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testGaussianBayesTreeB.cpp
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/* ----------------------------------------------------------------------------
* 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 <tests/smallExample.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam/linear/GaussianBayesTree.h>
#include <gtsam/linear/GaussianBayesNet.h>
#include <gtsam/linear/GaussianConditional.h>
#include <gtsam/linear/GaussianDensity.h>
#include <gtsam/linear/HessianFactor.h>
#include <gtsam/geometry/Rot2.h>
#include <CppUnitLite/TestHarness.h>
#include <boost/assign/std/list.hpp> // 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);}
/* ************************************************************************* */