testSymbolicBayesTree.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 testSymbolicBayesTree.cpp
 * @date sept 15, 2012
 * @author  Frank Dellaert
 * @author  Michael Kaess
 * @author  Viorela Ila
 */
 
#include <gtsam/inference/Symbol.h>
#include <gtsam/symbolic/SymbolicBayesNet.h>
#include <gtsam/symbolic/SymbolicBayesTree.h>
#include <gtsam/symbolic/tests/symbolicExampleGraphs.h>
 
#include <CppUnitLite/TestHarness.h>
#include <gtsam/base/TestableAssertions.h>
#include <iterator>
#include <type_traits>
 
using namespace std;
using namespace gtsam;
using namespace gtsam::symbol_shorthand;
 
static bool debug = false;
 
// Given a vector of shared pointers infer the type of the pointed-to objects
template<typename T>
using PointedToType = std::decay_t<decltype(**declval<T>().begin())>;
 
// Given a vector of shared pointers infer the type of the pointed-to objects
template<typename T>
using ValuesVector = std::vector<PointedToType<T>>;
 
// Return a vector of dereferenced values
template<typename T>
ValuesVector<T> deref(const T& v) {
  ValuesVector<T> result;
  for (auto& t : v)
    result.push_back(*t);
  return result;
}
 
 
/* ************************************************************************* */
TEST(SymbolicBayesTree, clear) {
  SymbolicBayesTree bayesTree = asiaBayesTree;
  bayesTree.clear();
 
  SymbolicBayesTree expected;
 
  // Check whether cleared BayesTree is equal to a new BayesTree
  CHECK(assert_equal(expected, bayesTree));
}
 
/* ************************************************************************* */
TEST(SymbolicBayesTree, clique_structure) {
  //        l1                  l2
  //    /    |                /  |
  // x1 --- x2 --- x3 --- x4 --- x5
  //                          \  |
  //                            l3
  SymbolicFactorGraph graph;
  graph.emplace_shared<SymbolicFactor>(X(1), L(1));
  graph.emplace_shared<SymbolicFactor>(X(1), X(2));
  graph.emplace_shared<SymbolicFactor>(X(2), L(1));
  graph.emplace_shared<SymbolicFactor>(X(2), X(3));
  graph.emplace_shared<SymbolicFactor>(X(3), X(4));
  graph.emplace_shared<SymbolicFactor>(X(4), L(2));
  graph.emplace_shared<SymbolicFactor>(X(4), X(5));
  graph.emplace_shared<SymbolicFactor>(L(2), X(5));
  graph.emplace_shared<SymbolicFactor>(X(4), L(3));
  graph.emplace_shared<SymbolicFactor>(X(5), L(3));
 
  SymbolicBayesTree expected;
  expected.insertRoot(
      NodeClique(Keys(X(2))(X(3)), 2,
                 Children(NodeClique(
                     Keys(X(4))(X(3)), 1,
                     Children(NodeClique(
                         Keys(X(5))(L(2))(X(4)), 2,
                         Children(LeafClique(Keys(L(3))(X(4))(X(5)), 1))))))(
                     LeafClique(Keys(X(1))(L(1))(X(2)), 2))));
 
  Ordering order{X(1), L(3), L(1), X(5), X(2), L(2), X(4), X(3)};
 
  SymbolicBayesTree actual = *graph.eliminateMultifrontal(order);
 
  EXPECT(assert_equal(expected, actual));
}
 
/* ************************************************************************* *
Bayes Tree for testing conversion to a forest of orphans needed for incremental.
       A,B
   C|A    E|B
   D|C    F|E
   */
/* ************************************************************************* */
TEST(BayesTree, removePath) {
  const Key _A_ = A(0), _B_ = B(0), _C_ = C(0), _D_ = D(0), _E_ = E(0),
            _F_ = F(0);
 
  SymbolicBayesTree bayesTreeOrig;
  auto left = NodeClique(Keys(_C_)(_A_), 1, {LeafClique(Keys(_D_)(_C_), 1)});
  auto right = NodeClique(Keys(_E_)(_B_), 1, {LeafClique(Keys(_F_)(_E_), 1)});
  bayesTreeOrig.insertRoot(NodeClique(Keys(_A_)(_B_), 2, {left, right}));
 
