gtsam/tests/testGaussianISAM.cpp

/**
 * @file    testGaussianISAM.cpp
 * @brief   Unit tests for GaussianISAM
 * @author  Michael Kaess
 */

#include <boost/foreach.hpp>
#include <boost/assign/std/list.hpp> // for operator +=
using namespace boost::assign;

#include <gtsam/CppUnitLite/TestHarness.h>

#define GTSAM_MAGIC_KEY

#include <gtsam/inference/Ordering.h>
#include <gtsam/linear/GaussianBayesNet.h>
#include <gtsam/inference/ISAM-inl.h>
#include <gtsam/linear/GaussianISAM.h>
#include <gtsam/slam/smallExample.h>

using namespace std;
using namespace gtsam;
using namespace example;

/* ************************************************************************* */
// Some numbers that should be consistent among all smoother tests

double sigmax1 = 0.786153, sigmax2 = 1.0/1.47292, sigmax3 = 0.671512, sigmax4 =
		0.669534, sigmax5 = sigmax3, sigmax6 = sigmax2, sigmax7 = sigmax1;

const double tol = 1e-4;

/* ************************************************************************* */
TEST( ISAM, iSAM_smoother )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);

	// run iSAM for every factor
	GaussianISAM actual;
	BOOST_FOREACH(boost::shared_ptr<GaussianFactor> factor, smoother) {
		GaussianFactorGraph factorGraph;
		factorGraph.push_back(factor);
		actual.update(factorGraph);
	}

	// Create expected Bayes Tree by solving smoother with "natural" ordering
	Ordering ordering;
	for (int t = 1; t <= 7; t++) ordering += symbol('x', t);
	GaussianISAM expected(smoother.eliminate(ordering));

	// Check whether BayesTree is correct
	CHECK(assert_equal(expected, actual));

	// obtain solution
	VectorConfig e; // expected solution
	Vector v = Vector_(2, 0., 0.);
	for (int i=1; i<=7; i++)
		e.insert(symbol('x', i), v);
	VectorConfig optimized = optimize(actual); // actual solution
	CHECK(assert_equal(e, optimized));
}

/* ************************************************************************* */
TEST( ISAM, iSAM_smoother2 )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);

	// Create initial tree from first 4 timestamps in reverse order !
	Ordering ord; ord += "x4","x3","x2","x1";
	GaussianFactorGraph factors1;
	for (int i=0;i<7;i++) factors1.push_back(smoother[i]);
	GaussianISAM actual(factors1.eliminate(ord));

	// run iSAM with remaining factors
	GaussianFactorGraph factors2;
	for (int i=7;i<13;i++) factors2.push_back(smoother[i]);
	actual.update(factors2);

	// Create expected Bayes Tree by solving smoother with "natural" ordering
	Ordering ordering;
	for (int t = 1; t <= 7; t++) ordering += symbol('x', t);
	GaussianISAM expected(smoother.eliminate(ordering));

	CHECK(assert_equal(expected, actual));
}

/* ************************************************************************* *
 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( BayesTree, linear_smoother_shortcuts )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);
	Ordering ordering;
	for (int t = 1; t <= 7; t++)
		ordering.push_back(symbol('x', t));

	// eliminate using the "natural" ordering
	GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);

	// Create the Bayes tree
	GaussianISAM bayesTree(chordalBayesNet);
	LONGS_EQUAL(6,bayesTree.size());

	// Check the conditional P(Root|Root)
	GaussianBayesNet empty;
	GaussianISAM::sharedClique R = bayesTree.root();
	GaussianBayesNet actual1 = R->shortcut<GaussianFactor>(R);
	CHECK(assert_equal(empty,actual1,tol));

