditional P(Root|Root)
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GaussianBayesNet empty;
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GaussianISAM::sharedClique R = bayesTree.root();
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GaussianBayesNet actual1 = R->shortcut(R);
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CHECK(assert_equal(empty,actual1,tol));
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// Check the conditional P(C2|Root)
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GaussianISAM::sharedClique C2 = bayesTree[ordering["x3"]];
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GaussianBayesNet actual2 = C2->shortcut(R);
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CHECK(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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GaussianConditional::shared_ptr p_x2_x4 = chordalBayesNet[ordering["x2"]];
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GaussianBayesNet expected3; expected3.push_back(p_x2_x4);
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GaussianISAM::sharedClique C3 = bayesTree[ordering["x1"]];
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GaussianBayesNet actual3 = C3->shortcut(R);
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CHECK(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 += "x1","x3","x5","x7","x2","x6","x4";
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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["x2"],zero(2),sigmax2_alt);
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// push_front(expected,ordering["x1"], zero(2), eye(2)*sqrt(2), ordering["x2"], -eye(2)*sqrt(2)/2, ones(2));
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// GaussianISAM::sharedClique R = bayesTree.root(), C3 = bayesTree[ordering["x1"]];
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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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// CHECK(assert_equal(expected,actual,tol));
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//}
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/* ************************************************************************* */
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TEST( BayesTree, 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 += "x1","x3","x5","x7","x2","x6","x4";
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GaussianFactorGraph smoother = createSmoother(7, ordering).first;
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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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GaussianBayesNet chordalBayesNet = *GaussianSequentialSolver(smoother).eliminate();
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GaussianISAM bayesTree(chordalBayesNet);
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// Conditional density elements reused by both tests
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const Vector sigma = ones(2);
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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;
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// Why does the sign get flipped on the prior?
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GaussianConditional::shared_ptr
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parent1(new GaussianConditional(ordering["x7"], zero(2), -1*I/sigmax7, ones(2)));
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expected1.push_front(parent1);
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push_front(expected1,ordering["x1"], zero(2), I/sigmax7, ordering["x7"], A/sigmax7, sigma);
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GaussianBayesNet actual1 = *bayesTree.jointBayesNet(ordering["x1"],ordering["x7"]);
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CHECK(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(ordering["x1"], zero(2), -1*I/sigmax1, ones(2)));
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// expected2.push_front(parent2);
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// push_front(expected2,ordering["x7"], zero(2), I/sigmax1, ordering["x1"], A/sigmax1, sigma);
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// GaussianBayesNet actual2 = *bayesTree.jointBayesNet(ordering["x7"],ordering["x1"]);
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// CHECK(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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GaussianBayesNet expected3;
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GaussianConditional::shared_ptr
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parent3(new GaussianConditional(ordering["x4"], zero(2), I/sigmax4, ones(2)));
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expected3.push_front(parent3);
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double sig14 = 0.784465;
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Matrix A14 = -0.0769231*I;
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push_front(expected3,ordering["x1"], zero(2), I/sig14, ordering["x4"], A14/sig14, sigma);
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GaussianBayesNet actual3 = *bayesTree.jointBayesNet(ordering["x1"],ordering["x4"]);
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CHECK(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(ordering["x1"], 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,ordering["x4"], zero(2), I/sig41, ordering["x1"], A41/sig41, sigma);
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// GaussianBayesNet actual4 = *bayesTree.jointBayesNet(ordering["x4"],ordering["x1"]);
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// CHECK(assert_equal(expected4,actual4,tol));
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}
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/* ************************************************************************* */
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TEST(BayesTree, simpleMarginal)
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{
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GaussianFactorGraph gfg;
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Matrix A12 = Rot2::fromDegrees(45.0).matrix();
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gfg.add(0, eye(2), zero(2), sharedSigma(2, 1.0));
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gfg.add(0, -eye(2), 1, eye(2), ones(2), sharedSigma(2, 1.0));
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gfg.add(1, -eye(2), 2, A12, ones(2), sharedSigma(2, 1.0));
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Matrix expected(GaussianSequentialSolver(gfg).marginalCovariance(2).second);
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Matrix actual(GaussianMultifrontalSolver(gfg).marginalCovariance(2).second);
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CHECK(assert_equal(expected, actual));
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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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