  SymbolicBayesTree bayesTree = bayesTreeOrig;
 
  // remove C, expected outcome: factor graph with ABC,
  // Bayes Tree now contains two orphan trees: D|C and E|B,F|E
  SymbolicFactorGraph expected;
  expected.emplace_shared<SymbolicFactor>(_A_, _B_);
  expected.emplace_shared<SymbolicFactor>(_C_, _A_);
  SymbolicBayesTree::Cliques expectedOrphans{bayesTree[_D_], bayesTree[_E_]};
 
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removePath(bayesTree[_C_], &bn, &orphans);
  SymbolicFactorGraph factors(bn);
  CHECK(assert_equal(expected, factors));
  CHECK(assert_container_equal(deref(expectedOrphans), deref(orphans)));
 
  bayesTree = bayesTreeOrig;
 
  // remove E: factor graph with EB; E|B removed from second orphan tree
  SymbolicFactorGraph expected2;
  expected2.emplace_shared<SymbolicFactor>(_A_, _B_);
  expected2.emplace_shared<SymbolicFactor>(_E_, _B_);
  SymbolicBayesTree::Cliques expectedOrphans2{bayesTree[_F_], bayesTree[_C_]};
 
  SymbolicBayesNet bn2;
  SymbolicBayesTree::Cliques orphans2;
  bayesTree.removePath(bayesTree[_E_], &bn2, &orphans2);
  SymbolicFactorGraph factors2(bn2);
  CHECK(assert_equal(expected2, factors2));
  CHECK(assert_container_equal(deref(expectedOrphans2), deref(orphans2)));
}
 
/* ************************************************************************* */
TEST(BayesTree, removePath2) {
  SymbolicBayesTree bayesTree = asiaBayesTree;
 
  // Call remove-path with clique B
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removePath(bayesTree[_B_], &bn, &orphans);
  SymbolicFactorGraph factors(bn);
 
  // Check expected outcome
  SymbolicFactorGraph expected;
  expected.emplace_shared<SymbolicFactor>(_E_, _L_, _B_);
  CHECK(assert_equal(expected, factors));
  SymbolicBayesTree::Cliques expectedOrphans{bayesTree[_S_], bayesTree[_T_],
                                             bayesTree[_X_]};
  CHECK(assert_container_equal(deref(expectedOrphans), deref(orphans)));
}
 
/* ************************************************************************* */
TEST(BayesTree, removePath3) {
  SymbolicBayesTree bayesTree = asiaBayesTree;
 
  // Call remove-path with clique T
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removePath(bayesTree[_T_], &bn, &orphans);
  SymbolicFactorGraph factors(bn);
 
  // Check expected outcome
  SymbolicFactorGraph expected;
  expected.emplace_shared<SymbolicFactor>(_E_, _L_, _B_);
  expected.emplace_shared<SymbolicFactor>(_T_, _E_, _L_);
  CHECK(assert_equal(expected, factors));
  SymbolicBayesTree::Cliques expectedOrphans{bayesTree[_S_], bayesTree[_X_]};
  CHECK(assert_container_equal(deref(expectedOrphans), deref(orphans)));
}
 
void getAllCliques(const SymbolicBayesTree::sharedClique& subtree,
                   SymbolicBayesTree::Cliques& cliques) {
  // Check if subtree exists
  if (subtree) {
    cliques.push_back(subtree);
    // Recursive call over all child cliques
    for (SymbolicBayesTree::sharedClique& childClique : subtree->children) {
      getAllCliques(childClique, cliques);
    }
  }
}
 
/* ************************************************************************* */
TEST(BayesTree, shortcutCheck) {
  const Key _A_ = 6, _B_ = 5, _C_ = 4, _D_ = 3, _E_ = 2, _F_ = 1, _G_ = 0;
  auto chain = SymbolicFactorGraph(SymbolicFactor(_A_))  //
      (SymbolicFactor(_B_, _A_))                         //
      (SymbolicFactor(_C_, _A_))                         //
      (SymbolicFactor(_D_, _C_))                         //
      (SymbolicFactor(_E_, _B_))                         //
      (SymbolicFactor(_F_, _E_))                         //
      (SymbolicFactor(_G_, _F_));
  Ordering ordering{_G_, _F_, _E_, _D_, _C_, _B_, _A_};
  SymbolicBayesTree bayesTree = *chain.eliminateMultifrontal(ordering);
 
