testHybridGaussianISAM.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
 
 * -------------------------------------------------------------------------- */
 
#include <gtsam/discrete/DiscreteBayesNet.h>
#include <gtsam/discrete/DiscreteDistribution.h>
#include <gtsam/discrete/DiscreteFactorGraph.h>
#include <gtsam/geometry/Pose2.h>
#include <gtsam/hybrid/HybridConditional.h>
#include <gtsam/hybrid/HybridGaussianISAM.h>
#include <gtsam/linear/GaussianBayesNet.h>
#include <gtsam/linear/GaussianFactorGraph.h>
#include <gtsam/nonlinear/PriorFactor.h>
#include <gtsam/sam/BearingRangeFactor.h>
 
#include "Switching.h"
 
// Include for test suite
#include <CppUnitLite/TestHarness.h>
 
using namespace std;
using namespace gtsam;
using symbol_shorthand::M;
using symbol_shorthand::W;
using symbol_shorthand::X;
using symbol_shorthand::Y;
using symbol_shorthand::Z;
 
/* ****************************************************************************/
namespace switching3 {
// ϕ(x0) ϕ(x1;z1) ϕ(x2;z2) ϕ(x0,x1,m0) ϕ(x1,x2,m1) ϕ(m0) ϕ(m0,m1)
const Switching switching(3);
const HybridGaussianFactorGraph &lfg = switching.linearizedFactorGraph();
 
// First update graph: ϕ(x0) ϕ(x0,x1,m0) ϕ(m0)
const HybridGaussianFactorGraph graph1{lfg.at(0), lfg.at(3), lfg.at(5)};
 
// Second update graph: ϕ(x1,x2,m1) ϕ(x1;z1) ϕ(x2;z2) ϕ(m0,m1)
const HybridGaussianFactorGraph graph2{lfg.at(4), lfg.at(1), lfg.at(2),
                                       lfg.at(6)};
}  // namespace switching3
 
/* ****************************************************************************/
// Test if we can perform elimination incrementally.
TEST(HybridGaussianISAM, IncrementalElimination) {
  using namespace switching3;
  HybridGaussianISAM isam;
 
  // Run first update step
  isam.update(graph1);
 
  // Check that after update we have 2 hybrid Bayes net nodes:
  // P(M0) and P(X0, X1 | M0)
  EXPECT_LONGS_EQUAL(2, isam.size());
  EXPECT(isam[M(0)]->conditional()->frontals() == KeyVector({M(0)}));
  EXPECT(isam[M(0)]->conditional()->parents() == KeyVector());
  EXPECT(isam[X(0)]->conditional()->frontals() == KeyVector({X(0), X(1)}));
  EXPECT(isam[X(0)]->conditional()->parents() == KeyVector({M(0)}));
 
  /********************************************************/
  // Run second update step
  isam.update(graph2);
 
  // Check that after update we have 3 hybrid Bayes net nodes:
  // P(X1, X2 | M0, M1) P(X1, X2 | M0, M1)
  EXPECT_LONGS_EQUAL(3, isam.size());
  EXPECT(isam[M(0)]->conditional()->frontals() == KeyVector({M(0), M(1)}));
  EXPECT(isam[M(0)]->conditional()->parents() == KeyVector());
  EXPECT(isam[X(1)]->conditional()->frontals() == KeyVector({X(1), X(2)}));
  EXPECT(isam[X(1)]->conditional()->parents() == KeyVector({M(0), M(1)}));
  EXPECT(isam[X(0)]->conditional()->frontals() == KeyVector{X(0)});
  EXPECT(isam[X(0)]->conditional()->parents() == KeyVector({X(1), M(0)}));
}
 
/* ****************************************************************************/
// Test if we can incrementally do the inference
TEST(HybridGaussianISAM, IncrementalInference) {
  using namespace switching3;
  HybridGaussianISAM isam;
 
  // Run update step
  isam.update(graph1);
 
  auto discreteConditional_m0 = isam[M(0)]->conditional()->asDiscrete();
  EXPECT(discreteConditional_m0->keys() == KeyVector({M(0)}));
 
  /********************************************************/
  // Second incremental update.
  isam.update(graph2);
 
  /********************************************************/
  // Run batch elimination so we can compare results.
  const Ordering ordering{X(0), X(1), X(2)};
 
  // Now we calculate the expected factors using full elimination
  const auto [expectedHybridBayesTree, expectedRemainingGraph] =
      switching.linearizedFactorGraph().eliminatePartialMultifrontal(ordering);
 
