/* ---------------------------------------------------------------------------- * 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 testSubgraphConditioner.cpp * @brief Unit tests for SubgraphPreconditioner * @author Frank Dellaert **/ #include #include #include #include #include #include #include #include #include #include #include #include using namespace boost::assign; using namespace std; using namespace gtsam; using namespace example; // define keys // Create key for simulated planar graph Symbol key(int x, int y) { return symbol_shorthand::X(1000*x+y); } /* ************************************************************************* */ TEST( SubgraphPreconditioner, planarOrdering ) { // Check canonical ordering Ordering expected, ordering = planarOrdering(3); expected += key(3, 3), key(2, 3), key(1, 3), key(3, 2), key(2, 2), key(1, 2), key(3, 1), key(2, 1), key(1, 1); CHECK(assert_equal(expected,ordering)); } /* ************************************************************************* */ /** unnormalized error */ static double error(const GaussianFactorGraph& fg, const VectorValues& x) { double total_error = 0.; BOOST_FOREACH(const GaussianFactor::shared_ptr& factor, fg) total_error += factor->error(x); return total_error; } /* ************************************************************************* */ TEST( SubgraphPreconditioner, planarGraph ) { // Check planar graph construction GaussianFactorGraph A; VectorValues xtrue; boost::tie(A, xtrue) = planarGraph(3); LONGS_EQUAL(13,A.size()); LONGS_EQUAL(9,xtrue.size()); DOUBLES_EQUAL(0,error(A,xtrue),1e-9); // check zero error for xtrue // Check that xtrue is optimal GaussianBayesNet::shared_ptr R1 = GaussianSequentialSolver(A).eliminate(); VectorValues actual = optimize(*R1); CHECK(assert_equal(xtrue,actual)); } /* ************************************************************************* */ TEST( SubgraphPreconditioner, splitOffPlanarTree ) { // Build a planar graph GaussianFactorGraph A; VectorValues xtrue; boost::tie(A, xtrue) = planarGraph(3); // Get the spanning tree and constraints, and check their sizes GaussianFactorGraph T, C; boost::tie(T, C) = splitOffPlanarTree(3, A); LONGS_EQUAL(9,T.size()); LONGS_EQUAL(4,C.size()); // Check that the tree can be solved to give the ground xtrue GaussianBayesNet::shared_ptr R1 = GaussianSequentialSolver(T).eliminate(); VectorValues xbar = optimize(*R1); CHECK(assert_equal(xtrue,xbar)); } /* ************************************************************************* */ TEST( SubgraphPreconditioner, system ) { // Build a planar graph GaussianFactorGraph Ab; VectorValues xtrue; size_t N = 3; boost::tie(Ab, xtrue) = planarGraph(N); // A*x-b // Get the spanning tree and corresponding ordering GaussianFactorGraph Ab1_, Ab2_; // A1*x-b1 and A2*x-b2 boost::tie(Ab1_, Ab2_) = splitOffPlanarTree(N, Ab); SubgraphPreconditioner::sharedFG Ab1(new GaussianFactorGraph(Ab1_)); SubgraphPreconditioner::sharedFG Ab2(new GaussianFactorGraph(Ab2_)); // Eliminate the spanning tree to build a prior SubgraphPreconditioner::sharedBayesNet Rc1 = GaussianSequentialSolver(Ab1_).eliminate(); // R1*x-c1 VectorValues xbar = optimize(*Rc1); // xbar = inv(R1)*c1 // Create Subgraph-preconditioned system VectorValues::shared_ptr xbarShared(new VectorValues(xbar)); // TODO: horrible SubgraphPreconditioner system(Ab2, Rc1, xbarShared); // Create zero config VectorValues zeros = VectorValues::Zero(xbar); // Set