  // bayesTree.saveGraph("BT1.dot");
 
  SymbolicBayesTree::sharedClique rootClique = bayesTree.roots().front();
  // rootClique->printTree();
  SymbolicBayesTree::Cliques allCliques;
  getAllCliques(rootClique, allCliques);
 
  for (SymbolicBayesTree::sharedClique& clique : allCliques) {
    // clique->print("Clique#");
    SymbolicBayesNet bn = clique->shortcut(rootClique);
    // bn.print("Shortcut:\n");
    // cout << endl;
  }
 
  // Check if all the cached shortcuts are cleared
  rootClique->deleteCachedShortcuts();
  for (SymbolicBayesTree::sharedClique& clique : allCliques) {
    bool notCleared = clique->cachedSeparatorMarginal().has_value();
    CHECK(notCleared == false);
  }
  EXPECT_LONGS_EQUAL(0, (long)rootClique->numCachedSeparatorMarginals());
 
  //  for(SymbolicBayesTree::sharedClique& clique: allCliques) {
  //    clique->print("Clique#");
  //    if(clique->cachedShortcut()){
  //      bn = clique->cachedShortcut().get();
  //      bn.print("Shortcut:\n");
  //    }
  //    else
  //      cout << "Not Initialized" << endl;
  //    cout << endl;
  //  }
}
 
/* ************************************************************************* */
TEST(BayesTree, removeTop) {
  SymbolicBayesTree bayesTree = asiaBayesTree;
 
  // create a new factor to be inserted
  // std::shared_ptr<IndexFactor> newFactor(new IndexFactor(_S_,_B_));
 
  // Remove the contaminated part of the Bayes tree
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removeTop(Keys(_B_)(_S_), &bn, &orphans);
 
  // Check expected outcome
  SymbolicBayesNet expected;
  expected.add(SymbolicConditional::FromKeys<KeyVector>(Keys(_E_)(_L_)(_B_), 3));
  expected.add(SymbolicConditional::FromKeys<KeyVector>(Keys(_S_)(_B_)(_L_), 1));
  CHECK(assert_equal(expected, bn));
 
  SymbolicBayesTree::Cliques expectedOrphans{bayesTree[_T_], bayesTree[_X_]};
  CHECK(assert_container_equal(deref(expectedOrphans), deref(orphans)));
 
  // Try removeTop again with a factor that should not change a thing
  // std::shared_ptr<IndexFactor> newFactor2(new IndexFactor(_B_));
  SymbolicBayesNet bn2;
  SymbolicBayesTree::Cliques orphans2;
  bayesTree.removeTop(Keys(_B_), &bn2, &orphans2);
  SymbolicFactorGraph factors2(bn2);
  SymbolicFactorGraph expected2;
  CHECK(assert_equal(expected2, factors2));
  SymbolicBayesTree::Cliques expectedOrphans2;
  CHECK(assert_container_equal(deref(expectedOrphans2), deref(orphans2)));
}
 
/* ************************************************************************* */
TEST(BayesTree, removeTop2) {
  SymbolicBayesTree bayesTree = asiaBayesTree;
 
  // create two factors to be inserted
  // SymbolicFactorGraph newFactors;
  // newFactors.push_factor(_B_);
  // newFactors.push_factor(_S_);
 
  // Remove the contaminated part of the Bayes tree
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removeTop(Keys(_T_), &bn, &orphans);
 
  // Check expected outcome
  auto expected = SymbolicBayesNet(
      SymbolicConditional::FromKeys<KeyVector>(Keys(_E_)(_L_)(_B_), 3))(
      SymbolicConditional::FromKeys<KeyVector>(Keys(_T_)(_E_)(_L_), 1));
  CHECK(assert_equal(expected, bn));
 
  SymbolicBayesTree::Cliques expectedOrphans{bayesTree[_S_], bayesTree[_X_]};
  CHECK(assert_container_equal(deref(expectedOrphans), deref(orphans)));
}
 
