Merge branch 'develop' of https://github.com/borglab/gtsam into dsf-gtsfm-to-gtsam-port

.github/scripts/python.sh

@@ -43,46 +43,68 @@ if [ -z ${PYTHON_VERSION+x} ]; then
     exit 127
 fi
 
-PYTHON="python${PYTHON_VERSION}"
+export PYTHON="python${PYTHON_VERSION}"
 
-if [[ $(uname) == "Darwin" ]]; then
+function install_dependencies()
+{
+  if [[ $(uname) == "Darwin" ]]; then
     brew install wget
-else
+  else
     # Install a system package required by our library
     sudo apt-get install -y wget libicu-dev python3-pip python3-setuptools
-fi
+  fi
 
-PATH=$PATH:$($PYTHON -c "import site; print(site.USER_BASE)")/bin
+  export PATH=$PATH:$($PYTHON -c "import site; print(site.USER_BASE)")/bin
 
-[ "${GTSAM_WITH_TBB:-OFF}" = "ON" ] && install_tbb
+  [ "${GTSAM_WITH_TBB:-OFF}" = "ON" ] && install_tbb
+
+  $PYTHON -m pip install -r $GITHUB_WORKSPACE/python/requirements.txt
+}
+
+function build()
+{
+  mkdir $GITHUB_WORKSPACE/build
+  cd $GITHUB_WORKSPACE/build
+
+  BUILD_PYBIND="ON"
+
+  cmake $GITHUB_WORKSPACE -DCMAKE_BUILD_TYPE=${CMAKE_BUILD_TYPE} \
+      -DGTSAM_BUILD_TESTS=OFF \
+      -DGTSAM_BUILD_UNSTABLE=${GTSAM_BUILD_UNSTABLE:-ON} \
+      -DGTSAM_USE_QUATERNIONS=OFF \
+      -DGTSAM_WITH_TBB=${GTSAM_WITH_TBB:-OFF} \
+      -DGTSAM_BUILD_EXAMPLES_ALWAYS=OFF \
+      -DGTSAM_BUILD_WITH_MARCH_NATIVE=OFF \
+      -DGTSAM_BUILD_PYTHON=${BUILD_PYBIND} \
+      -DGTSAM_UNSTABLE_BUILD_PYTHON=${GTSAM_BUILD_UNSTABLE:-ON} \
+      -DGTSAM_PYTHON_VERSION=$PYTHON_VERSION \
+      -DPYTHON_EXECUTABLE:FILEPATH=$(which $PYTHON) \
+      -DGTSAM_ALLOW_DEPRECATED_SINCE_V42=OFF \
+      -DCMAKE_INSTALL_PREFIX=$GITHUB_WORKSPACE/gtsam_install
 
 
-BUILD_PYBIND="ON"
+  # Set to 2 cores so that Actions does not error out during resource provisioning.
+  make -j2 install
 
-sudo $PYTHON -m pip install -r $GITHUB_WORKSPACE/python/requirements.txt
+  cd $GITHUB_WORKSPACE/build/python
+  $PYTHON -m pip install --user .
+}
 
-mkdir $GITHUB_WORKSPACE/build
+function test()
-cd $GITHUB_WORKSPACE/build
+{
+  cd $GITHUB_WORKSPACE/python/gtsam/tests
+  $PYTHON -m unittest discover -v
+}
 
-cmake $GITHUB_WORKSPACE -DCMAKE_BUILD_TYPE=${CMAKE_BUILD_TYPE} \
+# select between build or test
-    -DGTSAM_BUILD_TESTS=OFF \
+case $1 in
-    -DGTSAM_BUILD_UNSTABLE=${GTSAM_BUILD_UNSTABLE:-ON} \
+  -d)
-    -DGTSAM_USE_QUATERNIONS=OFF \
+    install_dependencies
-    -DGTSAM_WITH_TBB=${GTSAM_WITH_TBB:-OFF} \
+    ;;
-    -DGTSAM_BUILD_EXAMPLES_ALWAYS=OFF \
+  -b)
-    -DGTSAM_BUILD_WITH_MARCH_NATIVE=OFF \
+    build
-    -DGTSAM_BUILD_PYTHON=${BUILD_PYBIND} \
+    ;;
-    -DGTSAM_UNSTABLE_BUILD_PYTHON=${GTSAM_BUILD_UNSTABLE:-ON} \
+  -t)
-    -DGTSAM_PYTHON_VERSION=$PYTHON_VERSION \
+    test
-    -DPYTHON_EXECUTABLE:FILEPATH=$(which $PYTHON) \
+    ;;
-    -DGTSAM_ALLOW_DEPRECATED_SINCE_V42=OFF \
+esac
-    -DCMAKE_INSTALL_PREFIX=$GITHUB_WORKSPACE/gtsam_install
-
-
-# Set to 2 cores so that Actions does not error out during resource provisioning.
-make -j2 install
-
-cd $GITHUB_WORKSPACE/build/python
-$PYTHON -m pip install --user .
-cd $GITHUB_WORKSPACE/python/gtsam/tests
-$PYTHON -m unittest discover -v

.github/workflows/build-linux.yml

@@ -20,26 +20,26 @@ jobs:
         # Github Actions requires a single row to be added to the build matrix.
         # See https://help.github.com/en/articles/workflow-syntax-for-github-actions.
         name: [
-          ubuntu-18.04-gcc-5,
+          ubuntu-20.04-gcc-7,
-          ubuntu-18.04-gcc-9,
+          ubuntu-20.04-gcc-9,
-          ubuntu-18.04-clang-9,
+          ubuntu-20.04-clang-9,
         ]
 
         build_type: [Debug, Release]
         build_unstable: [ON]
         include:
-          - name: ubuntu-18.04-gcc-5
+          - name: ubuntu-20.04-gcc-7
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
-            version: "5"
+            version: "7"
 
-          - name: ubuntu-18.04-gcc-9
+          - name: ubuntu-20.04-gcc-9
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
 
-          - name: ubuntu-18.04-clang-9
+          - name: ubuntu-20.04-clang-9
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: clang
             version: "9"
 
@@ -60,9 +60,9 @@ jobs:
             gpg -a --export $LLVM_KEY | sudo apt-key add -
             sudo add-apt-repository "deb http://apt.llvm.org/bionic/ llvm-toolchain-bionic-9 main"
           fi
-          sudo apt-get -y update
 
-          sudo apt-get -y install cmake build-essential pkg-config libpython-dev python-numpy libicu-dev
+          sudo apt-get -y update
+          sudo apt-get -y install cmake build-essential pkg-config libpython3-dev python3-numpy libicu-dev
 
           if [ "${{ matrix.compiler }}" = "gcc" ]; then
             sudo apt-get install -y g++-${{ matrix.version }} g++-${{ matrix.version }}-multilib

.github/workflows/build-python.yml

@@ -19,34 +19,34 @@ jobs:
         # Github Actions requires a single row to be added to the build matrix.
         # See https://help.github.com/en/articles/workflow-syntax-for-github-actions.
         name: [
-          ubuntu-18.04-gcc-5,
+          ubuntu-20.04-gcc-7,
-          ubuntu-18.04-gcc-9,
+          ubuntu-20.04-gcc-9,
-          ubuntu-18.04-clang-9,
+          ubuntu-20.04-clang-9,
           macOS-11-xcode-13.4.1,
-          ubuntu-18.04-gcc-5-tbb,
+          ubuntu-20.04-gcc-7-tbb,
         ]
 
         build_type: [Debug, Release]
         python_version: [3]
         include:
-          - name: ubuntu-18.04-gcc-5
+          - name: ubuntu-20.04-gcc-7
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
-            version: "5"
+            version: "7"
 
-          - name: ubuntu-18.04-gcc-9
+          - name: ubuntu-20.04-gcc-9
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
 
-          - name: ubuntu-18.04-clang-9
+          - name: ubuntu-20.04-clang-9
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: clang
             version: "9"
 
           # NOTE temporarily added this as it is a required check.
-          - name: ubuntu-18.04-clang-9
+          - name: ubuntu-20.04-clang-9
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: clang
             version: "9"
             build_type: Debug
@@ -57,10 +57,10 @@ jobs:
             compiler: xcode
             version: "13.4.1"
 
-          - name: ubuntu-18.04-gcc-5-tbb
+          - name: ubuntu-20.04-gcc-7-tbb
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
-            version: "5"
+            version: "7"
             flag: tbb
 
     steps:
@@ -79,9 +79,9 @@ jobs:
             gpg -a --export $LLVM_KEY | sudo apt-key add -
             sudo add-apt-repository "deb http://apt.llvm.org/bionic/ llvm-toolchain-bionic-9 main"
           fi
+
           sudo apt-get -y update
-          
+          sudo apt-get -y install cmake build-essential pkg-config libpython3-dev python3-numpy libboost-all-dev
-          sudo apt-get -y install cmake build-essential pkg-config libpython-dev python-numpy libboost-all-dev
           
           if [ "${{ matrix.compiler }}" = "gcc" ]; then
             sudo apt-get install -y g++-${{ matrix.version }} g++-${{ matrix.version }}-multilib
@@ -117,11 +117,12 @@ jobs:
         uses: pierotofy/set-swap-space@master
         with:
           swap-size-gb: 6
-      - name: Build (Linux)
+      - name: Install Dependencies
-        if: runner.os == 'Linux'
         run: |
-          bash .github/scripts/python.sh
+          bash .github/scripts/python.sh -d
-      - name: Build (macOS)
+      - name: Build
-        if: runner.os == 'macOS'
         run: |
-          bash .github/scripts/python.sh
+          bash .github/scripts/python.sh -b
+      - name: Test
+        run: |
+          bash .github/scripts/python.sh -t

.github/workflows/build-special.yml

@@ -32,31 +32,31 @@ jobs:
 
         include:
           - name: ubuntu-gcc-deprecated
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
             flag: deprecated
 
           - name: ubuntu-gcc-quaternions
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
             flag: quaternions
 
           - name: ubuntu-gcc-tbb
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
             flag: tbb
 
           - name: ubuntu-cayleymap
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
             flag: cayley
 
           - name: ubuntu-system-libs
-            os: ubuntu-18.04
+            os: ubuntu-20.04
             compiler: gcc
             version: "9"
             flag: system-libs
@@ -74,9 +74,9 @@ jobs:
             gpg -a --export 15CF4D18AF4F7421 | sudo apt-key add -
             sudo add-apt-repository "deb http://apt.llvm.org/bionic/ llvm-toolchain-bionic-9 main"
           fi
-          sudo apt-get -y update
 
-          sudo apt-get -y install cmake build-essential pkg-config libpython-dev python-numpy libicu-dev
+          sudo apt-get -y update
+          sudo apt-get -y install cmake build-essential pkg-config libpython3-dev python3-numpy libicu-dev
 
           if [ "${{ matrix.compiler }}" = "gcc" ]; then
             sudo apt-get install -y g++-${{ matrix.version }} g++-${{ matrix.version }}-multilib

README.md

@@ -64,6 +64,29 @@ GTSAM 4.1 added a new pybind wrapper, and **removed** the deprecated functionali
 
 We provide support for [MATLAB](matlab/README.md) and [Python](python/README.md) wrappers for GTSAM. Please refer to the linked documents for more details.
 
