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operator returns pairs, extensive switching test

release/4.3a0
Frank Dellaert 2024-10-07 09:12:56 +09:00
parent 584a71fb94
commit e1c0d0e227
7 changed files with 180 additions and 75 deletions
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6
gtsam/hybrid/HybridGaussianConditional.cpp
View File

@ -273,13 +273,7 @@ std::shared_ptr<HybridGaussianFactor> HybridGaussianConditional::likelihood(
[&](const GaussianConditional::shared_ptr& conditional) -> GaussianFactorValuePair {
const auto likelihood_m = conditional->likelihood(given);
const double Cgm_Kgcm = conditional->negLogConstant() - negLogConstant_;
if (Cgm_Kgcm == 0.0) {
return {likelihood_m, 0.0};
} else {
// Add a constant to the likelihood in case the noise models
// are not all equal.
return {likelihood_m, Cgm_Kgcm};
}
});
return std::make_shared<HybridGaussianFactor>(discreteParentKeys, likelihoods);
}

4
gtsam/hybrid/HybridGaussianFactor.cpp
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@ -187,9 +187,9 @@ void HybridGaussianFactor::print(const std::string& s, const KeyFormatter& forma
}
/* *******************************************************************************/
HybridGaussianFactor::sharedFactor HybridGaussianFactor::operator()(
GaussianFactorValuePair HybridGaussianFactor::operator()(
const DiscreteValues& assignment) const {
return factors_(assignment).first;
return factors_(assignment);
}
/* *******************************************************************************/

2
gtsam/hybrid/HybridGaussianFactor.h
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@ -129,7 +129,7 @@ public:
/// @{
/// Get factor at a given discrete assignment.
sharedFactor operator()(const DiscreteValues &assignment) const;
GaussianFactorValuePair operator()(const DiscreteValues &assignment) const;
/**
* @brief Compute error of the HybridGaussianFactor as a tree.

12
gtsam/hybrid/HybridGaussianFactorGraph.cpp
View File

@ -81,7 +81,7 @@ static void printFactor(const std::shared_ptr<Factor>& factor,
if (assignment.empty())
hgf->print("HybridGaussianFactor:", keyFormatter);
else
hgf->operator()(assignment)->print("HybridGaussianFactor, component:", keyFormatter);
hgf->operator()(assignment).first->print("HybridGaussianFactor, component:", keyFormatter);
} else if (auto gf = std::dynamic_pointer_cast<GaussianFactor>(factor)) {
factor->print("GaussianFactor:\n", keyFormatter);
@ -329,6 +329,7 @@ static std::shared_ptr<Factor> createHybridGaussianFactor(const ResultTree& elim
const double negLogK = conditional->negLogConstant();
hf->constantTerm() += -2.0 * negLogK;
return {factor, negLogK};
return {factor, scalar + negLogK};
} else if (!conditional && !factor) {
return {nullptr, 0.0}; // TODO(frank): or should this be infinity?
} else {
@ -355,7 +356,9 @@ HybridGaussianFactorGraph::eliminate(const Ordering& keys) const {
DiscreteKeys discreteSeparator = GetDiscreteKeys(*this);
// Collect all the factors to create a set of Gaussian factor graphs in a
// decision tree indexed by all discrete keys involved.
// decision tree indexed by all discrete keys involved. Just like any hybrid factor, every
// assignment also has a scalar error, in this case the sum of all errors in the graph. This error
// is assignment-specific and accounts for any difference in noise models used.
HybridGaussianProductFactor productFactor = collectProductFactor();
// Convert factor graphs with a nullptr to an empty factor graph.
@ -374,11 +377,12 @@ HybridGaussianFactorGraph::eliminate(const Ordering& keys) const {
}
// Expensive elimination of product factor.
auto result = EliminatePreferCholesky(graph, keys);
auto result = EliminatePreferCholesky(graph, keys); /// <<<<<< MOST COMPUTE IS HERE
// Record whether there any continuous variables left
someContinuousLeft |= !result.second->empty();
// We pass on the scalar unmodified.
return {result, scalar};
};
@ -548,7 +552,7 @@ GaussianFactorGraph HybridGaussianFactorGraph::choose(const DiscreteValues& assi
} else if (auto gc = std::dynamic_pointer_cast<GaussianConditional>(f)) {
gfg.push_back(gf);
} else if (auto hgf = std::dynamic_pointer_cast<HybridGaussianFactor>(f)) {
gfg.push_back((*hgf)(assignment));
gfg.push_back((*hgf)(assignment).first);
} else if (auto hgc = std::dynamic_pointer_cast<HybridGaussianConditional>(f)) {
gfg.push_back((*hgc)(assignment));
} else if (auto hc = std::dynamic_pointer_cast<HybridConditional>(f)) {