  // The densities on X(0) should be the same
  auto x0_conditional = dynamic_pointer_cast<HybridGaussianConditional>(
      isam[X(0)]->conditional()->inner());
  auto expected_x0_conditional =
      dynamic_pointer_cast<HybridGaussianConditional>(
          (*expectedHybridBayesTree)[X(0)]->conditional()->inner());
  EXPECT(assert_equal(*x0_conditional, *expected_x0_conditional));
 
  // The densities on X(1) should be the same
  auto x1_conditional = dynamic_pointer_cast<HybridGaussianConditional>(
      isam[X(1)]->conditional()->inner());
  auto expected_x1_conditional =
      dynamic_pointer_cast<HybridGaussianConditional>(
          (*expectedHybridBayesTree)[X(1)]->conditional()->inner());
  EXPECT(assert_equal(*x1_conditional, *expected_x1_conditional));
 
  // The densities on X(2) should be the same
  auto x2_conditional = dynamic_pointer_cast<HybridGaussianConditional>(
      isam[X(2)]->conditional()->inner());
  auto expected_x2_conditional =
      dynamic_pointer_cast<HybridGaussianConditional>(
          (*expectedHybridBayesTree)[X(2)]->conditional()->inner());
  EXPECT(assert_equal(*x2_conditional, *expected_x2_conditional));
 
  // We only perform manual continuous elimination for 0,0.
  // The other discrete probabilities on M(2) are calculated the same way
  const Ordering discreteOrdering{M(0), M(1)};
  HybridBayesTree::shared_ptr discreteBayesTree =
      expectedRemainingGraph->eliminateMultifrontal(discreteOrdering);
 
  // Test the probability values with regression tests.
  auto discrete = isam[M(1)]->conditional()->asDiscrete();
  EXPECT(assert_equal(0.095292, (*discrete)({{M(0), 0}, {M(1), 0}}), 1e-5));
  EXPECT(assert_equal(0.282758, (*discrete)({{M(0), 1}, {M(1), 0}}), 1e-5));
  EXPECT(assert_equal(0.314175, (*discrete)({{M(0), 0}, {M(1), 1}}), 1e-5));
  EXPECT(assert_equal(0.307775, (*discrete)({{M(0), 1}, {M(1), 1}}), 1e-5));
 
  // Check that the clique conditional generated from incremental elimination
  // matches that of batch elimination.
  auto expectedConditional = (*discreteBayesTree)[M(1)]->conditional();
  auto actualConditional = isam[M(1)]->conditional();
  EXPECT(assert_equal(*expectedConditional, *actualConditional, 1e-6));
}
 
/* ****************************************************************************/
// Test if we can approximately do the inference
TEST(HybridGaussianISAM, ApproxInference) {
  Switching switching(4);
  HybridGaussianISAM incrementalHybrid;
  HybridGaussianFactorGraph graph1;
 
  // Add the 3 hybrid factors, x0-x1, x1-x2, x2-x3
  for (size_t i = 0; i < 3; i++) {
    graph1.push_back(switching.linearBinaryFactors.at(i));
  }
 
  // Add the Gaussian factors, 1 prior on x0,
  // 3 measurements on x1, x2, x3
  for (size_t i = 0; i <= 3; i++) {
    graph1.push_back(switching.linearUnaryFactors.at(i));
  }
 
  // Create ordering.
  Ordering ordering;
  for (size_t j = 0; j < 4; j++) {
    ordering.push_back(X(j));
  }
 
  // Now we calculate the actual factors using full elimination
  const auto [unPrunedHybridBayesTree, unPrunedRemainingGraph] =
      switching.linearizedFactorGraph().eliminatePartialMultifrontal(ordering);
 
  size_t maxNrLeaves = 5;
  incrementalHybrid.update(graph1);
 
  incrementalHybrid.prune(maxNrLeaves);
 
  /*
  unPruned factor is:
    Choice(m3)
    0 Choice(m2)
    0 0 Choice(m1)
    0 0 0 Leaf 0.11267528
    0 0 1 Leaf 0.18576102
    0 1 Choice(m1)
    0 1 0 Leaf 0.18754662
    0 1 1 Leaf 0.30623871
    1 Choice(m2)
    1 0 Choice(m1)
    1 0 0 Leaf 0.18576102
    1 0 1 Leaf 0.30622428
    1 1 Choice(m1)
    1 1 0 Leaf 0.30623871
    1 1 1 Leaf  0.5
 
  pruned factors is:
    Choice(m3)
    0 Choice(m2)
    0 0 Leaf    0
    0 1 Choice(m1)
    0 1 0 Leaf 0.18754662
    0 1 1 Leaf 0.30623871
    1 Choice(m2)
    1 0 Choice(m1)
    1 0 0 Leaf    0
    1 0 1 Leaf 0.30622428
    1 1 Choice(m1)
    1 1 0 Leaf 0.30623871
    1 1 1 Leaf  0.5
  */
 
  auto discreteConditional_m0 = *dynamic_pointer_cast<DiscreteConditional>(
      incrementalHybrid[M(0)]->conditional()->inner());
  EXPECT(discreteConditional_m0.keys() == KeyVector({M(0), M(1), M(2)}));
 