+## Citation
+
+If you are using GTSAM for academic work, please use the following citation:
+
+```
+@software{gtsam,
+  author       = {Frank Dellaert and Richard Roberts and Varun Agrawal and Alex Cunningham and Chris Beall and Duy-Nguyen Ta and Fan Jiang and lucacarlone and nikai and Jose Luis Blanco-Claraco and Stephen Williams and ydjian and John Lambert and Andy Melim and Zhaoyang Lv and Akshay Krishnan and Jing Dong and Gerry Chen and Krunal Chande and balderdash-devil and DiffDecisionTrees and Sungtae An and mpaluri and Ellon Paiva Mendes and Mike Bosse and Akash Patel and Ayush Baid and Paul Furgale and matthewbroadwaynavenio and roderick-koehle},
+  title        = {borglab/gtsam},
+  month        = may,
+  year         = 2022,
+  publisher    = {Zenodo},
+  version      = {4.2a7},
+  doi          = {10.5281/zenodo.5794541},
+  url          = {https://doi.org/10.5281/zenodo.5794541}
+}
+```
+
+You can also get the latest citation available from Zenodo below:
+
+[![DOI](https://zenodo.org/badge/86362856.svg)](https://doi.org/10.5281/zenodo.5794541)
+
+Specific formats are available in the bottom-right corner of the Zenodo page.
+
 ## The Preintegrated IMU Factor
 
 GTSAM includes a state of the art IMU handling scheme based on
@@ -73,7 +96,7 @@ GTSAM includes a state of the art IMU handling scheme based on
 Our implementation improves on this using integration on the manifold, as detailed in
 
 - Luca Carlone, Zsolt Kira, Chris Beall, Vadim Indelman, and Frank Dellaert, _"Eliminating conditionally independent sets in factor graphs: a unifying perspective based on smart factors"_, Int. Conf. on Robotics and Automation (ICRA), 2014. [[link]](https://ieeexplore.ieee.org/abstract/document/6907483)
-- Christian Forster, Luca Carlone, Frank Dellaert, and Davide Scaramuzza, "IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation", Robotics: Science and Systems (RSS), 2015. [[link]](http://www.roboticsproceedings.org/rss11/p06.pdf)
+- Christian Forster, Luca Carlone, Frank Dellaert, and Davide Scaramuzza, _"IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation"_, Robotics: Science and Systems (RSS), 2015. [[link]](http://www.roboticsproceedings.org/rss11/p06.pdf)
 
 If you are using the factor in academic work, please cite the publications above.
 

cmake/GtsamBuildTypes.cmake

@@ -190,7 +190,7 @@ if(${CMAKE_CXX_COMPILER_ID} STREQUAL "Clang")
 endif()
 
 if (NOT MSVC)
-  option(GTSAM_BUILD_WITH_MARCH_NATIVE  "Enable/Disable building with all instructions supported by native architecture (binary may not be portable!)" ON)
+  option(GTSAM_BUILD_WITH_MARCH_NATIVE  "Enable/Disable building with all instructions supported by native architecture (binary may not be portable!)" OFF)
   if(GTSAM_BUILD_WITH_MARCH_NATIVE AND (APPLE AND NOT CMAKE_SYSTEM_PROCESSOR STREQUAL "arm64"))
     # Add as public flag so all dependant projects also use it, as required
     # by Eigen to avid crashes due to SIMD vectorization:

cmake/HandleEigen.cmake

@@ -1,7 +1,10 @@
 ###############################################################################
 # Option for using system Eigen or GTSAM-bundled Eigen
-
+# Default: Use system's Eigen if found automatically:
-option(GTSAM_USE_SYSTEM_EIGEN "Find and use system-installed Eigen. If 'off', use the one bundled with GTSAM" OFF)
+find_package(Eigen3 QUIET)
+set(USE_SYSTEM_EIGEN_INITIAL_VALUE ${Eigen3_FOUND})
+option(GTSAM_USE_SYSTEM_EIGEN "Find and use system-installed Eigen. If 'off', use the one bundled with GTSAM" ${USE_SYSTEM_EIGEN_INITIAL_VALUE})
+unset(USE_SYSTEM_EIGEN_INITIAL_VALUE)
 
 if(NOT GTSAM_USE_SYSTEM_EIGEN)
   # This option only makes sense if using the embedded copy of Eigen, it is
@@ -11,7 +14,7 @@ endif()
 
 # Switch for using system Eigen or GTSAM-bundled Eigen
 if(GTSAM_USE_SYSTEM_EIGEN)
-    find_package(Eigen3 REQUIRED)
+    find_package(Eigen3 REQUIRED) # need to find again as REQUIRED
 
     # Use generic Eigen include paths e.g. <Eigen/Core>
     set(GTSAM_EIGEN_INCLUDE_FOR_INSTALL "${EIGEN3_INCLUDE_DIR}")

cmake/HandlePrintConfiguration.cmake

@@ -33,6 +33,7 @@ print_build_options_for_target(gtsam)
 
 print_config("Use System Eigen" "${GTSAM_USE_SYSTEM_EIGEN} (Using version: ${GTSAM_EIGEN_VERSION})")
 print_config("Use System Metis" "${GTSAM_USE_SYSTEM_METIS}")
+print_config("Using Boost version" "${Boost_VERSION}")
 
 if(GTSAM_USE_TBB)
     print_config("Use Intel TBB" "Yes (Version: ${TBB_VERSION})")

doc/refs.bib

@@ -1,26 +1,72 @@
+%% This BibTeX bibliography file was created using BibDesk.
+%% https://bibdesk.sourceforge.io/
+
+%% Created for Varun Agrawal at 2021-09-27 17:39:09 -0400 
+
+
+%% Saved with string encoding Unicode (UTF-8) 
+
+
+
+@article{Lupton12tro,
+	author = {Lupton, Todd and Sukkarieh, Salah},
+	date-added = {2021-09-27 17:38:56 -0400},
+	date-modified = {2021-09-27 17:39:09 -0400},
+	doi = {10.1109/TRO.2011.2170332},
+	journal = {IEEE Transactions on Robotics},
+	number = {1},
+	pages = {61-76},
+	title = {Visual-Inertial-Aided Navigation for High-Dynamic Motion in Built Environments Without Initial Conditions},
+	volume = {28},
+	year = {2012},
+	Bdsk-Url-1 = {https://doi.org/10.1109/TRO.2011.2170332}}
+
+@inproceedings{Forster15rss,
+	author = {Christian Forster and Luca Carlone and Frank Dellaert and Davide Scaramuzza},
+	booktitle = {Robotics: Science and Systems},
+	date-added = {2021-09-26 20:44:41 -0400},
+	date-modified = {2021-09-26 20:45:03 -0400},
+	title = {IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation},
+	year = {2015}}
+
 @article{Iserles00an,
-  title =	 {Lie-group methods},
+	author = {Iserles, Arieh and Munthe-Kaas, Hans Z and N{\o}rsett, Syvert P and Zanna, Antonella},
-  author =	 {Iserles, Arieh and Munthe-Kaas, Hans Z and
+	journal = {Acta Numerica 2000},
-                  N{\o}rsett, Syvert P and Zanna, Antonella},
+	pages = {215--365},
-  journal =	 {Acta Numerica 2000},
+	publisher = {Cambridge Univ Press},
-  volume =	 {9},
+	title = {Lie-group methods},
-  pages =	 {215--365},
+	volume = {9},
-  year =	 {2000},
+	year = {2000}}
-  publisher =	 {Cambridge Univ Press}
-}
 
 @book{Murray94book,
-  title =	 {A mathematical introduction to robotic manipulation},
+	author = {Murray, Richard M and Li, Zexiang and Sastry, S Shankar and Sastry, S Shankara},
-  author =	 {Murray, Richard M and Li, Zexiang and Sastry, S
+	publisher = {CRC press},
-                  Shankar and Sastry, S Shankara},
+	title = {A mathematical introduction to robotic manipulation},
-  year =	 {1994},
+	year = {1994}}
-  publisher =	 {CRC press}
-}
 
 @book{Spivak65book,
-  title =	 {Calculus on manifolds},
+	author = {Spivak, Michael},
-  author =	 {Spivak, Michael},
+	publisher = {WA Benjamin New York},
-  volume =	 {1},
+	title = {Calculus on manifolds},
-  year =	 {1965},
+	volume = {1},
-  publisher =	 {WA Benjamin New York}
+	year = {1965}}
-}
+
+@phdthesis{Nikolic16thesis,
+  title={Characterisation, calibration, and design of visual-inertial sensor systems for robot navigation},
+  author={Nikolic, Janosch},
+  year={2016},
+  school={ETH Zurich}
+}
+
+@book{Simon06book,
+  title={Optimal state estimation: Kalman, H infinity, and nonlinear approaches},
+  author={Simon, Dan},
+  year={2006},
+  publisher={John Wiley \& Sons}
+}
+
+@inproceedings{Trawny05report_IndirectKF,
+  title={Indirect Kalman Filter for 3 D Attitude Estimation},
+  author={Nikolas Trawny and Stergios I. Roumeliotis},
+  year={2005}
+}

examples/CombinedImuFactorsExample.cpp

@@ -60,13 +60,14 @@ namespace po = boost::program_options;
 
 po::variables_map parseOptions(int argc, char* argv[]) {
   po::options_description desc;
-  desc.add_options()("help,h", "produce help message")(
+  desc.add_options()("help,h", "produce help message")  // help message
-      "data_csv_path", po::value<string>()->default_value("imuAndGPSdata.csv"),
+      ("data_csv_path", po::value<string>()->default_value("imuAndGPSdata.csv"),
-      "path to the CSV file with the IMU data")(
+       "path to the CSV file with the IMU data")  // path to the data file
-      "output_filename",
+      ("output_filename",
-      po::value<string>()->default_value("imuFactorExampleResults.csv"),
+       po::value<string>()->default_value("imuFactorExampleResults.csv"),
-      "path to the result file to use")("use_isam", po::bool_switch(),
+       "path to the result file to use")  // filename to save results to
-                                        "use ISAM as the optimizer");
+      ("use_isam", po::bool_switch(),
+       "use ISAM as the optimizer");  // flag for ISAM optimizer
 