/* ************************************************************************* */
TEST(BayesTree, removeTop3) {
  auto graph = SymbolicFactorGraph(SymbolicFactor(L(5)))(SymbolicFactor(
      X(4), L(5)))(SymbolicFactor(X(2), X(4)))(SymbolicFactor(X(3), X(2)));
  Ordering ordering{X(3), X(2), X(4), L(5)};
  SymbolicBayesTree bayesTree = *graph.eliminateMultifrontal(ordering);
 
  // remove all
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removeTop(Keys(L(5))(X(4))(X(2))(X(3)), &bn, &orphans);
 
  auto expectedBn = SymbolicBayesNet(
      SymbolicConditional::FromKeys<KeyVector>(Keys(X(4))(L(5)), 2))(
      SymbolicConditional(X(2), X(4)))(SymbolicConditional(X(3), X(2)));
  EXPECT(assert_equal(expectedBn, bn));
  EXPECT(orphans.empty());
}
 
/* ************************************************************************* */
TEST(BayesTree, removeTop4) {
  auto graph = SymbolicFactorGraph(SymbolicFactor(L(5)))(SymbolicFactor(
      X(4), L(5)))(SymbolicFactor(X(2), X(4)))(SymbolicFactor(X(3), X(2)));
  Ordering ordering{X(3), X(2), X(4), L(5)};
  SymbolicBayesTree bayesTree = *graph.eliminateMultifrontal(ordering);
 
  // remove all
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removeTop(Keys(X(2))(L(5))(X(4))(X(3)), &bn, &orphans);
 
  auto expectedBn = SymbolicBayesNet(
      SymbolicConditional::FromKeys<KeyVector>(Keys(X(4))(L(5)), 2))(
      SymbolicConditional(X(2), X(4)))(SymbolicConditional(X(3), X(2)));
  EXPECT(assert_equal(expectedBn, bn));
  EXPECT(orphans.empty());
}
 
/* ************************************************************************* */
TEST(BayesTree, removeTop5) {
  // Remove top called with variables that are not in the Bayes tree
  auto graph = SymbolicFactorGraph(SymbolicFactor(L(5)))(SymbolicFactor(
      X(4), L(5)))(SymbolicFactor(X(2), X(4)))(SymbolicFactor(X(3), X(2)));
  Ordering ordering{X(3), X(2), X(4), L(5)};
  SymbolicBayesTree bayesTree = *graph.eliminateMultifrontal(ordering);
 
  // Remove nonexistant
  SymbolicBayesNet bn;
  SymbolicBayesTree::Cliques orphans;
  bayesTree.removeTop(Keys(X(10)), &bn, &orphans);
 
  SymbolicBayesNet expectedBn;
  EXPECT(assert_equal(expectedBn, bn));
  EXPECT(orphans.empty());
}
 
/* ************************************************************************* */
TEST(SymbolicBayesTree, thinTree) {
  // create a thin-tree Bayes net, a la Jean-Guillaume
  SymbolicBayesNet bayesNet;
  bayesNet.emplace_shared<SymbolicConditional>(14);
 
  bayesNet.emplace_shared<SymbolicConditional>(13, 14);
  bayesNet.emplace_shared<SymbolicConditional>(12, 14);
 
  bayesNet.emplace_shared<SymbolicConditional>(11, 13, 14);
  bayesNet.emplace_shared<SymbolicConditional>(10, 13, 14);
  bayesNet.emplace_shared<SymbolicConditional>(9, 12, 14);
  bayesNet.emplace_shared<SymbolicConditional>(8, 12, 14);
 
  bayesNet.emplace_shared<SymbolicConditional>(7, 11, 13);
  bayesNet.emplace_shared<SymbolicConditional>(6, 11, 13);
  bayesNet.emplace_shared<SymbolicConditional>(5, 10, 13);
  bayesNet.emplace_shared<SymbolicConditional>(4, 10, 13);
 
  bayesNet.emplace_shared<SymbolicConditional>(3, 9, 12);
  bayesNet.emplace_shared<SymbolicConditional>(2, 9, 12);
  bayesNet.emplace_shared<SymbolicConditional>(1, 8, 12);
  bayesNet.emplace_shared<SymbolicConditional>(0, 8, 12);
 
  if (debug) {
    GTSAM_PRINT(bayesNet);
    bayesNet.saveGraph("/tmp/symbolicBayesNet.dot");
  }
 
