305 lines
11 KiB
C++
305 lines
11 KiB
C++
/**
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* @file testGaussianBayesTree.cpp
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* @brief Unit tests for GaussianBayesTree
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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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#include "Ordering.h"
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#include "GaussianBayesNet.h"
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#include "BayesTree-inl.h"
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#include "GaussianBayesTree.h"
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#include "smallExample.h"
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using namespace std;
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using namespace gtsam;
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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 = 0.687131, sigmax3 = 0.671512, sigmax4 =
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0.669534, sigmax5 = sigmax3, sigmax6 = sigmax2, sigmax7 = sigmax1;
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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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GaussianFactorGraph smoother = createSmoother(7);
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Ordering ordering;
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for (int t = 1; t <= 7; t++)
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ordering.push_back(symbol('x', t));
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// eliminate using the "natural" ordering
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GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
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// Create the Bayes tree
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GaussianBayesTree 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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GaussianBayesTree::sharedClique R = bayesTree.root();
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GaussianBayesNet actual1 = R->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(empty,actual1,1e-4));
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// Check the conditional P(C2|Root)
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GaussianBayesTree::sharedClique C2 = bayesTree["x5"];
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GaussianBayesNet actual2 = C2->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(empty,actual2,1e-4));
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// Check the conditional P(C3|Root)
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Vector sigma3 = repeat(2, 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,"x5", zero(2), eye(2), "x6", A56, sigma3);
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GaussianBayesTree::sharedClique C3 = bayesTree["x4"];
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GaussianBayesNet actual3 = C3->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(expected3,actual3,1e-4));
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// Check the conditional P(C4|Root)
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Vector sigma4 = repeat(2, 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,"x4", zero(2), eye(2), "x6", A46, sigma4);
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GaussianBayesTree::sharedClique C4 = bayesTree["x3"];
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GaussianBayesNet actual4 = C4->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(expected4,actual4,1e-4));
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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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GaussianFactorGraph smoother = createSmoother(7);
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Ordering ordering;
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ordering += "x1","x3","x5","x7","x2","x6","x4";
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// eliminate using a "nested dissection" ordering
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GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
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VectorConfig expectedSolution;
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BOOST_FOREACH(string key, ordering)
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expectedSolution.insert(key,zero(2));
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VectorConfig actualSolution = optimize(chordalBayesNet);
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CHECK(assert_equal(expectedSolution,actualSolution,1e-4));
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// Create the Bayes tree
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GaussianBayesTree bayesTree(chordalBayesNet);
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LONGS_EQUAL(4,bayesTree.size());
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// Check marginal on x1
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GaussianBayesNet expected1 = simpleGaussian("x1", zero(2), sigmax1);
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GaussianBayesNet actual1 = bayesTree.marginalBayesNet<GaussianFactor>("x1");
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CHECK(assert_equal(expected1,actual1,1e-4));
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// Check marginal on x2
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GaussianBayesNet expected2 = simpleGaussian("x2", zero(2), sigmax2);
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GaussianBayesNet actual2 = bayesTree.marginalBayesNet<GaussianFactor>("x2");
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CHECK(assert_equal(expected2,actual2,1e-4));
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// Check marginal on x3
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GaussianBayesNet expected3 = simpleGaussian("x3", zero(2), sigmax3);
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GaussianBayesNet actual3 = bayesTree.marginalBayesNet<GaussianFactor>("x3");
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CHECK(assert_equal(expected3,actual3,1e-4));
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// Check marginal on x4
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GaussianBayesNet expected4 = simpleGaussian("x4", zero(2), sigmax4);
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GaussianBayesNet actual4 = bayesTree.marginalBayesNet<GaussianFactor>("x4");
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CHECK(assert_equal(expected4,actual4,1e-4));
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// Check marginal on x7 (should be equal to x1)
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GaussianBayesNet expected7 = simpleGaussian("x7", zero(2), sigmax7);
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GaussianBayesNet actual7 = bayesTree.marginalBayesNet<GaussianFactor>("x7");
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CHECK(assert_equal(expected7,actual7,1e-4));
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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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GaussianFactorGraph smoother = createSmoother(7);
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Ordering ordering;
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ordering += "x1","x3","x5","x7","x2","x6","x4";
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// Create the Bayes tree
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GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
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GaussianBayesTree bayesTree(chordalBayesNet);
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// Check the conditional P(Root|Root)
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GaussianBayesNet empty;
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GaussianBayesTree::sharedClique R = bayesTree.root();
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GaussianBayesNet actual1 = R->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(empty,actual1,1e-4));