   po::variables_map vm;
   po::store(po::parse_command_line(argc, argv, desc), vm);
@@ -106,7 +107,7 @@ boost::shared_ptr<PreintegratedCombinedMeasurements::Params> imuParams() {
       I_3x3 * 1e-8;  // error committed in integrating position from velocities
   Matrix33 bias_acc_cov = I_3x3 * pow(accel_bias_rw_sigma, 2);
   Matrix33 bias_omega_cov = I_3x3 * pow(gyro_bias_rw_sigma, 2);
-  Matrix66 bias_acc_omega_int =
+  Matrix66 bias_acc_omega_init =
       I_6x6 * 1e-5;  // error in the bias used for preintegration
 
   auto p = PreintegratedCombinedMeasurements::Params::MakeSharedD(0.0);
@@ -122,7 +123,7 @@ boost::shared_ptr<PreintegratedCombinedMeasurements::Params> imuParams() {
   // PreintegrationCombinedMeasurements params:
   p->biasAccCovariance = bias_acc_cov;      // acc bias in continuous
   p->biasOmegaCovariance = bias_omega_cov;  // gyro bias in continuous
-  p->biasAccOmegaInt = bias_acc_omega_int;
+  p->biasAccOmegaInt = bias_acc_omega_init;
 
   return p;
 }

examples/ImuFactorsExample.cpp

@@ -94,7 +94,7 @@ boost::shared_ptr<PreintegratedCombinedMeasurements::Params> imuParams() {
       I_3x3 * 1e-8;  // error committed in integrating position from velocities
   Matrix33 bias_acc_cov = I_3x3 * pow(accel_bias_rw_sigma, 2);
   Matrix33 bias_omega_cov = I_3x3 * pow(gyro_bias_rw_sigma, 2);
-  Matrix66 bias_acc_omega_int =
+  Matrix66 bias_acc_omega_init =
       I_6x6 * 1e-5;  // error in the bias used for preintegration
 
   auto p = PreintegratedCombinedMeasurements::Params::MakeSharedD(0.0);
@@ -110,7 +110,7 @@ boost::shared_ptr<PreintegratedCombinedMeasurements::Params> imuParams() {
   // PreintegrationCombinedMeasurements params:
   p->biasAccCovariance = bias_acc_cov;      // acc bias in continuous
   p->biasOmegaCovariance = bias_omega_cov;  // gyro bias in continuous
-  p->biasAccOmegaInt = bias_acc_omega_int;
+  p->biasAccOmegaInt = bias_acc_omega_init;
 
   return p;
 }

examples/README.md

@@ -33,7 +33,6 @@ The following examples illustrate some concepts from Georgia Tech's research pap
 ## 2D Pose SLAM 
 
 * **LocalizationExample.cpp**: modeling robot motion
-* **LocalizationExample2.cpp**: example with GPS like measurements
 * **Pose2SLAMExample**: A 2D Pose SLAM example using the predefined typedefs in gtsam/slam/pose2SLAM.h
 * **Pose2SLAMExample_advanced**: same, but uses an Optimizer object
 * **Pose2SLAMwSPCG**: solve a simple 3 by 3 grid of Pose2 SLAM problem by using easy SPCG interface

gtsam/base/Group.h

@@ -95,7 +95,7 @@ template<class Class>
 struct MultiplicativeGroupTraits {
   typedef group_tag structure_category;
   typedef multiplicative_group_tag group_flavor;
-  static Class Identity() { return Class::identity(); }
+  static Class Identity() { return Class::Identity(); }
   static Class Compose(const Class &g, const Class & h) { return g * h;}
   static Class Between(const Class &g, const Class & h) { return g.inverse() * h;}
   static Class Inverse(const Class &g) { return g.inverse();}
@@ -111,7 +111,7 @@ template<class Class>
 struct AdditiveGroupTraits {
   typedef group_tag structure_category;
   typedef additive_group_tag group_flavor;
-  static Class Identity() { return Class::identity(); }
+  static Class Identity() { return Class::Identity(); }
   static Class Compose(const Class &g, const Class & h) { return g + h;}
   static Class Between(const Class &g, const Class & h) { return h - g;}
   static Class Inverse(const Class &g) { return -g;}
@@ -147,7 +147,7 @@ public:
   DirectProduct(const G& g, const H& h):std::pair<G,H>(g,h) {}
 
   // identity
-  static DirectProduct identity() { return DirectProduct(); }
+  static DirectProduct Identity() { return DirectProduct(); }
 
   DirectProduct operator*(const DirectProduct& other) const {
     return DirectProduct(traits<G>::Compose(this->first, other.first),
@@ -181,7 +181,7 @@ public:
   DirectSum(const G& g, const H& h):std::pair<G,H>(g,h) {}
 
   // identity
-  static DirectSum identity() { return DirectSum(); }
+  static DirectSum Identity() { return DirectSum(); }
 
   DirectSum operator+(const DirectSum& other) const {
     return DirectSum(g()+other.g(), h()+other.h());

gtsam/base/Lie.h

@@ -177,7 +177,7 @@ struct LieGroupTraits: GetDimensionImpl<Class, Class::dimension> {
   /// @name Group
   /// @{
   typedef multiplicative_group_tag group_flavor;
-  static Class Identity() { return Class::identity();}
+  static Class Identity() { return Class::Identity();}
   /// @}
 
   /// @name Manifold

gtsam/base/ProductLieGroup.h

@@ -48,7 +48,7 @@ public:
   /// @name Group
   /// @{
   typedef multiplicative_group_tag group_flavor;
-  static ProductLieGroup identity() {return ProductLieGroup();}
+  static ProductLieGroup Identity() {return ProductLieGroup();}
 
   ProductLieGroup operator*(const ProductLieGroup& other) const {
     return ProductLieGroup(traits<G>::Compose(this->first,other.first),

gtsam/base/Vector.h

@@ -60,6 +60,7 @@ GTSAM_MAKE_VECTOR_DEFS(9)
 GTSAM_MAKE_VECTOR_DEFS(10)
 GTSAM_MAKE_VECTOR_DEFS(11)
 GTSAM_MAKE_VECTOR_DEFS(12)
+GTSAM_MAKE_VECTOR_DEFS(15)
 
 typedef Eigen::VectorBlock<Vector> SubVector;
 typedef Eigen::VectorBlock<const Vector> ConstSubVector;

gtsam/base/VectorSpace.h

@@ -169,7 +169,7 @@ struct HasVectorSpacePrereqs {
   Vector v;
 
   BOOST_CONCEPT_USAGE(HasVectorSpacePrereqs) {
-    p = Class::identity();  // identity
+    p = Class::Identity();  // identity
     q = p + p;              // addition
     q = p - p;              // subtraction
     v = p.vector();         // conversion to vector
@@ -192,7 +192,7 @@ struct VectorSpaceTraits: VectorSpaceImpl<Class, Class::dimension> {
   /// @name Group
   /// @{
   typedef additive_group_tag group_flavor;
-  static Class Identity() { return Class::identity();}
+  static Class Identity() { return Class::Identity();}
   /// @}
 
   /// @name Manifold

gtsam/base/tests/testGroup.cpp

@@ -29,7 +29,7 @@ class Symmetric: private Eigen::PermutationMatrix<N> {
       Eigen::PermutationMatrix<N>(P) {
   }
 public:
-  static Symmetric identity() { return Symmetric(); }
+  static Symmetric Identity() { return Symmetric(); }
   Symmetric() {
     Eigen::PermutationMatrix<N>::setIdentity();
   }

gtsam/base/treeTraversal-inst.h

@@ -221,6 +221,6 @@ void PrintForest(const FOREST& forest, std::string str,
   PrintForestVisitorPre visitor(keyFormatter);
   DepthFirstForest(forest, str, visitor);
 }
-}
+}  // namespace treeTraversal
 
-}
+}  // namespace gtsam

gtsam/basis/ParameterMatrix.h

@@ -189,9 +189,9 @@ class ParameterMatrix {
    * NOTE: The size at compile time is unknown so this identity is zero
    * length and thus not valid.
    */
-  inline static ParameterMatrix identity() {
+  inline static ParameterMatrix Identity() {
     // throw std::runtime_error(
-    //     "ParameterMatrix::identity(): Don't use this function");
+    //     "ParameterMatrix::Identity(): Don't use this function");
     return ParameterMatrix(0);
   }
 

gtsam/basis/basis.i

@@ -137,7 +137,7 @@ class FitBasis {
   static gtsam::GaussianFactorGraph::shared_ptr LinearGraph(
       const std::map<double, double>& sequence,
       const gtsam::noiseModel::Base* model, size_t N);
-  This::Parameters parameters() const;
+  gtsam::This::Parameters parameters() const;
 };
 
 }  // namespace gtsam

gtsam/basis/tests/testParameterMatrix.cpp

@@ -133,7 +133,7 @@ TEST(ParameterMatrix, VectorSpace) {
   // vector
   EXPECT(assert_equal(Vector::Ones(M * N), params.vector()));
   // identity
-  EXPECT(assert_equal(ParameterMatrix<M>::identity(),
+  EXPECT(assert_equal(ParameterMatrix<M>::Identity(),
                       ParameterMatrix<M>(Matrix::Zero(M, 0))));
 }
 

gtsam/discrete/DiscreteKey.cpp

@@ -48,4 +48,25 @@ namespace gtsam {
     return keys & key2;
   }
 
+  void DiscreteKeys::print(const std::string& s,
+                           const KeyFormatter& keyFormatter) const {
+    for (auto&& dkey : *this) {
+      std::cout << DefaultKeyFormatter(dkey.first) << " " << dkey.second
+                << std::endl;
+    }
+  }
+
+  bool DiscreteKeys::equals(const DiscreteKeys& other, double tol) const {
+    if (this->size() != other.size()) {
+      return false;
+    }
+
+    for (size_t i = 0; i < this->size(); i++) {
+      if (this->at(i).first != other.at(i).first ||
+          this->at(i).second != other.at(i).second) {
+        return false;
+      }
+    }
+    return true;
+  }
 }

gtsam/discrete/DiscreteKey.h

@@ -21,6 +21,7 @@
 #include <gtsam/global_includes.h>
 #include <gtsam/inference/Key.h>
 
+#include <boost/serialization/vector.hpp>
 #include <map>
 #include <string>
 #include <vector>
@@ -69,8 +70,30 @@ namespace gtsam {
       push_back(key);
       return *this;
     }
+
+    /// Print the keys and cardinalities.
+    void print(const std::string& s = "",
+               const KeyFormatter& keyFormatter = DefaultKeyFormatter) const;
+
+    /// Check equality to another DiscreteKeys object.
+    bool equals(const DiscreteKeys& other, double tol = 0) const;
+
+    /** Serialization function */
+    friend class boost::serialization::access;
+    template <class ARCHIVE>
+    void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
+      ar& boost::serialization::make_nvp(
+          "DiscreteKeys",
+          boost::serialization::base_object<std::vector<DiscreteKey>>(*this));
+    }
+
   }; // DiscreteKeys
 