up y0 as all zeros VectorValues y0 = zeros; // y1 = perturbed y0 VectorValues y1 = zeros; y1[1] = Vector_(2, 1.0, -1.0); // Check corresponding x values VectorValues expected_x1 = xtrue, x1 = system.x(y1); expected_x1[1] = Vector_(2, 2.01, 2.99); expected_x1[0] = Vector_(2, 3.01, 2.99); CHECK(assert_equal(xtrue, system.x(y0))); CHECK(assert_equal(expected_x1,system.x(y1))); // Check errors DOUBLES_EQUAL(0,error(Ab,xtrue),1e-9); DOUBLES_EQUAL(3,error(Ab,x1),1e-9); DOUBLES_EQUAL(0,error(system,y0),1e-9); DOUBLES_EQUAL(3,error(system,y1),1e-9); // Test gradient in x VectorValues expected_gx0 = zeros; VectorValues expected_gx1 = zeros; CHECK(assert_equal(expected_gx0,gradient(Ab,xtrue))); expected_gx1[2] = Vector_(2, -100., 100.); expected_gx1[4] = Vector_(2, -100., 100.); expected_gx1[1] = Vector_(2, 200., -200.); expected_gx1[3] = Vector_(2, -100., 100.); expected_gx1[0] = Vector_(2, 100., -100.); CHECK(assert_equal(expected_gx1,gradient(Ab,x1))); // Test gradient in y VectorValues expected_gy0 = zeros; VectorValues expected_gy1 = zeros; expected_gy1[2] = Vector_(2, 2., -2.); expected_gy1[4] = Vector_(2, -2., 2.); expected_gy1[1] = Vector_(2, 3., -3.); expected_gy1[3] = Vector_(2, -1., 1.); expected_gy1[0] = Vector_(2, 1., -1.); CHECK(assert_equal(expected_gy0,gradient(system,y0))); CHECK(assert_equal(expected_gy1,gradient(system,y1))); // Check it numerically for good measure // TODO use boost::bind(&SubgraphPreconditioner::error,&system,_1) // Vector numerical_g1 = numericalGradient (error, y1, 0.001); // Vector expected_g1 = Vector_(18, 0., 0., 0., 0., 2., -2., 0., 0., -2., 2., // 3., -3., 0., 0., -1., 1., 1., -1.); // CHECK(assert_equal(expected_g1,numerical_g1)); } /* ************************************************************************* */ TEST( SubgraphPreconditioner, conjugateGradients ) { // Build a planar graph GaussianFactorGraph Ab; VectorValues xtrue; size_t N = 3; boost::tie(Ab, xtrue) = planarGraph(N); // A*x-b // Get the spanning tree and corresponding ordering GaussianFactorGraph Ab1_, Ab2_; // A1*x-b1 and A2*x-b2 boost::tie(Ab1_, Ab2_) = splitOffPlanarTree(N, Ab); SubgraphPreconditioner::sharedFG Ab1(new GaussianFactorGraph(Ab1_)); SubgraphPreconditioner::sharedFG Ab2(new GaussianFactorGraph(Ab2_)); // Eliminate the spanning tree to build a prior Ordering ordering = planarOrdering(N); SubgraphPreconditioner::sharedBayesNet Rc1 = GaussianSequentialSolver(Ab1_).eliminate(); // R1*x-c1 VectorValues xbar = optimize(*Rc1); // xbar = inv(R1)*c1 // Create Subgraph-preconditioned system VectorValues::shared_ptr xbarShared(new VectorValues(xbar)); // TODO: horrible SubgraphPreconditioner system(Ab2, Rc1, xbarShared); // Create zero config y0 and perturbed config y1 VectorValues y0 = VectorValues::Zero(xbar); VectorValues y1 = y0; y1[1] = Vector_(2, 1.0, -1.0); VectorValues x1 = system.x(y1); // Solve for the remaining constraints using PCG ConjugateGradientParameters parameters; VectorValues actual = conjugateGradients(system, y1, parameters); CHECK(assert_equal(y0,actual)); // Compare with non preconditioned version: VectorValues actual2 = conjugateGradientDescent(Ab, x1, parameters); CHECK(assert_equal(xtrue,actual2,1e-4)); } /* ************************************************************************* */ int main() { TestResult tr; return TestRegistry::runAllTests(tr); } /* ************************************************************************* */