108
gtsam/hybrid/tests/testHybridBayesNet.cpp
View File

@ -18,9 +18,12 @@
* @date December 2021
*/
#include <gtsam/base/Testable.h>
#include <gtsam/discrete/DiscreteFactor.h>
#include <gtsam/hybrid/HybridBayesNet.h>
#include <gtsam/hybrid/HybridBayesTree.h>
#include <gtsam/hybrid/HybridConditional.h>
#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include "Switching.h"
@ -28,6 +31,7 @@
// Include for test suite
#include <CppUnitLite/TestHarness.h>
#include <memory>
using namespace std;
using namespace gtsam;
@ -113,7 +117,7 @@ TEST(HybridBayesNet, EvaluatePureDiscrete) {
}
/* ****************************************************************************/
// Test creation of a tiny hybrid Bayes net.
// Test API for a tiny hybrid Bayes net.
TEST(HybridBayesNet, Tiny) {
auto bayesNet = tiny::createHybridBayesNet(); // P(z|x,mode)P(x)P(mode)
EXPECT_LONGS_EQUAL(3, bayesNet.size());
@ -164,10 +168,8 @@ TEST(HybridBayesNet, Tiny) {
EXPECT(!pruned.equals(bayesNet));
// error
const double error0 = chosen0.error(vv) + gc0->negLogConstant() -
px->negLogConstant() - log(0.4);
const double error1 = chosen1.error(vv) + gc1->negLogConstant() -
px->negLogConstant() - log(0.6);
const double error0 = chosen0.error(vv) + gc0->negLogConstant() - px->negLogConstant() - log(0.4);
const double error1 = chosen1.error(vv) + gc1->negLogConstant() - px->negLogConstant() - log(0.6);
// print errors:
EXPECT_DOUBLES_EQUAL(error0, bayesNet.error(zero), 1e-9);
EXPECT_DOUBLES_EQUAL(error1, bayesNet.error(one), 1e-9);
@ -188,6 +190,23 @@ TEST(HybridBayesNet, Tiny) {
// toFactorGraph
auto fg = bayesNet.toFactorGraph({{Z(0), Vector1(5.0)}});
EXPECT_LONGS_EQUAL(3, fg.size());
GTSAM_PRINT(fg);
// Create the product factor for eliminating x0:
HybridGaussianFactorGraph factors_x0;
factors_x0.push_back(fg.at(0));
factors_x0.push_back(fg.at(1));
auto productFactor = factors_x0.collectProductFactor();
// Check that scalars are 0 and 1.79
EXPECT_DOUBLES_EQUAL(0.0, productFactor({{M(0), 0}}).second, 1e-9);
EXPECT_DOUBLES_EQUAL(1.791759, productFactor({{M(0), 1}}).second, 1e-5);
// Call eliminate and check scalar:
auto result = factors_x0.eliminate({X(0)});
GTSAM_PRINT(*result.first);
auto df = std::dynamic_pointer_cast<DecisionTreeFactor>(result.second);
GTSAM_PRINT(df->errorTree());
// Check that the ratio of probPrime to evaluate is the same for all modes.
std::vector<double> ratio(2);
@ -209,17 +228,13 @@ TEST(HybridBayesNet, Tiny) {
/* ****************************************************************************/
// Hybrid Bayes net P(X0|X1) P(X1|Asia) P(Asia).
namespace different_sigmas {
const auto gc = GaussianConditional::sharedMeanAndStddev(X(0), 2 * I_1x1, X(1),
Vector1(-4.0), 5.0);
const auto gc = GaussianConditional::sharedMeanAndStddev(X(0), 2 * I_1x1, X(1), Vector1(-4.0), 5.0);
const std::vector<std::pair<Vector, double>> parms{{Vector1(5), 2.0},
{Vector1(2), 3.0}};
const std::vector<std::pair<Vector, double>> parms{{Vector1(5), 2.0}, {Vector1(2), 3.0}};
const auto hgc = std::make_shared<HybridGaussianConditional>(Asia, X(1), parms);
const auto prior = std::make_shared<DiscreteConditional>(Asia, "99/1");
auto wrap = [](const auto& c) {
return std::make_shared<HybridConditional>(c);
};
auto wrap = [](const auto& c) { return std::make_shared<HybridConditional>(c); };
const HybridBayesNet bayesNet{wrap(gc), wrap(hgc), wrap(prior)};
// Create values at which to evaluate.
@ -233,8 +248,8 @@ TEST(HybridBayesNet, evaluateHybrid) {
const double conditionalProbability = gc->evaluate(values.continuous());