  // create a BayesTree out of a Bayes net
  SymbolicBayesTree bayesTree =
      *SymbolicFactorGraph(bayesNet).eliminateMultifrontal();
  if (debug) {
    GTSAM_PRINT(bayesTree);
    bayesTree.saveGraph("/tmp/SymbolicBayesTree.dot");
  }
 
  SymbolicBayesTree::Clique::shared_ptr R = bayesTree.roots().front();
 
  {
    // check shortcut P(S9||R) to root
    SymbolicBayesTree::Clique::shared_ptr c = bayesTree[9];
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(14, 11, 13));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  {
    // check shortcut P(S8||R) to root
    SymbolicBayesTree::Clique::shared_ptr c = bayesTree[8];
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(12, 14))(
        SymbolicConditional(14, 11, 13));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  {
    // check shortcut P(S4||R) to root
    SymbolicBayesTree::Clique::shared_ptr c = bayesTree[4];
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(10, 11, 13));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  {
    // check shortcut P(S2||R) to root
    SymbolicBayesTree::Clique::shared_ptr c = bayesTree[2];
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(9, 11, 12, 13))(
        SymbolicConditional(12, 11, 13));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  {
    // check shortcut P(S0||R) to root
    SymbolicBayesTree::Clique::shared_ptr c = bayesTree[0];
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(8, 11, 12, 13))(
        SymbolicConditional(12, 11, 13));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  SymbolicBayesNet::shared_ptr actualJoint;
 
  // Check joint P(8,2)
  if (false) {  // TODO, not disjoint
    actualJoint = bayesTree.jointBayesNet(8, 2);
    SymbolicBayesNet expected;
    expected.emplace_shared<SymbolicConditional>(8);
    expected.emplace_shared<SymbolicConditional>(2, 8);
    EXPECT(assert_equal(expected, *actualJoint));
  }
 
  // Check joint P(1,2)
  if (false) {  // TODO, not disjoint
    actualJoint = bayesTree.jointBayesNet(1, 2);
    SymbolicBayesNet expected;
    expected.emplace_shared<SymbolicConditional>(2);
    expected.emplace_shared<SymbolicConditional>(1, 2);
    EXPECT(assert_equal(expected, *actualJoint));
  }
 
  // Check joint P(2,6)
  if (true) {
    actualJoint = bayesTree.jointBayesNet(2, 6);
    SymbolicBayesNet expected;
    expected.emplace_shared<SymbolicConditional>(2, 6);
    expected.emplace_shared<SymbolicConditional>(6);
    EXPECT(assert_equal(expected, *actualJoint));
  }
 
  // Check joint P(4,6)
  if (false) {  // TODO, not disjoint
    actualJoint = bayesTree.jointBayesNet(4, 6);
    SymbolicBayesNet expected;
    expected.emplace_shared<SymbolicConditional>(6);
    expected.emplace_shared<SymbolicConditional>(4, 6);
    EXPECT(assert_equal(expected, *actualJoint));
  }
}
 
/* ************************************************************************* */
TEST(SymbolicBayesTree, forest_joint) {
  // Create forest
  sharedClique root1 = LeafClique(Keys(1), 1);
  sharedClique root2 = LeafClique(Keys(2), 1);
  SymbolicBayesTree bayesTree;
  bayesTree.insertRoot(root1);
  bayesTree.insertRoot(root2);
 
  // Check joint
  auto expected =
      SymbolicBayesNet(SymbolicConditional(1))(SymbolicConditional(2));
  SymbolicBayesNet actual = *bayesTree.jointBayesNet(1, 2);
 
  EXPECT(assert_equal(expected, actual));
}
 
/* ************************************************************************* *
 Bayes tree for smoother with "natural" ordering:
 C1 5 6
 C2   4 : 5
 C3     3 : 4
 C4       2 : 3
 C5         1 : 2
 C6           0 : 1
 **************************************************************************** */
 
