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