   /// Create a list from two keys
   GTSAM_EXPORT DiscreteKeys operator&(const DiscreteKey& key1, const DiscreteKey& key2);
-}
+
+  // traits
+  template <>
+  struct traits<DiscreteKeys> : public Testable<DiscreteKeys> {};
+
+  }  // namespace gtsam

gtsam/discrete/discrete.i

@@ -219,6 +219,16 @@ class DiscreteBayesTree {
 };
 
 #include <gtsam/discrete/DiscreteLookupDAG.h>
+
+class DiscreteLookupTable : gtsam::DiscreteConditional{
+  DiscreteLookupTable(size_t nFrontals, const gtsam::DiscreteKeys& keys,
+                      const gtsam::DecisionTreeFactor::ADT& potentials);
+  void print(
+    const std::string& s = "Discrete Lookup Table: ",
+    const gtsam::KeyFormatter& keyFormatter = gtsam::DefaultKeyFormatter) const;
+  size_t argmax(const gtsam::DiscreteValues& parentsValues) const;
+};
+
 class DiscreteLookupDAG {
   DiscreteLookupDAG();
   void push_back(const gtsam::DiscreteLookupTable* table);

gtsam/discrete/tests/testDiscreteFactor.cpp

@@ -16,14 +16,29 @@
  *  @author Duy-Nguyen Ta
  */
 
-#include <gtsam/base/Testable.h>
-#include <gtsam/discrete/DiscreteFactor.h>
 #include <CppUnitLite/TestHarness.h>
+#include <gtsam/base/Testable.h>
+#include <gtsam/base/serializationTestHelpers.h>
+#include <gtsam/discrete/DiscreteFactor.h>
+
 #include <boost/assign/std/map.hpp>
 using namespace boost::assign;
 
 using namespace std;
 using namespace gtsam;
+using namespace gtsam::serializationTestHelpers;
+
+/* ************************************************************************* */
+TEST(DisreteKeys, Serialization) {
+  DiscreteKeys keys;
+  keys& DiscreteKey(0, 2);
+  keys& DiscreteKey(1, 3);
+  keys& DiscreteKey(2, 4);
+
+  EXPECT(equalsObj<DiscreteKeys>(keys));
+  EXPECT(equalsXML<DiscreteKeys>(keys));
+  EXPECT(equalsBinary<DiscreteKeys>(keys));
+}
 
 /* ************************************************************************* */
 int main() {
@@ -31,4 +46,3 @@ int main() {
   return TestRegistry::runAllTests(tr);
 }
 /* ************************************************************************* */
-

gtsam/geometry/Cyclic.h

@@ -38,7 +38,7 @@ public:
   /// Default constructor yields identity
   Cyclic():i_(0) {
   }
-  static Cyclic identity() { return Cyclic();}
+  static Cyclic Identity() { return Cyclic();}
 
   /// Cast to size_t
   operator size_t() const {

gtsam/geometry/PinholeCamera.h

@@ -213,7 +213,7 @@ public:
   }
 
   /// for Canonical
-  static PinholeCamera identity() {
+  static PinholeCamera Identity() {
     return PinholeCamera(); // assumes that the default constructor is valid
   }
 

gtsam/geometry/PinholePose.h

@@ -412,7 +412,7 @@ public:
   }
 
   /// for Canonical
-  static PinholePose identity() {
+  static PinholePose Identity() {
     return PinholePose(); // assumes that the default constructor is valid
   }
 

gtsam/geometry/Pose2.h

@@ -119,7 +119,7 @@ public:
   /// @{
 
   /// identity for group operation
-  inline static Pose2 identity() { return Pose2(); }
+  inline static Pose2 Identity() { return Pose2(); }
 
   /// inverse
   GTSAM_EXPORT Pose2 inverse() const;

gtsam/geometry/Pose3.h

@@ -103,7 +103,7 @@ public:
   /// @{
 
   /// identity for group operation
-  static Pose3 identity() {
+  static Pose3 Identity() {
     return Pose3();
   }
 

gtsam/geometry/Rot2.h

@@ -107,8 +107,8 @@ namespace gtsam {
     /// @name Group
     /// @{
 
-    /** identity */
+    /** Identity */
-    inline static Rot2 identity() {  return Rot2(); }
+    inline static Rot2 Identity() {  return Rot2(); }
 
     /** The inverse rotation - negative angle */
     Rot2 inverse() const { return Rot2(c_, -s_);}

gtsam/geometry/Rot3.h

@@ -297,7 +297,7 @@ class GTSAM_EXPORT Rot3 : public LieGroup<Rot3, 3> {
     /// @{
 
     /// identity rotation for group operation
-    inline static Rot3 identity() {
+    inline static Rot3 Identity() {
       return Rot3();
     }
 

gtsam/geometry/SOn.h

@@ -178,13 +178,13 @@ class SO : public LieGroup<SO<N>, internal::DimensionSO(N)> {
 
   /// SO<N> identity for N >= 2
   template <int N_ = N, typename = IsFixed<N_>>
-  static SO identity() {
+  static SO Identity() {
     return SO();
   }
 
   /// SO<N> identity for N == Eigen::Dynamic
   template <int N_ = N, typename = IsDynamic<N_>>
-  static SO identity(size_t n = 0) {
+  static SO Identity(size_t n = 0) {
     return SO(n);
   }
 

gtsam/geometry/Similarity2.cpp

@@ -134,7 +134,7 @@ void Similarity2::print(const std::string& s) const {
             << std::endl;
 }
 
-Similarity2 Similarity2::identity() { return Similarity2(); }
+Similarity2 Similarity2::Identity() { return Similarity2(); }
 
 Similarity2 Similarity2::operator*(const Similarity2& S) const {
   return Similarity2(R_ * S.R_, ((1.0 / S.s_) * t_) + R_ * S.t_, s_ * S.s_);

gtsam/geometry/Similarity2.h

@@ -83,7 +83,7 @@ class GTSAM_EXPORT Similarity2 : public LieGroup<Similarity2, 4> {
   /// @{
 
   /// Return an identity transform
-  static Similarity2 identity();
+  static Similarity2 Identity();
 
   /// Composition
   Similarity2 operator*(const Similarity2& S) const;

gtsam/geometry/Similarity3.cpp

@@ -122,7 +122,7 @@ void Similarity3::print(const std::string& s) const {
   std::cout << "t: " << translation().transpose() << " s: " << scale() << std::endl;
 }
 
-Similarity3 Similarity3::identity() {
+Similarity3 Similarity3::Identity() {
   return Similarity3();
 }
 Similarity3 Similarity3::operator*(const Similarity3& S) const {

gtsam/geometry/Similarity3.h

@@ -84,7 +84,7 @@ class GTSAM_EXPORT Similarity3 : public LieGroup<Similarity3, 7> {
   /// @{
 
   /// Return an identity transform
-  static Similarity3 identity();
+  static Similarity3 Identity();
 
   /// Composition
   Similarity3 operator*(const Similarity3& S) const;

gtsam/geometry/SphericalCamera.h

@@ -88,7 +88,7 @@ class GTSAM_EXPORT SphericalCamera {
 
   /// Default constructor
   SphericalCamera()
-      : pose_(Pose3::identity()), emptyCal_(boost::make_shared<EmptyCal>()) {}
+      : pose_(Pose3()), emptyCal_(boost::make_shared<EmptyCal>()) {}
 
   /// Constructor with pose
   explicit SphericalCamera(const Pose3& pose)
@@ -198,9 +198,9 @@ class GTSAM_EXPORT SphericalCamera {
   }
 
   /// for Canonical
-  static SphericalCamera identity() {
+  static SphericalCamera Identity() {
     return SphericalCamera(
-        Pose3::identity());  // assumes that the default constructor is valid
+        Pose3::Identity());  // assumes that the default constructor is valid
   }
 
   /// for Linear Triangulation

gtsam/geometry/StereoPoint2.h

@@ -71,7 +71,7 @@ public:
   /// @{
 
   /// identity
-  inline static StereoPoint2 identity() {
+  inline static StereoPoint2 Identity() {
     return StereoPoint2();
   }
 

gtsam/geometry/geometry.i

@@ -16,7 +16,7 @@ class Point2 {
   bool equals(const gtsam::Point2& point, double tol) const;
 
   // Group
-  static gtsam::Point2 identity();
+  static gtsam::Point2 Identity();
 
   // Standard Interface
   double x() const;
@@ -73,7 +73,7 @@ class StereoPoint2 {
   bool equals(const gtsam::StereoPoint2& point, double tol) const;
 
   // Group
-  static gtsam::StereoPoint2 identity();
+  static gtsam::StereoPoint2 Identity();
   gtsam::StereoPoint2 inverse() const;
   gtsam::StereoPoint2 compose(const gtsam::StereoPoint2& p2) const;
   gtsam::StereoPoint2 between(const gtsam::StereoPoint2& p2) const;
@@ -115,7 +115,7 @@ class Point3 {
   bool equals(const gtsam::Point3& p, double tol) const;
 
   // Group
-  static gtsam::Point3 identity();
+  static gtsam::Point3 Identity();
 
   // Standard Interface
   Vector vector() const;
@@ -149,7 +149,7 @@ class Rot2 {
   bool equals(const gtsam::Rot2& rot, double tol) const;
 
   // Group
-  static gtsam::Rot2 identity();
+  static gtsam::Rot2 Identity();
   gtsam::Rot2 inverse();
   gtsam::Rot2 compose(const gtsam::Rot2& p2) const;
   gtsam::Rot2 between(const gtsam::Rot2& p2) const;
@@ -198,7 +198,7 @@ class SO3 {
   bool equals(const gtsam::SO3& other, double tol) const;
 
   // Group
-  static gtsam::SO3 identity();
+  static gtsam::SO3 Identity();
   gtsam::SO3 inverse() const;
   gtsam::SO3 between(const gtsam::SO3& R) const;
   gtsam::SO3 compose(const gtsam::SO3& R) const;
@@ -228,7 +228,7 @@ class SO4 {
   bool equals(const gtsam::SO4& other, double tol) const;
 
   // Group
-  static gtsam::SO4 identity();
+  static gtsam::SO4 Identity();
   gtsam::SO4 inverse() const;
   gtsam::SO4 between(const gtsam::SO4& Q) const;
   gtsam::SO4 compose(const gtsam::SO4& Q) const;
@@ -258,7 +258,7 @@ class SOn {
   bool equals(const gtsam::SOn& other, double tol) const;
 