  // Get the number of elements which are greater than 0.
  auto count = [](const double &value, int count) {
    return value > 0 ? count + 1 : count;
  };
  // Check that the number of leaves after pruning is 5.
  EXPECT_LONGS_EQUAL(5, discreteConditional_m0.fold(count, 0));
 
  // Check that the hybrid nodes of the bayes net match those of the pre-pruning
  // bayes net, at the same positions.
  auto &unPrunedLastDensity = *dynamic_pointer_cast<HybridGaussianConditional>(
      unPrunedHybridBayesTree->clique(X(3))->conditional()->inner());
  auto &lastDensity = *dynamic_pointer_cast<HybridGaussianConditional>(
      incrementalHybrid[X(3)]->conditional()->inner());
 
  std::vector<std::pair<DiscreteValues, double>> assignments =
      discreteConditional_m0.enumerate();
  // Loop over all assignments and check the pruned components
  for (auto &&av : assignments) {
    const DiscreteValues &assignment = av.first;
    const double value = av.second;
 
    if (value == 0.0) {
      EXPECT(lastDensity(assignment) == nullptr);
    } else {
      CHECK(lastDensity(assignment));
      EXPECT(assert_equal(*unPrunedLastDensity(assignment),
                          *lastDensity(assignment)));
    }
  }
}
 
/* ****************************************************************************/
// Test approximate inference with an additional pruning step.
TEST(HybridGaussianISAM, IncrementalApproximate) {
  Switching switching(5);
  HybridGaussianISAM incrementalHybrid;
  HybridGaussianFactorGraph graph;
 
  /***** Run Round 1 *****/
  // Add the 3 hybrid factors, x0-x1, x1-x2, x2-x3
  for (size_t i = 0; i < 3; i++) {
    graph.push_back(switching.linearBinaryFactors.at(i));
  }
 
  // Add the Gaussian factors, 1 prior on x0,
  // 3 measurements on x1, x2, x3
  for (size_t i = 0; i <= 3; i++) {
    graph.push_back(switching.linearUnaryFactors.at(i));
  }
 
  // Run update with pruning
  size_t maxComponents = 5;
  incrementalHybrid.update(graph, maxComponents);
 
  // Check if we have a bayes tree with 4 hybrid nodes,
  // each with 2, 4, 8, and 5 (pruned) leaves respectively.
  EXPECT_LONGS_EQUAL(4, incrementalHybrid.size());
  EXPECT_LONGS_EQUAL(
      2, incrementalHybrid[X(0)]->conditional()->asHybrid()->nrComponents());
  EXPECT_LONGS_EQUAL(
      3, incrementalHybrid[X(1)]->conditional()->asHybrid()->nrComponents());
  EXPECT_LONGS_EQUAL(
      5, incrementalHybrid[X(2)]->conditional()->asHybrid()->nrComponents());
  EXPECT_LONGS_EQUAL(
      5, incrementalHybrid[X(3)]->conditional()->asHybrid()->nrComponents());
 
  /***** Run Round 2 *****/
  graph = HybridGaussianFactorGraph();
  graph.push_back(switching.linearBinaryFactors.at(3));  // hybrid x3-x4
  graph.push_back(switching.linearUnaryFactors.at(4));   // x4
 
  // Run update with pruning a second time.
  incrementalHybrid.update(graph, maxComponents);
 
  // Check if we have a bayes tree with pruned hybrid nodes,
  // with 5 (pruned) leaves.
  CHECK_EQUAL(5, incrementalHybrid.size());
  EXPECT_LONGS_EQUAL(
      5, incrementalHybrid[X(3)]->conditional()->asHybrid()->nrComponents());
  EXPECT_LONGS_EQUAL(
      5, incrementalHybrid[X(4)]->conditional()->asHybrid()->nrComponents());
}
 
/* ************************************************************************/
// A GTSAM-only test for running inference on a single-legged robot.
// The leg links are represented by the chain X-Y-Z-W, where X is the base and
// W is the foot.
// We use BetweenFactor<Pose2> as constraints between each of the poses.
TEST(HybridGaussianISAM, NonTrivial) {
  /*************** Run Round 1 ***************/
  HybridNonlinearFactorGraph fg;
 