TEST(SymbolicBayesTree, linear_smoother_shortcuts) {
  // Create smoother with 7 nodes
  SymbolicFactorGraph smoother;
  smoother.push_factor(0);
  smoother.push_factor(0, 1);
  smoother.push_factor(1, 2);
  smoother.push_factor(2, 3);
  smoother.push_factor(3, 4);
  smoother.push_factor(4, 5);
  smoother.push_factor(5, 6);
 
  // Eliminate in numerical order 0..6
  Ordering ordering(smoother.keys());
  SymbolicBayesNet bayesNet = *smoother.eliminateSequential(ordering);
 
  if (debug) {
    GTSAM_PRINT(bayesNet);
    bayesNet.saveGraph("/tmp/symbolicBayesNet.dot");
  }
 
  // create a BayesTree
  SymbolicBayesTree bayesTree = *smoother.eliminateMultifrontal(ordering);
  if (debug) {
    GTSAM_PRINT(bayesTree);
    bayesTree.saveGraph("/tmp/SymbolicBayesTree.dot");
  }
 
  SymbolicBayesTree::Clique::shared_ptr R = bayesTree.roots().front();
 
  {
    // check shortcut P(S2||R) to root
    SymbolicBayesTree::Clique::shared_ptr c =
        bayesTree[4];  // 4 is frontal in C2
    SymbolicBayesNet shortcut = c->shortcut(R);
    SymbolicBayesNet expected;
    EXPECT(assert_equal(expected, shortcut));
  }
 
  {
    // check shortcut P(S3||R) to root
    SymbolicBayesTree::Clique::shared_ptr c =
        bayesTree[3];  // 3 is frontal in C3
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(4, 5));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  {
    // check shortcut P(S4||R) to root
    SymbolicBayesTree::Clique::shared_ptr c =
        bayesTree[2];  // 2 is frontal in C4
    SymbolicBayesNet shortcut = c->shortcut(R);
    auto expected = SymbolicBayesNet(SymbolicConditional(3, 5));
    EXPECT(assert_equal(expected, shortcut));
  }
}
 
/* ************************************************************************* */
// from testSymbolicJunctionTree, which failed at one point
TEST(SymbolicBayesTree, complicatedMarginal) {
  // Create the conditionals to go in the BayesTree
  sharedClique cur;
  sharedClique root = LeafClique(Keys(11)(12), 2);
  cur = root;
 
  root->children.push_back(LeafClique(Keys(9)(10)(11)(12), 2));
  root->children.back()->parent_ = root;
 
  root->children.push_back(LeafClique(Keys(7)(8)(11), 2));
  root->children.back()->parent_ = root;
  cur = root->children.back();
 
  cur->children.push_back(LeafClique(Keys(5)(6)(7)(8), 2));
  cur->children.back()->parent_ = cur;
  cur = cur->children.back();
 
  cur->children.push_back(LeafClique(Keys(3)(4)(6), 2));
  cur->children.back()->parent_ = cur;
 
  cur->children.push_back(LeafClique(Keys(1)(2)(5), 2));
  cur->children.back()->parent_ = cur;
 
  // Create Bayes Tree
  SymbolicBayesTree bt;
  bt.insertRoot(root);
  if (debug) {
    GTSAM_PRINT(bt);
    bt.saveGraph("/tmp/SymbolicBayesTree.dot");
  }
 
  // Shortcut on 9
  {
    SymbolicBayesTree::Clique::shared_ptr c = bt[9];
    SymbolicBayesNet shortcut = c->shortcut(root);
    EXPECT(assert_equal(SymbolicBayesNet(), shortcut));
  }
 
  // Shortcut on 7
  {
    SymbolicBayesTree::Clique::shared_ptr c = bt[7];
    SymbolicBayesNet shortcut = c->shortcut(root);
    EXPECT(assert_equal(SymbolicBayesNet(), shortcut));
  }
 
  // Shortcut on 5
  {
    SymbolicBayesTree::Clique::shared_ptr c = bt[5];
    SymbolicBayesNet shortcut = c->shortcut(root);
    auto expected = SymbolicBayesNet(SymbolicConditional(7, 8, 11))(
        SymbolicConditional(8, 11));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  // Shortcut on 3
  {
    SymbolicBayesTree::Clique::shared_ptr c = bt[3];
    SymbolicBayesNet shortcut = c->shortcut(root);
    auto expected = SymbolicBayesNet(SymbolicConditional(6, 11));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  // Shortcut on 1
  {
    SymbolicBayesTree::Clique::shared_ptr c = bt[1];
    SymbolicBayesNet shortcut = c->shortcut(root);
    auto expected = SymbolicBayesNet(SymbolicConditional(5, 11));
    EXPECT(assert_equal(expected, shortcut));
  }
 