   // Group
-  static gtsam::SOn identity();
+  static gtsam::SOn Identity();
   gtsam::SOn inverse() const;
   gtsam::SOn between(const gtsam::SOn& Q) const;
   gtsam::SOn compose(const gtsam::SOn& Q) const;
@@ -322,7 +322,7 @@ class Rot3 {
   bool equals(const gtsam::Rot3& rot, double tol) const;
 
   // Group
-  static gtsam::Rot3 identity();
+  static gtsam::Rot3 Identity();
   gtsam::Rot3 inverse() const;
   gtsam::Rot3 compose(const gtsam::Rot3& p2) const;
   gtsam::Rot3 between(const gtsam::Rot3& p2) const;
@@ -380,7 +380,7 @@ class Pose2 {
   bool equals(const gtsam::Pose2& pose, double tol) const;
 
   // Group
-  static gtsam::Pose2 identity();
+  static gtsam::Pose2 Identity();
   gtsam::Pose2 inverse() const;
   gtsam::Pose2 compose(const gtsam::Pose2& p2) const;
   gtsam::Pose2 between(const gtsam::Pose2& p2) const;
@@ -444,7 +444,7 @@ class Pose3 {
   bool equals(const gtsam::Pose3& pose, double tol) const;
 
   // Group
-  static gtsam::Pose3 identity();
+  static gtsam::Pose3 Identity();
   gtsam::Pose3 inverse() const;
   gtsam::Pose3 inverse(Eigen::Ref<Eigen::MatrixXd> H) const;
   gtsam::Pose3 compose(const gtsam::Pose3& pose) const;
@@ -1126,10 +1126,10 @@ class TriangulationResult {
   Status status;
   TriangulationResult(const gtsam::Point3& p);
   const gtsam::Point3& get() const;
-  static TriangulationResult Degenerate();
+  static gtsam::TriangulationResult Degenerate();
-  static TriangulationResult Outlier();
+  static gtsam::TriangulationResult Outlier();
-  static TriangulationResult FarPoint();
+  static gtsam::TriangulationResult FarPoint();
-  static TriangulationResult BehindCamera();
+  static gtsam::TriangulationResult BehindCamera();
   bool valid() const;
   bool degenerate() const;
   bool outlier() const;

gtsam/geometry/tests/testPose2.cpp

@@ -902,7 +902,7 @@ TEST(Pose2 , TransformCovariance3) {
 
 /* ************************************************************************* */
 TEST(Pose2, Print) {
-  Pose2 pose(Rot2::identity(), Point2(1, 2));
+  Pose2 pose(Rot2::Identity(), Point2(1, 2));
 
   // Generate the expected output
   string s = "Planar Pose";

gtsam/geometry/tests/testPose3.cpp

@@ -1133,7 +1133,7 @@ Pose3 testing_interpolate(const Pose3& t1, const Pose3& t2, double gamma) { retu
 
 TEST(Pose3, interpolateJacobians) {
   {
-    Pose3 X = Pose3::identity();
+    Pose3 X = Pose3::Identity();
     Pose3 Y(Rot3::Rz(M_PI_2), Point3(1, 0, 0));
     double t = 0.5;
     Pose3 expectedPoseInterp(Rot3::Rz(M_PI_4), Point3(0.5, -0.207107, 0)); // note: different from test above: this is full Pose3 interpolation
@@ -1147,10 +1147,10 @@ TEST(Pose3, interpolateJacobians) {
     EXPECT(assert_equal(expectedJacobianY,actualJacobianY,1e-6));
   }
   {
-    Pose3 X = Pose3::identity();
+    Pose3 X = Pose3::Identity();
-    Pose3 Y(Rot3::identity(), Point3(1, 0, 0));
+    Pose3 Y(Rot3::Identity(), Point3(1, 0, 0));
     double t = 0.3;
-    Pose3 expectedPoseInterp(Rot3::identity(), Point3(0.3, 0, 0));
+    Pose3 expectedPoseInterp(Rot3::Identity(), Point3(0.3, 0, 0));
     Matrix actualJacobianX, actualJacobianY;
     EXPECT(assert_equal(expectedPoseInterp, interpolate(X, Y, t, actualJacobianX, actualJacobianY), 1e-5));
 
@@ -1161,7 +1161,7 @@ TEST(Pose3, interpolateJacobians) {
     EXPECT(assert_equal(expectedJacobianY,actualJacobianY,1e-6));
   }
   {
-    Pose3 X = Pose3::identity();
+    Pose3 X = Pose3::Identity();
     Pose3 Y(Rot3::Rz(M_PI_2), Point3(0, 0, 0));
     double t = 0.5;
     Pose3 expectedPoseInterp(Rot3::Rz(M_PI_4), Point3(0, 0, 0));
@@ -1204,7 +1204,7 @@ TEST(Pose3, Create) {
 
 /* ************************************************************************* */
 TEST(Pose3, Print) {
-  Pose3 pose(Rot3::identity(), Point3(1, 2, 3));
+  Pose3 pose(Rot3::Identity(), Point3(1, 2, 3));
 
   // Generate the expected output
   std::string expected = "R: [\n\t1, 0, 0;\n\t0, 1, 0;\n\t0, 0, 1\n]\nt: 1 2 3\n";

gtsam/geometry/tests/testSimilarity2.cpp

@@ -33,8 +33,6 @@ static const Point2 P(0.2, 0.7);
 static const Rot2 R = Rot2::fromAngle(0.3);
 static const double s = 4;
 
-const double degree = M_PI / 180;
-
 //******************************************************************************
 TEST(Similarity2, Concepts) {
   BOOST_CONCEPT_ASSERT((IsGroup<Similarity2>));

gtsam/geometry/tests/testSimilarity3.cpp

@@ -203,11 +203,11 @@ TEST(Similarity3, ExpLogMap) {
 
   Vector7 zeros;
   zeros << 0, 0, 0, 0, 0, 0, 0;
-  Vector7 logIdentity = Similarity3::Logmap(Similarity3::identity());
+  Vector7 logIdentity = Similarity3::Logmap(Similarity3::Identity());
   EXPECT(assert_equal(zeros, logIdentity));
 
   Similarity3 expZero = Similarity3::Expmap(zeros);
-  Similarity3 ident = Similarity3::identity();
+  Similarity3 ident = Similarity3::Identity();
   EXPECT(assert_equal(expZero, ident));
 
   // Compare to matrix exponential, using expm in Lie.h
@@ -391,7 +391,7 @@ TEST(Similarity3, Optimization) {
   NonlinearFactorGraph graph;
   graph.addPrior(key, prior, model);
 
-  // Create initial estimate with identity transform
+  // Create initial estimate with Identity transform
   Values initial;
   initial.insert<Similarity3>(key, Similarity3());
 

gtsam/gtsam.i

@@ -66,7 +66,7 @@ class KeySet {
   void serialize() const;
 };
 
-// Actually a vector<Key>
+// Actually a vector<Key>, needed for Matlab
 class KeyVector {
   KeyVector();
   KeyVector(const gtsam::KeyVector& other);

gtsam/hybrid/GaussianMixture.cpp

@@ -119,11 +119,36 @@ void GaussianMixture::print(const std::string &s,
       "", [&](Key k) { return formatter(k); },
       [&](const GaussianConditional::shared_ptr &gf) -> std::string {
         RedirectCout rd;
-        if (!gf->empty())
+        if (gf && !gf->empty())
           gf->print("", formatter);
         else
           return {"nullptr"};
         return rd.str();
       });
 }
+
+/* *******************************************************************************/
+void GaussianMixture::prune(const DecisionTreeFactor &decisionTree) {
+  // Functional which loops over all assignments and create a set of
+  // GaussianConditionals
+  auto pruner = [&decisionTree](
+                    const Assignment<Key> &choices,
+                    const GaussianConditional::shared_ptr &conditional)
+      -> GaussianConditional::shared_ptr {
+    // typecast so we can use this to get probability value
+    DiscreteValues values(choices);
+
+    if (decisionTree(values) == 0.0) {
+      // empty aka null pointer
+      boost::shared_ptr<GaussianConditional> null;
+      return null;
+    } else {
+      return conditional;
+    }
+  };
+
+  auto pruned_conditionals = conditionals_.apply(pruner);
+  conditionals_.root_ = pruned_conditionals.root_;
+}
+
 }  // namespace gtsam

gtsam/hybrid/GaussianMixture.h

@@ -21,6 +21,7 @@
 
 #include <gtsam/discrete/DecisionTree-inl.h>
 #include <gtsam/discrete/DecisionTree.h>
+#include <gtsam/discrete/DecisionTreeFactor.h>
 #include <gtsam/discrete/DiscreteKey.h>
 #include <gtsam/hybrid/HybridFactor.h>
 #include <gtsam/inference/Conditional.h>
@@ -30,11 +31,14 @@ namespace gtsam {
 
 /**
  * @brief A conditional of gaussian mixtures indexed by discrete variables, as
- * part of a Bayes Network.
+ * part of a Bayes Network. This is the result of the elimination of a
+ * continuous variable in a hybrid scheme, such that the remaining variables are
+ * discrete+continuous.
  *
- * Represents the conditional density P(X | M, Z) where X is a continuous random
+ * Represents the conditional density P(X | M, Z) where X is the set of
- * variable, M is the selection of discrete variables corresponding to a subset
+ * continuous random variables, M is the selection of discrete variables
- * of the Gaussian variables and Z is parent of this node
+ * corresponding to a subset of the Gaussian variables and Z is parent of this
+ * node .
  *
  * The probability P(x|y,z,...) is proportional to
  * \f$ \sum_i k_i \exp - \frac{1}{2} |R_i x - (d_i - S_i y - T_i z - ...)|^2 \f$
@@ -118,7 +122,7 @@ class GTSAM_EXPORT GaussianMixture
   /// Test equality with base HybridFactor
   bool equals(const HybridFactor &lf, double tol = 1e-9) const override;
 
-  /* print utility */
+  /// Print utility
   void print(
       const std::string &s = "GaussianMixture\n",
       const KeyFormatter &formatter = DefaultKeyFormatter) const override;
@@ -128,6 +132,15 @@ class GTSAM_EXPORT GaussianMixture
   /// Getter for the underlying Conditionals DecisionTree
   const Conditionals &conditionals();
 
+  /**
+   * @brief Prune the decision tree of Gaussian factors as per the discrete
+   * `decisionTree`.
+   *
+   * @param decisionTree A pruned decision tree of discrete keys where the
+   * leaves are probabilities.
+   */
+  void prune(const DecisionTreeFactor &decisionTree);
+
   /**
    * @brief Merge the Gaussian Factor Graphs in `this` and `sum` while
    * maintaining the decision tree structure.