	// Check the conditional P(C2|Root)
	GaussianISAM::sharedClique C2 = bayesTree["x5"];
	GaussianBayesNet actual2 = C2->shortcut<GaussianFactor>(R);
	CHECK(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);
	GaussianBayesNet expected3;
	push_front(expected3,"x5", zero(2), eye(2)/sigma3, "x6", A56/sigma3, ones(2));
	GaussianISAM::sharedClique C3 = bayesTree["x4"];
	GaussianBayesNet actual3 = C3->shortcut<GaussianFactor>(R);
	CHECK(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);
	GaussianBayesNet expected4;
	push_front(expected4,"x4", zero(2), eye(2)/sigma4, "x6", A46/sigma4, ones(2));
	GaussianISAM::sharedClique C4 = bayesTree["x3"];
	GaussianBayesNet actual4 = C4->shortcut<GaussianFactor>(R);
	CHECK(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( BayesTree, balanced_smoother_marginals )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);
	Ordering ordering;
	ordering += "x1","x3","x5","x7","x2","x6","x4";

	// eliminate using a "nested dissection" ordering
	GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);

	VectorConfig expectedSolution;
	BOOST_FOREACH(string key, ordering)
	expectedSolution.insert(key,zero(2));
	VectorConfig actualSolution = optimize(chordalBayesNet);
	CHECK(assert_equal(expectedSolution,actualSolution,tol));

	// Create the Bayes tree
	GaussianISAM bayesTree(chordalBayesNet);
	LONGS_EQUAL(4,bayesTree.size());

	double tol=1e-5;

	// Check marginal on x1
	GaussianBayesNet expected1 = simpleGaussian("x1", zero(2), sigmax1);
	GaussianBayesNet actual1 = bayesTree.marginalBayesNet<GaussianFactor>("x1");
	CHECK(assert_equal(expected1,actual1,tol));

	// Check marginal on x2
	double sigx2 = 0.68712938; // FIXME: this should be corrected analytically
	GaussianBayesNet expected2 = simpleGaussian("x2", zero(2), sigx2);
	GaussianBayesNet actual2 = bayesTree.marginalBayesNet<GaussianFactor>("x2");
	CHECK(assert_equal(expected2,actual2,tol)); // FAILS

	// Check marginal on x3
	GaussianBayesNet expected3 = simpleGaussian("x3", zero(2), sigmax3);
	GaussianBayesNet actual3 = bayesTree.marginalBayesNet<GaussianFactor>("x3");
	CHECK(assert_equal(expected3,actual3,tol));

	// Check marginal on x4
	GaussianBayesNet expected4 = simpleGaussian("x4", zero(2), sigmax4);
	GaussianBayesNet actual4 = bayesTree.marginalBayesNet<GaussianFactor>("x4");
	CHECK(assert_equal(expected4,actual4,tol));

	// Check marginal on x7 (should be equal to x1)
	GaussianBayesNet expected7 = simpleGaussian("x7", zero(2), sigmax7);
	GaussianBayesNet actual7 = bayesTree.marginalBayesNet<GaussianFactor>("x7");
	CHECK(assert_equal(expected7,actual7,tol));
}

/* ************************************************************************* */
TEST( BayesTree, balanced_smoother_shortcuts )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);
	Ordering ordering;
	ordering += "x1","x3","x5","x7","x2","x6","x4";

	// Create the Bayes tree
	GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
	GaussianISAM bayesTree(chordalBayesNet);

	// Check the conditional P(Root|Root)
	GaussianBayesNet empty;
	GaussianISAM::sharedClique R = bayesTree.root();
	GaussianBayesNet actual1 = R->shortcut<GaussianFactor>(R);
	CHECK(assert_equal(empty,actual1,tol));

	// Check the conditional P(C2|Root)
	GaussianISAM::sharedClique C2 = bayesTree["x3"];
	GaussianBayesNet actual2 = C2->shortcut<GaussianFactor>(R);
	CHECK(assert_equal(empty,actual2,tol));

	// Check the conditional P(C3|Root), which should be equal to P(x2|x4)
	GaussianConditional::shared_ptr p_x2_x4 = chordalBayesNet["x2"];
	GaussianBayesNet expected3; expected3.push_back(p_x2_x4);
	GaussianISAM::sharedClique C3 = bayesTree["x1"];
	GaussianBayesNet actual3 = C3->shortcut<GaussianFactor>(R);
	CHECK(assert_equal(expected3,actual3,tol));
}

/* ************************************************************************* */
TEST( BayesTree, balanced_smoother_clique_marginals )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);
	Ordering ordering;
	ordering += "x1","x3","x5","x7","x2","x6","x4";

	// Create the Bayes tree
	GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
	GaussianISAM bayesTree(chordalBayesNet);

	// Check the clique marginal P(C3)
	double sigmax2_alt = 1/1.45533; // THIS NEEDS TO BE CHECKED!
	GaussianBayesNet expected = simpleGaussian("x2",zero(2),sigmax2_alt);
	push_front(expected,"x1", zero(2), eye(2)*sqrt(2), "x2", -eye(2)*sqrt(2)/2, ones(2));
	GaussianISAM::sharedClique R = bayesTree.root(), C3 = bayesTree["x1"];
	FactorGraph<GaussianFactor> marginal = C3->marginal<GaussianFactor>(R);
	GaussianBayesNet actual = eliminate<GaussianFactor,GaussianConditional>(marginal,C3->keys());
	CHECK(assert_equal(expected,actual,tol));
}

/* ************************************************************************* */
TEST( BayesTree, balanced_smoother_joint )
{
	// Create smoother with 7 nodes
	GaussianFactorGraph smoother = createSmoother(7);
	Ordering ordering;
	ordering += "x1","x3","x5","x7","x2","x6","x4";

	// Create the Bayes tree, expected to look like:
	//	 x5 x6 x4
	//	   x3 x2 : x4
	//	     x1 : x2
	//	   x7 : x6
	GaussianBayesNet chordalBayesNet = smoother.eliminate(ordering);
	GaussianISAM bayesTree(chordalBayesNet);

	// Conditional density elements reused by both tests
	const Vector sigma = ones(2);
	const Matrix I = eye(2), A = -0.00429185*I;

	// Check the joint density P(x1,x7) factored as P(x1|x7)P(x7)
	GaussianBayesNet expected1;
	// Why does the sign get flipped on the prior?
	GaussianConditional::shared_ptr
		parent1(new GaussianConditional("x7", zero(2), -1*I/sigmax7, ones(2)));
	expected1.push_front(parent1);
	push_front(expected1,"x1", zero(2), I/sigmax7, "x7", A/sigmax7, sigma);
	GaussianBayesNet actual1 = bayesTree.jointBayesNet<GaussianFactor>("x1","x7");
	CHECK(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("x1", zero(2), -1*I/sigmax1, ones(2)));
		expected2.push_front(parent2);
	push_front(expected2,"x7", zero(2), I/sigmax1, "x1", A/sigmax1, sigma);
	GaussianBayesNet actual2 = bayesTree.jointBayesNet<GaussianFactor>("x7","x1");
	CHECK(assert_equal(expected2,actual2,tol));

	// Check the joint density P(x1,x4), i.e. with a root variable
	GaussianBayesNet expected3;
	GaussianConditional::shared_ptr
			parent3(new GaussianConditional("x4", zero(2), I/sigmax4, ones(2)));
		expected3.push_front(parent3);
	double sig14 = 0.784465;
	Matrix A14 = -0.0769231*I;
	push_front(expected3,"x1", zero(2), I/sig14, "x4", A14/sig14, sigma);
	GaussianBayesNet actual3 = bayesTree.jointBayesNet<GaussianFactor>("x1","x4");
	CHECK(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("x1", zero(2), -1.0*I/sigmax1, ones(2)));
		expected4.push_front(parent4);
	double sig41 = 0.668096;
	Matrix A41 = -0.055794*I;
	push_front(expected4,"x4", zero(2), I/sig41, "x1", A41/sig41, sigma);
	GaussianBayesNet actual4 = bayesTree.jointBayesNet<GaussianFactor>("x4","x1");
	CHECK(assert_equal(expected4,actual4,tol));
}

/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr);}
/* ************************************************************************* */