const double mixtureProbability = hgc->evaluate(values);
EXPECT_DOUBLES_EQUAL(conditionalProbability * mixtureProbability * 0.99,
bayesNet.evaluate(values), 1e-9);
EXPECT_DOUBLES_EQUAL(
conditionalProbability * mixtureProbability * 0.99, bayesNet.evaluate(values), 1e-9);
}
/* ****************************************************************************/
@ -256,14 +271,10 @@ TEST(HybridBayesNet, Choose) {
EXPECT_LONGS_EQUAL(4, gbn.size());
EXPECT(assert_equal(*(*hybridBayesNet->at(0)->asHybrid())(assignment),
*gbn.at(0)));
EXPECT(assert_equal(*(*hybridBayesNet->at(1)->asHybrid())(assignment),
*gbn.at(1)));
EXPECT(assert_equal(*(*hybridBayesNet->at(2)->asHybrid())(assignment),
*gbn.at(2)));
EXPECT(assert_equal(*(*hybridBayesNet->at(3)->asHybrid())(assignment),
*gbn.at(3)));
EXPECT(assert_equal(*(*hybridBayesNet->at(0)->asHybrid())(assignment), *gbn.at(0)));
EXPECT(assert_equal(*(*hybridBayesNet->at(1)->asHybrid())(assignment), *gbn.at(1)));
EXPECT(assert_equal(*(*hybridBayesNet->at(2)->asHybrid())(assignment), *gbn.at(2)));
EXPECT(assert_equal(*(*hybridBayesNet->at(3)->asHybrid())(assignment), *gbn.at(3)));
}
/* ****************************************************************************/
@ -300,8 +311,7 @@ TEST(HybridBayesNet, OptimizeAssignment) {
TEST(HybridBayesNet, Optimize) {
Switching s(4, 1.0, 0.1, {0, 1, 2, 3}, "1/1 1/1");
HybridBayesNet::shared_ptr hybridBayesNet =
s.linearizedFactorGraph.eliminateSequential();
HybridBayesNet::shared_ptr hybridBayesNet = s.linearizedFactorGraph.eliminateSequential();
HybridValues delta = hybridBayesNet->optimize();
@ -328,8 +338,7 @@ TEST(HybridBayesNet, Pruning) {
// ϕ(x0) ϕ(x0,x1,m0) ϕ(x1,x2,m1) ϕ(x0;z0) ϕ(x1;z1) ϕ(x2;z2) ϕ(m0) ϕ(m0,m1)
Switching s(3);
HybridBayesNet::shared_ptr posterior =
s.linearizedFactorGraph.eliminateSequential();
HybridBayesNet::shared_ptr posterior = s.linearizedFactorGraph.eliminateSequential();
EXPECT_LONGS_EQUAL(5, posterior->size());
// Optimize
@ -355,12 +364,9 @@ TEST(HybridBayesNet, Pruning) {
logProbability += posterior->at(0)->asHybrid()->logProbability(hybridValues);
logProbability += posterior->at(1)->asHybrid()->logProbability(hybridValues);
logProbability += posterior->at(2)->asHybrid()->logProbability(hybridValues);
logProbability +=
posterior->at(3)->asDiscrete()->logProbability(hybridValues);
logProbability +=
posterior->at(4)->asDiscrete()->logProbability(hybridValues);
EXPECT_DOUBLES_EQUAL(logProbability, posterior->logProbability(hybridValues),
1e-9);
logProbability += posterior->at(3)->asDiscrete()->logProbability(hybridValues);
logProbability += posterior->at(4)->asDiscrete()->logProbability(hybridValues);
EXPECT_DOUBLES_EQUAL(logProbability, posterior->logProbability(hybridValues), 1e-9);
// Check agreement with discrete posterior
// double density = exp(logProbability);
@ -381,8 +387,7 @@ TEST(HybridBayesNet, Pruning) {
TEST(HybridBayesNet, Prune) {
Switching s(4);
HybridBayesNet::shared_ptr posterior =
s.linearizedFactorGraph.eliminateSequential();
HybridBayesNet::shared_ptr posterior = s.linearizedFactorGraph.eliminateSequential();
EXPECT_LONGS_EQUAL(7, posterior->size());
HybridValues delta = posterior->optimize();
@ -399,8 +404,7 @@ TEST(HybridBayesNet, Prune) {
TEST(HybridBayesNet, UpdateDiscreteConditionals) {
Switching s(4);
HybridBayesNet::shared_ptr posterior =
s.linearizedFactorGraph.eliminateSequential();
HybridBayesNet::shared_ptr posterior = s.linearizedFactorGraph.eliminateSequential();
EXPECT_LONGS_EQUAL(7, posterior->size());
DiscreteConditional joint;