gtsam/hybrid/GaussianMixtureFactor.cpp

@@ -51,7 +51,7 @@ GaussianMixtureFactor GaussianMixtureFactor::FromFactors(
 void GaussianMixtureFactor::print(const std::string &s,
                                   const KeyFormatter &formatter) const {
   HybridFactor::print(s, formatter);
-  std::cout << "]{\n";
+  std::cout << "{\n";
   factors_.print(
       "", [&](Key k) { return formatter(k); },
       [&](const GaussianFactor::shared_ptr &gf) -> std::string {

gtsam/hybrid/GaussianMixtureFactor.h

@@ -22,7 +22,7 @@
 
 #include <gtsam/discrete/DecisionTree.h>
 #include <gtsam/discrete/DiscreteKey.h>
-#include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/hybrid/HybridGaussianFactor.h>
 #include <gtsam/linear/GaussianFactor.h>
 
 namespace gtsam {
@@ -108,7 +108,7 @@ class GTSAM_EXPORT GaussianMixtureFactor : public HybridFactor {
   bool equals(const HybridFactor &lf, double tol = 1e-9) const override;
 
   void print(
-      const std::string &s = "HybridFactor\n",
+      const std::string &s = "GaussianMixtureFactor\n",
       const KeyFormatter &formatter = DefaultKeyFormatter) const override;
   /// @}
 

gtsam/hybrid/HybridBayesNet.cpp

@@ -10,7 +10,166 @@
  * @file   HybridBayesNet.cpp
  * @brief  A bayes net of Gaussian Conditionals indexed by discrete keys.
  * @author Fan Jiang
+ * @author Varun Agrawal
+ * @author Shangjie Xue
  * @date   January 2022
  */
 
+#include <gtsam/discrete/DiscreteBayesNet.h>
+#include <gtsam/discrete/DiscreteFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesNet.h>
+#include <gtsam/hybrid/HybridValues.h>
+
+namespace gtsam {
+
+/* ************************************************************************* */
+/// Return the DiscreteKey vector as a set.
+static std::set<DiscreteKey> DiscreteKeysAsSet(const DiscreteKeys &dkeys) {
+  std::set<DiscreteKey> s;
+  s.insert(dkeys.begin(), dkeys.end());
+  return s;
+}
+
+/* ************************************************************************* */
+HybridBayesNet HybridBayesNet::prune(
+    const DecisionTreeFactor::shared_ptr &discreteFactor) const {
+  /* To Prune, we visitWith every leaf in the GaussianMixture.
+   * For each leaf, using the assignment we can check the discrete decision tree
+   * for 0.0 probability, then just set the leaf to a nullptr.
+   *
+   * We can later check the GaussianMixture for just nullptrs.
+   */
+
+  HybridBayesNet prunedBayesNetFragment;
+
+  // Functional which loops over all assignments and create a set of
+  // GaussianConditionals
+  auto pruner = [&](const Assignment<Key> &choices,
+                    const GaussianConditional::shared_ptr &conditional)
+      -> GaussianConditional::shared_ptr {
+    // typecast so we can use this to get probability value
+    DiscreteValues values(choices);
+
+    if ((*discreteFactor)(values) == 0.0) {
+      // empty aka null pointer
+      boost::shared_ptr<GaussianConditional> null;
+      return null;
+    } else {
+      return conditional;
+    }
+  };
+
+  // Go through all the conditionals in the
+  // Bayes Net and prune them as per discreteFactor.
+  for (size_t i = 0; i < this->size(); i++) {
+    HybridConditional::shared_ptr conditional = this->at(i);
+
+    GaussianMixture::shared_ptr gaussianMixture =
+        boost::dynamic_pointer_cast<GaussianMixture>(conditional->inner());
+
+    if (gaussianMixture) {
+      // We may have mixtures with less discrete keys than discreteFactor so we
+      // skip those since the label assignment does not exist.
+      auto gmKeySet = DiscreteKeysAsSet(gaussianMixture->discreteKeys());
+      auto dfKeySet = DiscreteKeysAsSet(discreteFactor->discreteKeys());
+      if (gmKeySet != dfKeySet) {
+        // Add the gaussianMixture which doesn't have to be pruned.
+        prunedBayesNetFragment.push_back(
+            boost::make_shared<HybridConditional>(gaussianMixture));
+        continue;
+      }
+
+      // Run the pruning to get a new, pruned tree
+      GaussianMixture::Conditionals prunedTree =
+          gaussianMixture->conditionals().apply(pruner);
+
+      DiscreteKeys discreteKeys = gaussianMixture->discreteKeys();
+      // reverse keys to get a natural ordering
+      std::reverse(discreteKeys.begin(), discreteKeys.end());
+
+      // Convert from boost::iterator_range to KeyVector
+      // so we can pass it to constructor.
+      KeyVector frontals(gaussianMixture->frontals().begin(),
+                         gaussianMixture->frontals().end()),
+          parents(gaussianMixture->parents().begin(),
+                  gaussianMixture->parents().end());
+
+      // Create the new gaussian mixture and add it to the bayes net.
+      auto prunedGaussianMixture = boost::make_shared<GaussianMixture>(
+          frontals, parents, discreteKeys, prunedTree);
+
+      // Type-erase and add to the pruned Bayes Net fragment.
+      prunedBayesNetFragment.push_back(
+          boost::make_shared<HybridConditional>(prunedGaussianMixture));
+
+    } else {
+      // Add the non-GaussianMixture conditional
+      prunedBayesNetFragment.push_back(conditional);
+    }
+  }
+
+  return prunedBayesNetFragment;
+}
+
+/* ************************************************************************* */
+GaussianMixture::shared_ptr HybridBayesNet::atMixture(size_t i) const {
+  return factors_.at(i)->asMixture();
+}
+
+/* ************************************************************************* */
+GaussianConditional::shared_ptr HybridBayesNet::atGaussian(size_t i) const {
+  return factors_.at(i)->asGaussian();
+}
+
+/* ************************************************************************* */
+DiscreteConditional::shared_ptr HybridBayesNet::atDiscrete(size_t i) const {
+  return factors_.at(i)->asDiscreteConditional();
+}
+
+/* ************************************************************************* */
+GaussianBayesNet HybridBayesNet::choose(
+    const DiscreteValues &assignment) const {
+  GaussianBayesNet gbn;
+  for (size_t idx = 0; idx < size(); idx++) {
+    if (factors_.at(idx)->isHybrid()) {
+      // If factor is hybrid, select based on assignment.
+      GaussianMixture gm = *this->atMixture(idx);
+      gbn.push_back(gm(assignment));
+
+    } else if (factors_.at(idx)->isContinuous()) {
+      // If continuous only, add gaussian conditional.
+      gbn.push_back((this->atGaussian(idx)));
+
+    } else if (factors_.at(idx)->isDiscrete()) {
+      // If factor at `idx` is discrete-only, we simply continue.
+      continue;
+    }
+  }
+
+  return gbn;
+}
+
+/* *******************************************************************************/
+HybridValues HybridBayesNet::optimize() const {
+  // Solve for the MPE
+  DiscreteBayesNet discrete_bn;
+  for (auto &conditional : factors_) {
+    if (conditional->isDiscrete()) {
+      discrete_bn.push_back(conditional->asDiscreteConditional());
+    }
+  }
+
+  DiscreteValues mpe = DiscreteFactorGraph(discrete_bn).optimize();
+
+  // Given the MPE, compute the optimal continuous values.
+  GaussianBayesNet gbn = this->choose(mpe);
+  return HybridValues(mpe, gbn.optimize());
+}
+
+/* *******************************************************************************/
+VectorValues HybridBayesNet::optimize(const DiscreteValues &assignment) const {
+  GaussianBayesNet gbn = this->choose(assignment);
+  return gbn.optimize();
+}
+
+}  // namespace gtsam

gtsam/hybrid/HybridBayesNet.h

@@ -17,8 +17,12 @@
 
 #pragma once
 
+#include <gtsam/discrete/DecisionTreeFactor.h>
+#include <gtsam/global_includes.h>
 #include <gtsam/hybrid/HybridConditional.h>
+#include <gtsam/hybrid/HybridValues.h>
 #include <gtsam/inference/BayesNet.h>
+#include <gtsam/linear/GaussianBayesNet.h>
 
 namespace gtsam {
 
@@ -34,8 +38,94 @@ class GTSAM_EXPORT HybridBayesNet : public BayesNet<HybridConditional> {
   using shared_ptr = boost::shared_ptr<HybridBayesNet>;
   using sharedConditional = boost::shared_ptr<ConditionalType>;
 
+  /// @name Standard Constructors
+  /// @{
+
   /** Construct empty bayes net */
   HybridBayesNet() = default;
+
+  /// @}
+  /// @name Testable
+  /// @{
+
+  /** Check equality */
+  bool equals(const This &bn, double tol = 1e-9) const {
+    return Base::equals(bn, tol);
+  }
+
+  /// print graph
+  void print(
+      const std::string &s = "",
+      const KeyFormatter &formatter = DefaultKeyFormatter) const override {
+    Base::print(s, formatter);
+  }
+
+  /// @}
+  /// @name Standard Interface
+  /// @{
+
+  /// Add HybridConditional to Bayes Net
+  using Base::add;
+
+  /// Add a discrete conditional to the Bayes Net.
+  void add(const DiscreteKey &key, const std::string &table) {
+    push_back(
+        HybridConditional(boost::make_shared<DiscreteConditional>(key, table)));
+  }
+
+  /// Get a specific Gaussian mixture by index `i`.
+  GaussianMixture::shared_ptr atMixture(size_t i) const;
+
+  /// Get a specific Gaussian conditional by index `i`.
+  GaussianConditional::shared_ptr atGaussian(size_t i) const;
+
+  /// Get a specific discrete conditional by index `i`.
+  DiscreteConditional::shared_ptr atDiscrete(size_t i) const;
+
+  /**
+   * @brief Get the Gaussian Bayes Net which corresponds to a specific discrete
+   * value assignment.
+   *
+   * @param assignment The discrete value assignment for the discrete keys.
+   * @return GaussianBayesNet
+   */
+  GaussianBayesNet choose(const DiscreteValues &assignment) const;
+
+  /**
+   * @brief Solve the HybridBayesNet by first computing the MPE of all the
+   * discrete variables and then optimizing the continuous variables based on
+   * the MPE assignment.
+   *
+   * @return HybridValues
+   */
+  HybridValues optimize() const;
+
+  /**
+   * @brief Given the discrete assignment, return the optimized estimate for the
+   * selected Gaussian BayesNet.
+   *
+   * @param assignment An assignment of discrete values.
+   * @return Values
+   */
+  VectorValues optimize(const DiscreteValues &assignment) const;
+
+  /// Prune the Hybrid Bayes Net given the discrete decision tree.
+  HybridBayesNet prune(
+      const DecisionTreeFactor::shared_ptr &discreteFactor) const;
+
+  /// @}
+
+ private:
+  /** Serialization function */
+  friend class boost::serialization::access;
+  template <class ARCHIVE>
+  void serialize(ARCHIVE &ar, const unsigned int /*version*/) {
+    ar &BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
+  }
 };
 
