/* ---------------------------------------------------------------------------- * 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 testGaussianISAM.cpp * @brief Unit tests for GaussianISAM * @author Michael Kaess */ #include #include #include #include #include #include #include #include #include #include // for operator += using namespace boost::assign; using namespace std; using namespace gtsam; using namespace example; using symbol_shorthand::X; using symbol_shorthand::L; /* ************************************************************************* */ // Some numbers that should be consistent among all smoother tests static double sigmax1 = 0.786153, /*sigmax2 = 1.0/1.47292,*/ sigmax3 = 0.671512, sigmax4 = 0.669534 /*, sigmax5 = sigmax3, sigmax6 = sigmax2*/, sigmax7 = sigmax1; static const double tol = 1e-4; /* ************************************************************************* * Bayes tree for smoother with "natural" ordering: C1 x6 x7 C2 x5 : x6 C3 x4 : x5 C4 x3 : x4 C5 x2 : x3 C6 x1 : x2 **************************************************************************** */ TEST( GaussianBayesTree, linear_smoother_shortcuts ) { // Create smoother with 7 nodes GaussianFactorGraph smoother = createSmoother(7); GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(); // Create the Bayes tree LONGS_EQUAL(6, (long)bayesTree.size()); // Check the conditional P(Root|Root) GaussianBayesNet empty; GaussianBayesTree::sharedClique R = bayesTree.roots().front(); GaussianBayesNet actual1 = R->shortcut(R); EXPECT(assert_equal(empty,actual1,tol)); // Check the conditional P(C2|Root) GaussianBayesTree::sharedClique C2 = bayesTree[X(5)]; GaussianBayesNet actual2 = C2->shortcut(R); EXPECT(assert_equal(empty,actual2,tol)); // Check the conditional P(C3|Root) double sigma3 = 0.61808; Matrix A56 = (Matrix(2,2) << -0.382022,0.,0.,-0.382022).finished(); GaussianBayesNet expected3; expected3 += GaussianConditional(X(5), Z_2x1, I_2x2/sigma3, X(6), A56/sigma3); GaussianBayesTree::sharedClique C3 = bayesTree[X(4)]; GaussianBayesNet actual3 = C3->shortcut(R); EXPECT(assert_equal(expected3,actual3,tol)); // Check the conditional P(C4|Root) double sigma4 = 0.661968; Matrix A46 = (Matrix(2,2) << -0.146067,0.,0.,-0.146067).finished(); GaussianBayesNet expected4; expected4 += GaussianConditional(X(4), Z_2x1, I_2x2/sigma4, X(6), A46/sigma4); GaussianBayesTree::sharedClique C4 = bayesTree[X(3)]; GaussianBayesNet actual4 = C4->shortcut(R); EXPECT(assert_equal(expected4,actual4,tol)); } /* ************************************************************************* * Bayes tree for smoother with "nested dissection" ordering: Node[x1] P(x1 | x2) Node[x3] P(x3 | x2 x4) Node[x5] P(x5 | x4 x6) Node[x7] P(x7 | x6) Node[x2] P(x2 | x4) Node[x6] P(x6 | x4) Node[x4] P(x4) becomes C1 x5 x6 x4 C2 x3 x2 : x4 C3 x1 : x2 C4 x7 : x6 ************************************************************************* */ TEST(GaussianBayesTree, balanced_smoother_marginals) { // Create smoother with 7 nodes GaussianFactorGraph smoother = createSmoother(7); // Create the Bayes tree Ordering ordering; ordering += X(1), X(3), X(5), X(7), X(2), X(6), X(4); GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering); VectorValues actualSolution = bayesTree.optimize(); VectorValues expectedSolution = VectorValues::Zero(actualSolution); EXPECT(assert_equal(expectedSolution, actualSolution, tol)); LONGS_EQUAL(4, bayesTree.size()); double tol = 1e-5; // Check marginal on x1 JacobianFactor actual1 = *bayesTree.marginalFactor(X(1)); Matrix expectedCovX1 = I_2x2 * (sigmax1 * sigmax1); auto m = bayesTree.marginalFactor(X(1), EliminateCholesky); Matrix actualCovarianceX1 = m->information().inverse(); EXPECT(assert_equal(expectedCovX1, actualCovarianceX1, tol)); // Check marginal on x2 double sigmax2 = 0.68712938; // FIXME: this should be corrected analytically JacobianFactor actual2 = *bayesTree.marginalFactor(X(2)); Matrix expectedCovX2 = I_2x2 * (sigmax2 * sigmax2); EXPECT(assert_equal(expectedCovX2, actual2.information().inverse(), tol)); // Check marginal on x3 JacobianFactor actual3 = *bayesTree.marginalFactor(X(3)); Matrix expectedCovX3 = I_2x2 * (sigmax3 * sigmax3); EXPECT(assert_equal(expectedCovX3, actual3.information().inverse(), tol)); // Check marginal on x4 JacobianFactor actual4 = *bayesTree.marginalFactor(X(4)); Matrix expectedCovX4 = I_2x2 * (sigmax4 * sigmax4); EXPECT(assert_equal(expectedCovX4, actual4.information().inverse(), tol)); // Check marginal on x7 (should be equal to x1) JacobianFactor actual7 = *bayesTree.marginalFactor(X(7)); Matrix expectedCovX7 = I_2x2 * (sigmax7 * sigmax7); EXPECT(assert_equal(expectedCovX7, actual7.information().inverse(), tol)); } /* ************************************************************************* */ TEST( GaussianBayesTree, balanced_smoother_shortcuts ) { // Create smoother with 7 nodes GaussianFactorGraph smoother = createSmoother(7); // Create the Bayes tree Ordering ordering; ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4); GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering); // Check the conditional P(Root|Root) GaussianBayesNet empty; GaussianBayesTree::sharedClique R = bayesTree.roots().front(); GaussianBayesNet actual1 = R->shortcut(R); EXPECT(assert_equal(empty,actual1,tol)); // Check the conditional P(C2|Root) GaussianBayesTree::sharedClique C2 = bayesTree[X(3)]; GaussianBayesNet actual2 = C2->shortcut(R); EXPECT(assert_equal(empty,actual2,tol)); // Check the conditional P(C3|Root), which should be equal to P(x2|x4) /** TODO: Note for multifrontal conditional: * p_x2_x4 is now an element conditional of the multifrontal conditional bayesTree[ordering[X(2)]]->conditional() * We don't know yet how to take it out. */ // GaussianConditional::shared_ptr p_x2_x4 = bayesTree[ordering[X(2)]]->conditional(); // p_x2_x4->print("Conditional p_x2_x4: "); // GaussianBayesNet expected3(p_x2_x4); // GaussianISAM::sharedClique C3 = isamTree[ordering[X(1)]]; // GaussianBayesNet actual3 = GaussianISAM::shortcut(C3,R); // EXPECT(assert_equal(expected3,actual3,tol)); } ///* ************************************************************************* */ //TEST( BayesTree, balanced_smoother_clique_marginals ) //{ // // Create smoother with 7 nodes // Ordering ordering; // ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4); // GaussianFactorGraph smoother = createSmoother(7, ordering).first; // // // Create the Bayes tree // GaussianBayesNet chordalBayesNet = *GaussianSequentialSolver(smoother).eliminate(); // GaussianISAM bayesTree(chordalBayesNet); // // // Check the clique marginal P(C3) // double sigmax2_alt = 1/1.45533; // THIS NEEDS TO BE CHECKED! // GaussianBayesNet expected = simpleGaussian(ordering[X(2)],Z_2x1,sigmax2_alt); // push_front(expected,ordering[X(1)], Z_2x1, eye(2)*sqrt(2), ordering[X(2)], -eye(2)*sqrt(2)/2, ones(2)); // GaussianISAM::sharedClique R = bayesTree.root(), C3 = bayesTree[ordering[X(1)]]; // GaussianFactorGraph marginal = C3->marginal(R); // GaussianVariableIndex varIndex(marginal); // Permutation toFront(Permutation::PullToFront(C3->keys(), varIndex.size())); // Permutation toFrontInverse(*toFront.inverse()); // varIndex.permute(toFront); // for(const GaussianFactor::shared_ptr& factor: marginal) { // factor->permuteWithInverse(toFrontInverse); } // GaussianBayesNet actual = *inference::EliminateUntil(marginal, C3->keys().size(), varIndex); // actual.permuteWithInverse(toFront); // EXPECT(assert_equal(expected,actual,tol)); //} /* ************************************************************************* */ TEST( GaussianBayesTree, balanced_smoother_joint ) { // Create smoother with 7 nodes Ordering ordering; ordering += X(1),X(3),X(5),X(7),X(2),X(6),X(4); GaussianFactorGraph smoother = createSmoother(7); // Create the Bayes tree, expected to look like: // x5 x6 x4 // x3 x2 : x4 // x1 : x2 // x7 : x6 GaussianBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering); // Conditional