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// Check the conditional P(C2|Root)
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GaussianBayesTree::sharedClique C2 = bayesTree["x3"];
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GaussianBayesNet actual2 = C2->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(empty,actual2,1e-4));
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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["x2"];
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GaussianBayesNet expected3; expected3.push_back(p_x2_x4);
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GaussianBayesTree::sharedClique C3 = bayesTree["x1"];
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GaussianBayesNet actual3 = C3->shortcut<GaussianFactor>(R);
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CHECK(assert_equal(expected3,actual3,1e-4));
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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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GaussianFactorGraph smoother = createSmoother(7);
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Ordering ordering;
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ordering += "x1","x3","x5","x7","x2","x6","x4";
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// Create the Bayes tree
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GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
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GaussianBayesTree bayesTree(chordalBayesNet);
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// Check the clique marginal P(C3)
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GaussianBayesNet expected = simpleGaussian("x2",zero(2),sigmax2);
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Vector sigma = repeat(2, 0.707107);
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Matrix A12 = (-0.5)*eye(2);
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push_front(expected,"x1", zero(2), eye(2), "x2", A12, sigma);
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GaussianBayesTree::sharedClique R = bayesTree.root(), C3 = bayesTree["x1"];
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FactorGraph<GaussianFactor> marginal = C3->marginal<GaussianFactor>(R);
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GaussianBayesNet actual = eliminate<GaussianFactor,GaussianConditional>(marginal,C3->keys());
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CHECK(assert_equal(expected,actual,1e-4));
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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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GaussianFactorGraph smoother = createSmoother(7);
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Ordering ordering;
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ordering += "x1","x3","x5","x7","x2","x6","x4";
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// Create the Bayes tree
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GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
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GaussianBayesTree bayesTree(chordalBayesNet);
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// Conditional density elements reused by both tests
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Vector sigma = repeat(2, 0.786146);
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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 = simpleGaussian("x7", zero(2), sigmax7);
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push_front(expected1,"x1", zero(2), I, "x7", A, sigma);
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GaussianBayesNet actual1 = bayesTree.jointBayesNet<GaussianFactor>("x1","x7");
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CHECK(assert_equal(expected1,actual1,1e-4));
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// Check the joint density P(x7,x1) factored as P(x7|x1)P(x1)
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GaussianBayesNet expected2 = simpleGaussian("x1", zero(2), sigmax1);
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push_front(expected2,"x7", zero(2), I, "x1", A, sigma);
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GaussianBayesNet actual2 = bayesTree.jointBayesNet<GaussianFactor>("x7","x1");
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CHECK(assert_equal(expected2,actual2,1e-4));
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// Check the joint density P(x1,x4), i.e. with a root variable
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GaussianBayesNet expected3 = simpleGaussian("x4", zero(2), sigmax4);
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Vector sigma14 = repeat(2, 0.784465);
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Matrix A14 = -0.0769231*I;
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push_front(expected3,"x1", zero(2), I, "x4", A14, sigma14);
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GaussianBayesNet actual3 = bayesTree.jointBayesNet<GaussianFactor>("x1","x4");
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CHECK(assert_equal(expected3,actual3,1e-4));
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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 = simpleGaussian("x1", zero(2), sigmax1);
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Vector sigma41 = repeat(2, 0.668096);
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Matrix A41 = -0.055794*I;
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push_front(expected4,"x4", zero(2), I, "x1", A41, sigma41);
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GaussianBayesNet actual4 = bayesTree.jointBayesNet<GaussianFactor>("x4","x1");
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CHECK(assert_equal(expected4,actual4,1e-4));
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}
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/* ************************************************************************* */
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TEST( BayesTree, iSAM_smoother )
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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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// run iSAM for every factor
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GaussianBayesTree 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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Ordering ordering;
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for (int t = 1; t <= 7; t++) ordering += symbol('x', t);
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GaussianBayesTree expected(smoother.eliminate(ordering));
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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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VectorConfig e; // expected solution
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Vector v = Vector_(2, 0., 0.);
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for (int i=1; i<=7; i++)
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e.insert(symbol('x', i), v);
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VectorConfig 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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TEST( BayesTree, 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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// 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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GaussianBayesTree actual(factors1.eliminate(ord));
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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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// 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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GaussianBayesTree expected(smoother.eliminate(ordering));
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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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