+/// traits
+template <>
+struct traits<HybridBayesNet> : public Testable<HybridBayesNet> {};
+
 }  // namespace gtsam

gtsam/hybrid/HybridBayesTree.cpp

@@ -18,10 +18,13 @@
  */
 
 #include <gtsam/base/treeTraversal-inst.h>
+#include <gtsam/discrete/DiscreteBayesNet.h>
+#include <gtsam/discrete/DiscreteFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesNet.h>
 #include <gtsam/hybrid/HybridBayesTree.h>
 #include <gtsam/inference/BayesTree-inst.h>
 #include <gtsam/inference/BayesTreeCliqueBase-inst.h>
+#include <gtsam/linear/GaussianJunctionTree.h>
 
 namespace gtsam {
 
@@ -35,4 +38,110 @@ bool HybridBayesTree::equals(const This& other, double tol) const {
   return Base::equals(other, tol);
 }
 
+/* ************************************************************************* */
+HybridValues HybridBayesTree::optimize() const {
+  DiscreteBayesNet dbn;
+  DiscreteValues mpe;
+
+  auto root = roots_.at(0);
+  // Access the clique and get the underlying hybrid conditional
+  HybridConditional::shared_ptr root_conditional = root->conditional();
+
+  // The root should be discrete only, we compute the MPE
+  if (root_conditional->isDiscrete()) {
+    dbn.push_back(root_conditional->asDiscreteConditional());
+    mpe = DiscreteFactorGraph(dbn).optimize();
+  } else {
+    throw std::runtime_error(
+        "HybridBayesTree root is not discrete-only. Please check elimination "
+        "ordering or use continuous factor graph.");
+  }
+
+  VectorValues values = optimize(mpe);
+  return HybridValues(mpe, values);
+}
+
+/* ************************************************************************* */
+/**
+ * @brief Helper class for Depth First Forest traversal on the HybridBayesTree.
+ *
+ * When traversing the tree, the pre-order visitor will receive an instance of
+ * this class with the parent clique data.
+ */
+struct HybridAssignmentData {
+  const DiscreteValues assignment_;
+  GaussianBayesTree::sharedNode parentClique_;
+  // The gaussian bayes tree that will be recursively created.
+  GaussianBayesTree* gaussianbayesTree_;
+
+  /**
+   * @brief Construct a new Hybrid Assignment Data object.
+   *
+   * @param assignment The MPE assignment for the optimal Gaussian cliques.
+   * @param parentClique The clique from the parent node of the current node.
+   * @param gbt The Gaussian Bayes Tree being generated during tree traversal.
+   */
+  HybridAssignmentData(const DiscreteValues& assignment,
+                       const GaussianBayesTree::sharedNode& parentClique,
+                       GaussianBayesTree* gbt)
+      : assignment_(assignment),
+        parentClique_(parentClique),
+        gaussianbayesTree_(gbt) {}
+
+  /**
+   * @brief A function used during tree traversal that operators on each node
+   * before visiting the node's children.
+   *
+   * @param node The current node being visited.
+   * @param parentData The HybridAssignmentData from the parent node.
+   * @return HybridAssignmentData
+   */
+  static HybridAssignmentData AssignmentPreOrderVisitor(
+      const HybridBayesTree::sharedNode& node,
+      HybridAssignmentData& parentData) {
+    // Extract the gaussian conditional from the Hybrid clique
+    HybridConditional::shared_ptr hybrid_conditional = node->conditional();
+    GaussianConditional::shared_ptr conditional;
+    if (hybrid_conditional->isHybrid()) {
+      conditional = (*hybrid_conditional->asMixture())(parentData.assignment_);
+    } else if (hybrid_conditional->isContinuous()) {
+      conditional = hybrid_conditional->asGaussian();
+    } else {
+      // Discrete only conditional, so we set to empty gaussian conditional
+      conditional = boost::make_shared<GaussianConditional>();
+    }
+
+    // Create the GaussianClique for the current node
+    auto clique = boost::make_shared<GaussianBayesTree::Node>(conditional);
+    // Add the current clique to the GaussianBayesTree.
+    parentData.gaussianbayesTree_->addClique(clique, parentData.parentClique_);
+
+    // Create new HybridAssignmentData where the current node is the parent
+    // This will be passed down to the children nodes
+    HybridAssignmentData data(parentData.assignment_, clique,
+                              parentData.gaussianbayesTree_);
+    return data;
+  }
+};
+
+/* *************************************************************************
+ */
+VectorValues HybridBayesTree::optimize(const DiscreteValues& assignment) const {
+  GaussianBayesTree gbt;
+  HybridAssignmentData rootData(assignment, 0, &gbt);
+  {
+    treeTraversal::no_op visitorPost;
+    // Limits OpenMP threads since we're mixing TBB and OpenMP
+    TbbOpenMPMixedScope threadLimiter;
+    treeTraversal::DepthFirstForestParallel(
+        *this, rootData, HybridAssignmentData::AssignmentPreOrderVisitor,
+        visitorPost);
+  }
+
+  VectorValues result = gbt.optimize();
+
+  // Return the optimized bayes net result.
+  return result;
+}
+
 }  // namespace gtsam

gtsam/hybrid/HybridBayesTree.h

@@ -70,13 +70,46 @@ class GTSAM_EXPORT HybridBayesTree : public BayesTree<HybridBayesTreeClique> {
   /** Check equality */
   bool equals(const This& other, double tol = 1e-9) const;
 
+  /**
+   * @brief Optimize the hybrid Bayes tree by computing the MPE for the current
+   * set of discrete variables and using it to compute the best continuous
+   * update delta.
+   *
+   * @return HybridValues
+   */
+  HybridValues optimize() const;
+
+  /**
+   * @brief Recursively optimize the BayesTree to produce a vector solution.
+   *
+   * @param assignment The discrete values assignment to select the Gaussian
+   * mixtures.
+   * @return VectorValues
+   */
+  VectorValues optimize(const DiscreteValues& assignment) const;
+
   /// @}
+
+ private:
+  /** Serialization function */
+  friend class boost::serialization::access;
+  template <class ARCHIVE>
+  void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
+    ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
+  }
 };
 
+/// traits
+template <>
+struct traits<HybridBayesTree> : public Testable<HybridBayesTree> {};
+
 /**
  * @brief Class for Hybrid Bayes tree orphan subtrees.
  *
- * This does special stuff for the hybrid case
+ * This object stores parent keys in our base type factor so that
+ * eliminating those parent keys will pull this subtree into the
+ * elimination.
+ * This does special stuff for the hybrid case.
  *
  * @tparam CLIQUE
  */

gtsam/hybrid/HybridConditional.h

@@ -69,7 +69,7 @@ class GTSAM_EXPORT HybridConditional
       BaseConditional;  ///< Typedef to our conditional base class
 
  protected:
-  // Type-erased pointer to the inner type
+  /// Type-erased pointer to the inner type
   boost::shared_ptr<Factor> inner_;
 
  public:
@@ -127,8 +127,7 @@ class GTSAM_EXPORT HybridConditional
    * @param gaussianMixture Gaussian Mixture Conditional used to create the
    * HybridConditional.
    */
-  HybridConditional(
+  HybridConditional(boost::shared_ptr<GaussianMixture> gaussianMixture);
-      boost::shared_ptr<GaussianMixture> gaussianMixture);
 
   /**
    * @brief Return HybridConditional as a GaussianMixture
@@ -140,6 +139,17 @@ class GTSAM_EXPORT HybridConditional
     return boost::static_pointer_cast<GaussianMixture>(inner_);
   }
 
+  /**
+   * @brief Return HybridConditional as a GaussianConditional
+   *
+   * @return GaussianConditional::shared_ptr
+   */
+  GaussianConditional::shared_ptr asGaussian() {
+    if (!isContinuous())
+      throw std::invalid_argument("Not a continuous conditional");
+    return boost::static_pointer_cast<GaussianConditional>(inner_);
+  }
+
   /**
    * @brief Return conditional as a DiscreteConditional
    *
@@ -168,10 +178,19 @@ class GTSAM_EXPORT HybridConditional
   /// Get the type-erased pointer to the inner type
   boost::shared_ptr<Factor> inner() { return inner_; }
 
-};  // DiscreteConditional
+ private:
+  /** Serialization function */
+  friend class boost::serialization::access;
+  template <class Archive>
+  void serialize(Archive& ar, const unsigned int /*version*/) {
+    ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(BaseFactor);
+    ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(BaseConditional);
+  }
+
+};  // HybridConditional
 
 // traits
 template <>
-struct traits<HybridConditional> : public Testable<DiscreteConditional> {};
+struct traits<HybridConditional> : public Testable<HybridConditional> {};
 
 }  // namespace gtsam

gtsam/hybrid/HybridFactor.cpp

@@ -52,7 +52,6 @@ DiscreteKeys CollectDiscreteKeys(const DiscreteKeys &key1,
 HybridFactor::HybridFactor(const KeyVector &keys)
     : Base(keys),
       isContinuous_(true),
-      nrContinuous_(keys.size()),
       continuousKeys_(keys) {}
 
 /* ************************************************************************ */
@@ -62,7 +61,6 @@ HybridFactor::HybridFactor(const KeyVector &continuousKeys,
       isDiscrete_((continuousKeys.size() == 0) && (discreteKeys.size() != 0)),
       isContinuous_((continuousKeys.size() != 0) && (discreteKeys.size() == 0)),
       isHybrid_((continuousKeys.size() != 0) && (discreteKeys.size() != 0)),
-      nrContinuous_(continuousKeys.size()),
       discreteKeys_(discreteKeys),
       continuousKeys_(continuousKeys) {}
 
@@ -78,7 +76,8 @@ bool HybridFactor::equals(const HybridFactor &lf, double tol) const {
   const This *e = dynamic_cast<const This *>(&lf);
   return e != nullptr && Base::equals(*e, tol) &&
          isDiscrete_ == e->isDiscrete_ && isContinuous_ == e->isContinuous_ &&
-         isHybrid_ == e->isHybrid_ && nrContinuous_ == e->nrContinuous_;
+         isHybrid_ == e->isHybrid_ && continuousKeys_ == e->continuousKeys_ &&
+         discreteKeys_ == e->discreteKeys_;
 }
 