  // Add a prior on pose x0 at the origin.
  // A prior factor consists of a mean  and
  // a noise model (covariance matrix)
  Pose2 prior(0.0, 0.0, 0.0);  // prior mean is at origin
  auto priorNoise = noiseModel::Diagonal::Sigmas(
      Vector3(0.3, 0.3, 0.1));  // 30cm std on x,y, 0.1 rad on theta
  fg.emplace_shared<PriorFactor<Pose2>>(X(0), prior, priorNoise);
 
  // create a noise model for the landmark measurements
  auto poseNoise = noiseModel::Isotropic::Sigma(3, 0.1);
 
  // We model a robot's single leg as X - Y - Z - W
  // where X is the base link and W is the foot link.
 
  // Add connecting poses similar to PoseFactors in GTD
  fg.emplace_shared<BetweenFactor<Pose2>>(X(0), Y(0), Pose2(0, 1.0, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Y(0), Z(0), Pose2(0, 1.0, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Z(0), W(0), Pose2(0, 1.0, 0),
                                          poseNoise);
 
  // Create initial estimate
  Values initial;
  initial.insert(X(0), Pose2(0.0, 0.0, 0.0));
  initial.insert(Y(0), Pose2(0.0, 1.0, 0.0));
  initial.insert(Z(0), Pose2(0.0, 2.0, 0.0));
  initial.insert(W(0), Pose2(0.0, 3.0, 0.0));
 
  HybridGaussianFactorGraph gfg = *fg.linearize(initial);
  fg = HybridNonlinearFactorGraph();
 
  HybridGaussianISAM inc;
 
  // Update without pruning
  // The result is a HybridBayesNet with no discrete variables
  // (equivalent to a GaussianBayesNet).
  // Factorization is:
  // `P(X | measurements) = P(W0|Z0) P(Z0|Y0) P(Y0|X0) P(X0)`
  inc.update(gfg);
 
  /*************** Run Round 2 ***************/
  using PlanarMotionModel = BetweenFactor<Pose2>;
 
  // Add odometry factor with discrete modes.
  Pose2 odometry(1.0, 0.0, 0.0);
  auto noise_model = noiseModel::Isotropic::Sigma(3, 1.0);
  std::vector<NoiseModelFactor::shared_ptr> components;
  components.emplace_back(
      new PlanarMotionModel(W(0), W(1), odometry, noise_model));  // moving
  components.emplace_back(
      new PlanarMotionModel(W(0), W(1), Pose2(0, 0, 0), noise_model));  // still
  fg.emplace_shared<HybridNonlinearFactor>(DiscreteKey(M(1), 2), components);
 
  // Add equivalent of ImuFactor
  fg.emplace_shared<BetweenFactor<Pose2>>(X(0), X(1), Pose2(1.0, 0.0, 0),
                                          poseNoise);
  // PoseFactors-like at k=1
  fg.emplace_shared<BetweenFactor<Pose2>>(X(1), Y(1), Pose2(0, 1, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Y(1), Z(1), Pose2(0, 1, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Z(1), W(1), Pose2(-1, 1, 0),
                                          poseNoise);
 
  initial.insert(X(1), Pose2(1.0, 0.0, 0.0));
  initial.insert(Y(1), Pose2(1.0, 1.0, 0.0));
  initial.insert(Z(1), Pose2(1.0, 2.0, 0.0));
  // The leg link did not move so we set the expected pose accordingly.
  initial.insert(W(1), Pose2(0.0, 3.0, 0.0));
 
  gfg = *fg.linearize(initial);
  fg = HybridNonlinearFactorGraph();
 
  // Update without pruning
  // The result is a HybridBayesNet with 1 discrete variable M(1).
  // P(X | measurements) = P(W0|Z0, W1, M1) P(Z0|Y0, W1, M1) P(Y0|X0, W1, M1)
  //                       P(X0 | X1, W1, M1) P(W1|Z1, X1, M1) P(Z1|Y1, X1, M1)
  //                       P(Y1 | X1, M1)P(X1 | M1)P(M1)
  // The MHS tree is a 1 level tree for time indices (1,) with 2 leaves.
  inc.update(gfg);
 
  /*************** Run Round 3 ***************/
  // Add odometry factor with discrete modes.
  components.clear();
  components.emplace_back(
      new PlanarMotionModel(W(1), W(2), odometry, noise_model));  // moving
  components.emplace_back(
      new PlanarMotionModel(W(1), W(2), Pose2(0, 0, 0), noise_model));  // still
  fg.emplace_shared<HybridNonlinearFactor>(DiscreteKey(M(2), 2), components);
 