@ -412,8 +416,7 @@ TEST(HybridBayesNet, UpdateDiscreteConditionals) {
auto prunedDecisionTree = joint.prune(maxNrLeaves);
#ifdef GTSAM_DT_MERGING
EXPECT_LONGS_EQUAL(maxNrLeaves + 2 /*2 zero leaves*/,
prunedDecisionTree.nrLeaves());
EXPECT_LONGS_EQUAL(maxNrLeaves + 2 /*2 zero leaves*/, prunedDecisionTree.nrLeaves());
#else
EXPECT_LONGS_EQUAL(8 /*full tree*/, prunedDecisionTree.nrLeaves());
#endif
@ -421,16 +424,14 @@ TEST(HybridBayesNet, UpdateDiscreteConditionals) {
// regression
// NOTE(Frank): I had to include *three* non-zeroes here now.
DecisionTreeFactor::ADT potentials(
s.modes,
std::vector<double>{0, 0, 0, 0.28739288, 0, 0.43106901, 0, 0.2815381});
s.modes, std::vector<double>{0, 0, 0, 0.28739288, 0, 0.43106901, 0, 0.2815381});
DiscreteConditional expectedConditional(3, s.modes, potentials);
// Prune!
auto pruned = posterior->prune(maxNrLeaves);
// Functor to verify values against the expectedConditional
auto checker = [&](const Assignment<Key>& assignment,
double probability) -> double {
auto checker = [&](const Assignment<Key>& assignment, double probability) -> double {
// typecast so we can use this to get probability value
DiscreteValues choices(assignment);
if (prunedDecisionTree(choices) == 0) {
@ -445,8 +446,7 @@ TEST(HybridBayesNet, UpdateDiscreteConditionals) {
CHECK(pruned.at(0)->asDiscrete());
auto pruned_discrete_conditionals = pruned.at(0)->asDiscrete();
auto discrete_conditional_tree =
std::dynamic_pointer_cast<DecisionTreeFactor::ADT>(
pruned_discrete_conditionals);
std::dynamic_pointer_cast<DecisionTreeFactor::ADT>(pruned_discrete_conditionals);
// The checker functor verifies the values for us.
discrete_conditional_tree->apply(checker);
@ -460,13 +460,10 @@ TEST(HybridBayesNet, Sampling) {
auto noise_model = noiseModel::Diagonal::Sigmas(Vector1(1.0));
nfg.emplace_shared<PriorFactor<double>>(X(0), 0.0, noise_model);
auto zero_motion =
std::make_shared<BetweenFactor<double>>(X(0), X(1), 0, noise_model);
auto one_motion =
std::make_shared<BetweenFactor<double>>(X(0), X(1), 1, noise_model);
auto zero_motion = std::make_shared<BetweenFactor<double>>(X(0), X(1), 0, noise_model);
auto one_motion = std::make_shared<BetweenFactor<double>>(X(0), X(1), 1, noise_model);
nfg.emplace_shared<HybridNonlinearFactor>(
DiscreteKey(M(0), 2),
std::vector<NoiseModelFactor::shared_ptr>{zero_motion, one_motion});
DiscreteKey(M(0), 2), std::vector<NoiseModelFactor::shared_ptr>{zero_motion, one_motion});
DiscreteKey mode(M(0), 2);
nfg.emplace_shared<DiscreteDistribution>(mode, "1/1");
@ -538,18 +535,17 @@ TEST(HybridBayesNet, ErrorTreeWithConditional) {
hbn.emplace_shared<GaussianConditional>(x0, Vector1(0.0), I_1x1, prior_model);
// Add measurement P(z0 | x0)
hbn.emplace_shared<GaussianConditional>(z0, Vector1(0.0), -I_1x1, x0, I_1x1,
measurement_model);
hbn.emplace_shared<GaussianConditional>(z0, Vector1(0.0), -I_1x1, x0, I_1x1, measurement_model);
// Add hybrid motion model
double mu = 0.0;
double sigma0 = 1e2, sigma1 = 1e-2;
auto model0 = noiseModel::Isotropic::Sigma(1, sigma0);
auto model1 = noiseModel::Isotropic::Sigma(1, sigma1);
auto c0 = make_shared<GaussianConditional>(f01, Vector1(mu), I_1x1, x1, I_1x1,
x0, -I_1x1, model0),
c1 = make_shared<GaussianConditional>(f01, Vector1(mu), I_1x1, x1, I_1x1,
x0, -I_1x1, model1);
auto c0 =
make_shared<GaussianConditional>(f01, Vector1(mu), I_1x1, x1, I_1x1, x0, -I_1x1, model0),
c1 =
make_shared<GaussianConditional>(f01, Vector1(mu), I_1x1, x1, I_1x1, x0, -I_1x1, model1);
DiscreteKey m1(M(2), 2);
hbn.emplace_shared<HybridGaussianConditional>(m1, std::vector{c0, c1});