  // Marginal on 5
  {
    SymbolicFactor::shared_ptr actual = bt.marginalFactor(5);
    EXPECT(assert_equal(SymbolicFactor(5), *actual, 1e-1));
  }
 
  // Shortcut on 6
  {
    SymbolicFactor::shared_ptr actual = bt.marginalFactor(6);
    EXPECT(assert_equal(SymbolicFactor(6), *actual, 1e-1));
  }
}
 
/* ************************************************************************* */
TEST(SymbolicBayesTree, COLAMDvsMETIS) {
  // create circular graph
  SymbolicFactorGraph sfg;
  sfg.push_factor(0, 1);
  sfg.push_factor(1, 2);
  sfg.push_factor(2, 3);
  sfg.push_factor(3, 4);
  sfg.push_factor(4, 5);
  sfg.push_factor(0, 5);
 
  // COLAMD
  {
    Ordering ordering = Ordering::Create(Ordering::COLAMD, sfg);
    EXPECT(assert_equal(Ordering{0, 5, 1, 4, 2, 3}, ordering));
 
    //  - P( 4 2 3)
    //  | - P( 1 | 2 4)
    //  | | - P( 5 | 1 4)
    //  | | | - P( 0 | 1 5)
    SymbolicBayesTree expected;
    expected.insertRoot(  //
        NodeClique(
            Keys(4)(2)(3), 3,
            Children(  //
                NodeClique(
                    Keys(1)(2)(4), 1,
                    Children(  //
                        NodeClique(Keys(5)(1)(4), 1,
                                   Children(  //
                                       LeafClique(Keys(0)(1)(5), 1))))))));
 
    SymbolicBayesTree actual = *sfg.eliminateMultifrontal(ordering);
    EXPECT(assert_equal(expected, actual));
  }
 
#ifdef GTSAM_SUPPORT_NESTED_DISSECTION
  // METIS
  {
    Ordering ordering = Ordering::Create(Ordering::METIS, sfg);
// Linux and Mac split differently when using Metis
#if defined(__APPLE__)
    EXPECT(assert_equal(Ordering{5, 4, 2, 1, 0, 3}, ordering));
#elif defined(_WIN32)
    EXPECT(assert_equal(Ordering{4, 3, 1, 0, 5, 2}, ordering));
#else
    EXPECT(assert_equal(Ordering{3, 2, 5, 0, 4, 1}, ordering));
#endif
 
    //  - P( 1 0 3)
    //  | - P( 4 | 0 3)
    //  | | - P( 5 | 0 4)
    //  | - P( 2 | 1 3)
    SymbolicBayesTree expected;
#if defined(__APPLE__)
    expected.insertRoot(
        NodeClique(Keys(1)(0)(3), 3,
                   Children(                         //
                       NodeClique(Keys(4)(0)(3), 1,  //
                                  {LeafClique(Keys(5)(0)(4), 1)}))(
                       LeafClique(Keys(2)(1)(3), 1))));
#elif defined(_WIN32)
    expected.insertRoot(
        NodeClique(Keys(3)(5)(2), 3,
                   Children(                         //
                       NodeClique(Keys(4)(3)(5), 1,  //
                                  {LeafClique(Keys(0)(2)(5), 1)}))(
                       LeafClique(Keys(1)(0)(2), 1))));
#else
    expected.insertRoot(
        NodeClique(Keys(2)(4)(1), 3,
                   Children(                         //
                       NodeClique(Keys(0)(1)(4), 1,  //
                                  {LeafClique(Keys(5)(0)(4), 1)}))(
                       LeafClique(Keys(3)(2)(4), 1))));
#endif
    SymbolicBayesTree actual = *sfg.eliminateMultifrontal(ordering);
    EXPECT(assert_equal(expected, actual));
  }
#endif
}
 
/* ************************************************************************* */
int main() {
  TestResult tr;
  return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */