C++ GaussianFactorGraph::eliminateMultifrontal方法代码示例

/* ************************************************************************* */
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( ISAM, iSAM_smoother )
{
  Ordering ordering;
  for (int t = 1; t <= 7; t++) ordering += X(t);

  // Create smoother with 7 nodes
  GaussianFactorGraph smoother = createSmoother(7);

  // run iSAM for every factor
  GaussianISAM actual;
  for(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
  GaussianBayesTree expected = *smoother.eliminateMultifrontal(ordering);

  // Verify sigmas in the bayes tree
  for(const GaussianBayesTree::sharedClique& clique: expected.nodes() | br::map_values) {
    GaussianConditional::shared_ptr conditional = clique->conditional();
    EXPECT(!conditional->get_model());
  }

  // Check whether BayesTree is correct
  EXPECT(assert_equal(GaussianFactorGraph(expected).augmentedHessian(), GaussianFactorGraph(actual).augmentedHessian()));

  // obtain solution
  VectorValues e; // expected solution
  for (int t = 1; t <= 7; t++) e.insert(X(t), Vector::Zero(2));
  VectorValues optimized = actual.optimize(); // actual solution
  EXPECT(assert_equal(e, optimized));
}

// Create a planar factor graph and eliminate
double timePlanarSmootherEliminate(int N, bool old = true) {
  GaussianFactorGraph fg = planarGraph(N).get<0>();
  clock_t start = clock();
  fg.eliminateMultifrontal();
  clock_t end = clock ();
  double dif = (double)(end - start) / CLOCKS_PER_SEC;
  return dif;
}

/* ************************************************************************* */
TEST (Serialization, gaussian_bayes_tree) {
  const Key x1=1, x2=2, x3=3, x4=4;
  const Ordering chainOrdering = Ordering(list_of(x2)(x1)(x3)(x4));
  const SharedDiagonal chainNoise = noiseModel::Isotropic::Sigma(1, 0.5);
  const GaussianFactorGraph chain = list_of
    (JacobianFactor(x2, (Matrix(1, 1) << 1.), x1, (Matrix(1, 1) << 1.), (Vector(1) << 1.),  chainNoise))
    (JacobianFactor(x2, (Matrix(1, 1) << 1.), x3, (Matrix(1, 1) << 1.), (Vector(1) << 1.),  chainNoise))
    (JacobianFactor(x3, (Matrix(1, 1) << 1.), x4, (Matrix(1, 1) << 1.), (Vector(1) << 1.),  chainNoise))
    (JacobianFactor(x4, (Matrix(1, 1) << 1.), (Vector(1) << 1.),  chainNoise));

  GaussianBayesTree init = *chain.eliminateMultifrontal(chainOrdering);
  GaussianBayesTree expected = *chain.eliminateMultifrontal(chainOrdering);
  GaussianBayesTree actual;

  std::string serialized = serialize(init);
  deserialize(serialized, actual);
  EXPECT(assert_equal(expected, actual));
}

/* ************************************************************************* */
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 = eye(2), 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), zero(2), I/sigmax7, X(7), A/sigmax7))
    (GaussianConditional(X(7), zero(2), -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), zero(2), -1*I/sigmax1, ones(2)));
  //    expected2.push_front(parent2);
  //  push_front(expected2,X(7), zero(2), 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), zero(2), I/sig14, X(4), A14/sig14))
    (GaussianConditional(X(4), zero(2), 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), zero(2), -1.0*I/sigmax1, ones(2)));
  //    expected4.push_front(parent4);
  //  double sig41 = 0.668096;
  //  Matrix A41 = -0.055794*I;
  //  push_front(expected4,X(4), zero(2), I/sig41, X(1), A41/sig41, sigma);
  //  GaussianBayesNet actual4 = *bayesTree.jointBayesNet(X(4),X(1));
  //  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, (long)bayesTree.size());

  double tol=1e-5;

  // Check marginal on x1
  JacobianFactor expected1 = GaussianDensity::FromMeanAndStddev(X(1), zero(2), sigmax1);
  JacobianFactor actual1 = *bayesTree.marginalFactor(X(1));
  Matrix expectedCovarianceX1 = eye(2,2) * (sigmax1 * sigmax1);
  Matrix actualCovarianceX1;
  GaussianFactor::shared_ptr m = bayesTree.marginalFactor(X(1), EliminateCholesky);
  actualCovarianceX1 = bayesTree.marginalFactor(X(1), EliminateCholesky)->information().inverse();
  EXPECT(assert_equal(expectedCovarianceX1, actualCovarianceX1, tol));
  EXPECT(assert_equal(expected1,actual1,tol));

  // Check marginal on x2
  double sigx2 = 0.68712938; // FIXME: this should be corrected analytically
  JacobianFactor expected2 = GaussianDensity::FromMeanAndStddev(X(2), zero(2), sigx2);
  JacobianFactor actual2 = *bayesTree.marginalFactor(X(2));
  EXPECT(assert_equal(expected2,actual2,tol));

  // Check marginal on x3
  JacobianFactor expected3 = GaussianDensity::FromMeanAndStddev(X(3), zero(2), sigmax3);
  JacobianFactor actual3 = *bayesTree.marginalFactor(X(3));
  EXPECT(assert_equal(expected3,actual3,tol));

  // Check marginal on x4
  JacobianFactor expected4 = GaussianDensity::FromMeanAndStddev(X(4), zero(2), sigmax4);
  JacobianFactor actual4 = *bayesTree.marginalFactor(X(4));
  EXPECT(assert_equal(expected4,actual4,tol));

  // Check marginal on x7 (should be equal to x1)
  JacobianFactor expected7 = GaussianDensity::FromMeanAndStddev(X(7), zero(2), sigmax7);
  JacobianFactor actual7 = *bayesTree.marginalFactor(X(7));
  EXPECT(assert_equal(expected7,actual7,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();

  EXPECT(assert_equal(expectedJointJ, actualJointJ));
}