2
gtsam/hybrid/tests/testHybridGaussianConditional.cpp
View File

@ -217,7 +217,7 @@ TEST(HybridGaussianConditional, Likelihood2) {
// Check the detailed JacobianFactor calculation for mode==1.
{
// We have a JacobianFactor
const auto gf1 = (*likelihood)(assignment1);
const auto [gf1, _] = (*likelihood)(assignment1);
const auto jf1 = std::dynamic_pointer_cast<JacobianFactor>(gf1);
CHECK(jf1);

119
gtsam/hybrid/tests/testHybridGaussianFactorGraph.cpp
View File

@ -165,8 +165,119 @@ TEST(HybridGaussianFactorGraph, eliminateFullSequentialSimple) {
EXPECT_LONGS_EQUAL(4, result->size());
}
/*
****************************************************************************/
/* ************************************************************************* */
// Test API for the smallest switching network.
// None of these are regression tests.
TEST(HybridBayesNet, Switching) {
const double betweenSigma = 0.3, priorSigma = 0.1;
Switching s(2, betweenSigma, priorSigma);
const HybridGaussianFactorGraph& graph = s.linearizedFactorGraph;
EXPECT_LONGS_EQUAL(4, graph.size());
// Create some continuous and discrete values
VectorValues continuousValues{{X(0), Vector1(0.1)}, {X(1), Vector1(1.2)}};
DiscreteValues modeZero{{M(0), 0}}, modeOne{{M(0), 1}};
// Get the hybrid gaussian factor and check it is as expected
auto hgf = std::dynamic_pointer_cast<HybridGaussianFactor>(graph.at(1));
CHECK(hgf);
// Get factors and scalars for both modes
auto [factor0, scalar0] = (*hgf)(modeZero);
auto [factor1, scalar1] = (*hgf)(modeOne);
CHECK(factor0);
CHECK(factor1);
// Check scalars against negLogConstant of noise model
auto betweenModel = noiseModel::Isotropic::Sigma(1, betweenSigma);
EXPECT_DOUBLES_EQUAL(betweenModel->negLogConstant(), scalar0, 1e-9);
EXPECT_DOUBLES_EQUAL(betweenModel->negLogConstant(), scalar1, 1e-9);
// Check error for M(0) = 0
HybridValues values0{continuousValues, modeZero};
double expectedError0 = 0;
for (const auto& factor : graph) expectedError0 += factor->error(values0);
EXPECT_DOUBLES_EQUAL(expectedError0, graph.error(values0), 1e-5);
// Check error for M(0) = 1
HybridValues values1{continuousValues, modeOne};
double expectedError1 = 0;
for (const auto& factor : graph) expectedError1 += factor->error(values1);
EXPECT_DOUBLES_EQUAL(expectedError1, graph.error(values1), 1e-5);
// Check errorTree
AlgebraicDecisionTree<Key> actualErrors = graph.errorTree(continuousValues);
// Create expected error tree
AlgebraicDecisionTree<Key> expectedErrors(M(0), expectedError0, expectedError1);
// Check that the actual error tree matches the expected one
EXPECT(assert_equal(expectedErrors, actualErrors, 1e-5));
// Check probPrime
double probPrime0 = graph.probPrime(values0);
EXPECT_DOUBLES_EQUAL(std::exp(-expectedError0), probPrime0, 1e-5);
double probPrime1 = graph.probPrime(values1);
EXPECT_DOUBLES_EQUAL(std::exp(-expectedError1), probPrime1, 1e-5);
// Check discretePosterior
AlgebraicDecisionTree<Key> posterior = graph.discretePosterior(continuousValues);
double sum = probPrime0 + probPrime1;
AlgebraicDecisionTree<Key> expectedPosterior(M(0), probPrime0 / sum, probPrime1 / sum);
EXPECT(assert_equal(expectedPosterior, posterior, 1e-5));
// Make the clique of factors connected to x0:
HybridGaussianFactorGraph factors_x0;
factors_x0.push_back(graph.at(0));
factors_x0.push_back(hgf);
// Test collectProductFactor
auto productFactor = factors_x0.collectProductFactor();
// For M(0) = 0
auto [gaussianFactor0, actualScalar0] = productFactor(modeZero);
EXPECT(gaussianFactor0.size() == 2);
EXPECT_DOUBLES_EQUAL((*hgf)(modeZero).second, actualScalar0, 1e-5);
// For M(0) = 1
auto [gaussianFactor1, actualScalar1] = productFactor(modeOne);
EXPECT(gaussianFactor1.size() == 2);
EXPECT_DOUBLES_EQUAL((*hgf)(modeOne).second, actualScalar1, 1e-5);
// Test eliminate
Ordering ordering{X(0)};
auto [conditional, factor] = factors_x0.eliminate(ordering);
// Check the conditional
CHECK(conditional);
EXPECT(conditional->isHybrid());
auto hybridConditional = conditional->asHybrid();
CHECK(hybridConditional);
EXPECT_LONGS_EQUAL(1, hybridConditional->nrFrontals()); // x0
EXPECT_LONGS_EQUAL(2, hybridConditional->nrParents()); // x1, m0
// Check the remaining factor
EXPECT(factor);
EXPECT(std::dynamic_pointer_cast<HybridGaussianFactor>(factor));
auto hybridFactor = std::dynamic_pointer_cast<HybridGaussianFactor>(factor);
EXPECT_LONGS_EQUAL(2, hybridFactor->keys().size()); // x1, m0
// Check that the conditional and remaining factor are consistent for both modes
for (auto&& mode : {modeZero, modeOne}) {
auto gc = (*hybridConditional)(mode);
auto gf = (*hybridFactor)(mode);
// The error of the original factors should equal the sum of errors of the conditional and
// remaining factor, modulo the normalization constant of the conditional.
double originalError = factors_x0.error({continuousValues, mode});
EXPECT_DOUBLES_EQUAL(
originalError,
gc->negLogConstant() + gc->error(continuousValues) + gf.first->error(continuousValues),
1e-9);
}
}
/* ************************************************************************* */
// Select a particular continuous factor graph given a discrete assignment
TEST(HybridGaussianFactorGraph, DiscreteSelection) {
Switching s(3);
@ -410,12 +521,12 @@ TEST(HybridGaussianFactorGraph, collectProductFactor) {
// Expected decision tree with two factor graphs:
// f(x0;mode=0)P(x0)
GaussianFactorGraph expectedFG0{(*hybrid)(d0), prior};
GaussianFactorGraph expectedFG0{(*hybrid)(d0).first, prior};
EXPECT(assert_equal(expectedFG0, actual(d0).first, 1e-5));
EXPECT(assert_equal(0.0, actual(d0).second, 1e-5));
// f(x0;mode=1)P(x0)
GaussianFactorGraph expectedFG1{(*hybrid)(d1), prior};
GaussianFactorGraph expectedFG1{(*hybrid)(d1).first, prior};
EXPECT(assert_equal(expectedFG1, actual(d1).first, 1e-5));
EXPECT(assert_equal(1.79176, actual(d1).second, 1e-5));
}