density elements reused by both tests const Matrix I = I_2x2, A = -0.00429185*I; // Check the joint density P(x1,x7) factored as P(x1|x7)P(x7) GaussianBayesNet expected1 = list_of // Why does the sign get flipped on the prior? (GaussianConditional(X(1), Z_2x1, I/sigmax7, X(7), A/sigmax7)) (GaussianConditional(X(7), Z_2x1, -1*I/sigmax7)); GaussianBayesNet actual1 = *bayesTree.jointBayesNet(X(1),X(7)); EXPECT(assert_equal(expected1, actual1, tol)); // // Check the joint density P(x7,x1) factored as P(x7|x1)P(x1) // GaussianBayesNet expected2; // GaussianConditional::shared_ptr // parent2(new GaussianConditional(X(1), Z_2x1, -1*I/sigmax1, ones(2))); // expected2.push_front(parent2); // push_front(expected2,X(7), Z_2x1, I/sigmax1, X(1), A/sigmax1, sigma); // GaussianBayesNet actual2 = *bayesTree.jointBayesNet(X(7),X(1)); // EXPECT(assert_equal(expected2,actual2,tol)); // Check the joint density P(x1,x4), i.e. with a root variable double sig14 = 0.784465; Matrix A14 = -0.0769231*I; GaussianBayesNet expected3 = list_of (GaussianConditional(X(1), Z_2x1, I/sig14, X(4), A14/sig14)) (GaussianConditional(X(4), Z_2x1, I/sigmax4)); GaussianBayesNet actual3 = *bayesTree.jointBayesNet(X(1),X(4)); EXPECT(assert_equal(expected3,actual3,tol)); // // Check the joint density P(x4,x1), i.e. with a root variable, factored the other way // GaussianBayesNet expected4; // GaussianConditional::shared_ptr // parent4(new GaussianConditional(X(1), Z_2x1, -1.0*I/sigmax1, ones(2))); // expected4.push_front(parent4); // double sig41 = 0.668096; // Matrix A41 = -0.055794*I; // push_front(expected4,X(4), Z_2x1, I/sig41, X(1), A41/sig41, sigma); // GaussianBayesNet actual4 = *bayesTree.jointBayesNet(X(4),X(1)); // EXPECT(assert_equal(expected4,actual4,tol)); } /* ************************************************************************* */ TEST(GaussianBayesTree, shortcut_overlapping_separator) { // Test computing shortcuts when the separator overlaps. This previously // would have highlighted a problem where information was duplicated. // Create factor graph: // f(1,2,5) // f(3,4,5) // f(5,6) // f(6,7) GaussianFactorGraph fg; noiseModel::Diagonal::shared_ptr model = noiseModel::Unit::Create(1); fg.add(1, (Matrix(1, 1) << 1.0).finished(), 3, (Matrix(1, 1) << 2.0).finished(), 5, (Matrix(1, 1) << 3.0).finished(), (Vector(1) << 4.0).finished(), model); fg.add(1, (Matrix(1, 1) << 5.0).finished(), (Vector(1) << 6.0).finished(), model); fg.add(2, (Matrix(1, 1) << 7.0).finished(), 4, (Matrix(1, 1) << 8.0).finished(), 5, (Matrix(1, 1) << 9.0).finished(), (Vector(1) << 10.0).finished(), model); fg.add(2, (Matrix(1, 1) << 11.0).finished(), (Vector(1) << 12.0).finished(), model); fg.add(5, (Matrix(1, 1) << 13.0).finished(), 6, (Matrix(1, 1) << 14.0).finished(), (Vector(1) << 15.0).finished(), model); fg.add(6, (Matrix(1, 1) << 17.0).finished(), 7, (Matrix(1, 1) << 18.0).finished(), (Vector(1) << 19.0).finished(), model); fg.add(7, (Matrix(1, 1) << 20.0).finished(), (Vector(1) << 21.0).finished(), model); // Eliminate into BayesTree // c(6,7) // c(5|6) // c(1,2|5) // c(3,4|5) Ordering ordering(fg.keys()); GaussianBayesTree bt = *fg.eliminateMultifrontal(ordering); // eliminate in increasing key order, fg.keys() is sorted. GaussianFactorGraph joint = *bt.joint(1,2, EliminateQR); Matrix expectedJointJ = (Matrix(2,3) << 5, 0, 6, 0, -11, -12 ).finished(); Matrix actualJointJ = joint.augmentedJacobian(); // PR 315: sign of rows in joint are immaterial if (signbit(expectedJointJ(0, 2)) != signbit(actualJointJ(0, 2))) expectedJointJ.row(0) = -expectedJointJ.row(0); if (signbit(expectedJointJ(1, 2)) != signbit(actualJointJ(1, 2))) expectedJointJ.row(1) = -expectedJointJ.row(1); EXPECT(assert_equal(expectedJointJ, actualJointJ)); } /* ************************************************************************* */ int main() { TestResult tr; return TestRegistry::runAllTests(tr);} /* ************************************************************************* */