  // Add equivalent of ImuFactor
  fg.emplace_shared<BetweenFactor<Pose2>>(X(1), X(2), Pose2(1.0, 0.0, 0),
                                          poseNoise);
  // PoseFactors-like at k=1
  fg.emplace_shared<BetweenFactor<Pose2>>(X(2), Y(2), Pose2(0, 1, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Y(2), Z(2), Pose2(0, 1, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Z(2), W(2), Pose2(-2, 1, 0),
                                          poseNoise);
 
  initial.insert(X(2), Pose2(2.0, 0.0, 0.0));
  initial.insert(Y(2), Pose2(2.0, 1.0, 0.0));
  initial.insert(Z(2), Pose2(2.0, 2.0, 0.0));
  initial.insert(W(2), Pose2(0.0, 3.0, 0.0));
 
  gfg = *fg.linearize(initial);
  fg = HybridNonlinearFactorGraph();
 
  // Now we prune!
  // P(X | measurements) = P(W0|Z0, W1, M1) P(Z0|Y0, W1, M1) P(Y0|X0, W1, M1)
  //                       P(X0 | X1, W1, M1) P(W1|W2, Z1, X1, M1, M2)
  //                       P(Z1| W2, Y1, X1, M1, M2) P(Y1 | W2, X1, M1, M2)
  //                       P(X1 | W2, X2, M1, M2) P(W2|Z2, X2, M1, M2)
  //                       P(Z2|Y2, X2, M1, M2) P(Y2 | X2, M1, M2)
  //                       P(X2 | M1, M2) P(M1, M2)
  // The MHS at this point should be a 2 level tree on (1, 2).
  // 1 has 2 choices, and 2 has 4 choices.
  inc.update(gfg);
  inc.prune(2);
 
  /*************** Run Round 4 ***************/
  // Add odometry factor with discrete modes.
  components.clear();
  components.emplace_back(
      new PlanarMotionModel(W(2), W(3), odometry, noise_model));  // moving
  components.emplace_back(
      new PlanarMotionModel(W(2), W(3), Pose2(0, 0, 0), noise_model));  // still
  fg.emplace_shared<HybridNonlinearFactor>(DiscreteKey(M(3), 2), components);
 
  // Add equivalent of ImuFactor
  fg.emplace_shared<BetweenFactor<Pose2>>(X(2), X(3), Pose2(1.0, 0.0, 0),
                                          poseNoise);
  // PoseFactors-like at k=3
  fg.emplace_shared<BetweenFactor<Pose2>>(X(3), Y(3), Pose2(0, 1, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Y(3), Z(3), Pose2(0, 1, 0),
                                          poseNoise);
  fg.emplace_shared<BetweenFactor<Pose2>>(Z(3), W(3), Pose2(-3, 1, 0),
                                          poseNoise);
 
  initial.insert(X(3), Pose2(3.0, 0.0, 0.0));
  initial.insert(Y(3), Pose2(3.0, 1.0, 0.0));
  initial.insert(Z(3), Pose2(3.0, 2.0, 0.0));
  initial.insert(W(3), Pose2(0.0, 3.0, 0.0));
 
  gfg = *fg.linearize(initial);
  fg = HybridNonlinearFactorGraph();
 
  // Keep pruning!
  inc.update(gfg, 3);
 
  // The final discrete graph should not be empty since we have eliminated
  // all continuous variables.
  auto discreteTree = inc[M(3)]->conditional()->asDiscrete();
  EXPECT_LONGS_EQUAL(3, discreteTree->size());
 
  // Test if the optimal discrete mode assignment is (1, 1, 1).
  DiscreteFactorGraph discreteGraph;
  discreteGraph.push_back(discreteTree);
  DiscreteValues optimal_assignment = discreteGraph.optimize();
 
  DiscreteValues expected_assignment;
  expected_assignment[M(1)] = 1;
  expected_assignment[M(2)] = 1;
  expected_assignment[M(3)] = 1;
 
  EXPECT(assert_equal(expected_assignment, optimal_assignment));
 
  // Test if pruning worked correctly by checking that we only have 3 leaves in
  // the last node.
  auto lastConditional = inc[X(3)]->conditional()->asHybrid();
  EXPECT_LONGS_EQUAL(3, lastConditional->nrComponents());
}
 
/* ************************************************************************* */
int main() {
  TestResult tr;
  return TestRegistry::runAllTests(tr);
}