 /* ************************************************************************ */
@@ -88,17 +87,23 @@ void HybridFactor::print(const std::string &s,
   if (isContinuous_) std::cout << "Continuous ";
   if (isDiscrete_) std::cout << "Discrete ";
   if (isHybrid_) std::cout << "Hybrid ";
-  for (size_t c=0; c<continuousKeys_.size(); c++) {
+  std::cout << "[";
+  for (size_t c = 0; c < continuousKeys_.size(); c++) {
     std::cout << formatter(continuousKeys_.at(c));
     if (c < continuousKeys_.size() - 1) {
       std::cout << " ";
     } else {
-      std::cout << "; ";
+      std::cout << (discreteKeys_.size() > 0 ? "; " : "");
     }
   }
-  for(auto && discreteKey: discreteKeys_) {
+  for (size_t d = 0; d < discreteKeys_.size(); d++) {
-    std::cout << formatter(discreteKey.first) << " ";
+    std::cout << formatter(discreteKeys_.at(d).first);
+    if (d < discreteKeys_.size() - 1) {
+      std::cout << " ";
+    }
+    
   }
+  std::cout << "]";
 }
 
 }  // namespace gtsam

gtsam/hybrid/HybridFactor.h

@@ -47,11 +47,9 @@ class GTSAM_EXPORT HybridFactor : public Factor {
   bool isContinuous_ = false;
   bool isHybrid_ = false;
 
-  size_t nrContinuous_ = 0;
-
  protected:
+  // Set of DiscreteKeys for this factor.
   DiscreteKeys discreteKeys_;
-
   /// Record continuous keys for book-keeping
   KeyVector continuousKeys_;
 
@@ -120,12 +118,28 @@ class GTSAM_EXPORT HybridFactor : public Factor {
   bool isHybrid() const { return isHybrid_; }
 
   /// Return the number of continuous variables in this factor.
-  size_t nrContinuous() const { return nrContinuous_; }
+  size_t nrContinuous() const { return continuousKeys_.size(); }
 
-  /// Return vector of discrete keys.
+  /// Return the discrete keys for this factor.
-  DiscreteKeys discreteKeys() const { return discreteKeys_; }
+  const DiscreteKeys &discreteKeys() const { return discreteKeys_; }
+
+  /// Return only the continuous keys for this factor.
+  const KeyVector &continuousKeys() const { return continuousKeys_; }
 
   /// @}
+
+ private:
+  /** Serialization function */
+  friend class boost::serialization::access;
+  template <class ARCHIVE>
+  void serialize(ARCHIVE &ar, const unsigned int /*version*/) {
+    ar &BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
+    ar &BOOST_SERIALIZATION_NVP(isDiscrete_);
+    ar &BOOST_SERIALIZATION_NVP(isContinuous_);
+    ar &BOOST_SERIALIZATION_NVP(isHybrid_);
+    ar &BOOST_SERIALIZATION_NVP(discreteKeys_);
+    ar &BOOST_SERIALIZATION_NVP(continuousKeys_);
+  }
 };
 // HybridFactor
 

gtsam/hybrid/HybridFactorGraph.h

@@ -0,0 +1,140 @@
+/* ----------------------------------------------------------------------------
+
+ * 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   HybridFactorGraph.h
+ * @brief  Hybrid factor graph base class that uses type erasure
+ * @author Varun Agrawal
+ * @date   May 28, 2022
+ */
+
+#pragma once
+
+#include <gtsam/discrete/DiscreteFactor.h>
+#include <gtsam/hybrid/HybridDiscreteFactor.h>
+#include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/inference/FactorGraph.h>
+#include <gtsam/inference/Ordering.h>
+
+#include <boost/format.hpp>
+namespace gtsam {
+
+using SharedFactor = boost::shared_ptr<Factor>;
+
+/**
+ * Hybrid Factor Graph
+ * -----------------------
+ * This is the base hybrid factor graph.
+ * Everything inside needs to be hybrid factor or hybrid conditional.
+ */
+class HybridFactorGraph : public FactorGraph<HybridFactor> {
+ public:
+  using Base = FactorGraph<HybridFactor>;
+  using This = HybridFactorGraph;              ///< this class
+  using shared_ptr = boost::shared_ptr<This>;  ///< shared_ptr to This
+
+  using Values = gtsam::Values;  ///< backwards compatibility
+  using Indices = KeyVector;     ///> map from keys to values
+
+ protected:
+  /// Check if FACTOR type is derived from DiscreteFactor.
+  template <typename FACTOR>
+  using IsDiscrete = typename std::enable_if<
+      std::is_base_of<DiscreteFactor, FACTOR>::value>::type;
+
+  /// Check if FACTOR type is derived from HybridFactor.
+  template <typename FACTOR>
+  using IsHybrid = typename std::enable_if<
+      std::is_base_of<HybridFactor, FACTOR>::value>::type;
+
+ public:
+  /// @name Constructors
+  /// @{
+
+  /// Default constructor
+  HybridFactorGraph() = default;
+
+  /**
+   * Implicit copy/downcast constructor to override explicit template container
+   * constructor. In BayesTree this is used for:
+   * `cachedSeparatorMarginal_.reset(*separatorMarginal)`
+   * */
+  template <class DERIVEDFACTOR>
+  HybridFactorGraph(const FactorGraph<DERIVEDFACTOR>& graph) : Base(graph) {}
+
+  /// @}
+
+  // Allow use of selected FactorGraph methods:
+  using Base::empty;
+  using Base::reserve;
+  using Base::size;
+  using Base::operator[];
+  using Base::add;
+  using Base::push_back;
+  using Base::resize;
+
+  /**
+   * Add a discrete factor *pointer* to the internal discrete graph
+   * @param discreteFactor - boost::shared_ptr to the factor to add
+   */
+  template <typename FACTOR>
+  IsDiscrete<FACTOR> push_discrete(
+      const boost::shared_ptr<FACTOR>& discreteFactor) {
+    Base::push_back(boost::make_shared<HybridDiscreteFactor>(discreteFactor));
+  }
+
+  /**
+   * Add a discrete-continuous (Hybrid) factor *pointer* to the graph
+   * @param hybridFactor - boost::shared_ptr to the factor to add
+   */
+  template <typename FACTOR>
+  IsHybrid<FACTOR> push_hybrid(const boost::shared_ptr<FACTOR>& hybridFactor) {
+    Base::push_back(hybridFactor);
+  }
+
+  /// delete emplace_shared.
+  template <class FACTOR, class... Args>
+  void emplace_shared(Args&&... args) = delete;
+
+  /// Construct a factor and add (shared pointer to it) to factor graph.
+  template <class FACTOR, class... Args>
+  IsDiscrete<FACTOR> emplace_discrete(Args&&... args) {
+    auto factor = boost::allocate_shared<FACTOR>(
+        Eigen::aligned_allocator<FACTOR>(), std::forward<Args>(args)...);
+    push_discrete(factor);
+  }
+
+  /// Construct a factor and add (shared pointer to it) to factor graph.
+  template <class FACTOR, class... Args>
+  IsHybrid<FACTOR> emplace_hybrid(Args&&... args) {
+    auto factor = boost::allocate_shared<FACTOR>(
+        Eigen::aligned_allocator<FACTOR>(), std::forward<Args>(args)...);
+    push_hybrid(factor);
+  }
+
+  /**
+   * @brief Add a single factor shared pointer to the hybrid factor graph.
+   * Dynamically handles the factor type and assigns it to the correct
+   * underlying container.
+   *
+   * @param sharedFactor The factor to add to this factor graph.
+   */
+  void push_back(const SharedFactor& sharedFactor) {
+    if (auto p = boost::dynamic_pointer_cast<DiscreteFactor>(sharedFactor)) {
+      push_discrete(p);
+    }
+    if (auto p = boost::dynamic_pointer_cast<HybridFactor>(sharedFactor)) {
+      push_hybrid(p);
+    }
+  }
+};
+
+}  // namespace gtsam

gtsam/hybrid/HybridGaussianFactor.h

@@ -37,6 +37,8 @@ class GTSAM_EXPORT HybridGaussianFactor : public HybridFactor {
   using This = HybridGaussianFactor;
   using shared_ptr = boost::shared_ptr<This>;
 
+  HybridGaussianFactor() = default;
+
   // Explicit conversion from a shared ptr of GF
   explicit HybridGaussianFactor(GaussianFactor::shared_ptr other);
 
@@ -52,7 +54,7 @@ class GTSAM_EXPORT HybridGaussianFactor : public HybridFactor {
 
   /// GTSAM print utility.
   void print(
-      const std::string &s = "HybridFactor\n",
+      const std::string &s = "HybridGaussianFactor\n",
       const KeyFormatter &formatter = DefaultKeyFormatter) const override;
 
   /// @}

gtsam/hybrid/HybridGaussianFactorGraph.cpp

@@ -98,6 +98,12 @@ GaussianMixtureFactor::Sum sumFrontals(
     } else if (f->isContinuous()) {
       deferredFactors.push_back(
           boost::dynamic_pointer_cast<HybridGaussianFactor>(f)->inner());
+
+    } else if (f->isDiscrete()) {
+      // Don't do anything for discrete-only factors
+      // since we want to eliminate continuous values only.
+      continue;
+
     } else {
       // We need to handle the case where the object is actually an
       // BayesTreeOrphanWrapper!
@@ -106,8 +112,8 @@ GaussianMixtureFactor::Sum sumFrontals(
       if (!orphan) {
         auto &fr = *f;
         throw std::invalid_argument(
-            std::string("factor is discrete in continuous elimination") +
+            std::string("factor is discrete in continuous elimination ") +
-            typeid(fr).name());
+            demangle(typeid(fr).name()));
       }
     }
   }
@@ -129,9 +135,9 @@ continuousElimination(const HybridGaussianFactorGraph &factors,
   for (auto &fp : factors) {
     if (auto ptr = boost::dynamic_pointer_cast<HybridGaussianFactor>(fp)) {
       gfg.push_back(ptr->inner());
-    } else if (auto p =
+    } else if (auto ptr = boost::static_pointer_cast<HybridConditional>(fp)) {
-                   boost::static_pointer_cast<HybridConditional>(fp)->inner()) {
+      gfg.push_back(
-      gfg.push_back(boost::static_pointer_cast<GaussianConditional>(p));
+          boost::static_pointer_cast<GaussianConditional>(ptr->inner()));
     } else {
       // It is an orphan wrapped conditional
     }
@@ -147,18 +153,20 @@ std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr>
 discreteElimination(const HybridGaussianFactorGraph &factors,
                     const Ordering &frontalKeys) {
   DiscreteFactorGraph dfg;
-  for (auto &fp : factors) {
+
-    if (auto ptr = boost::dynamic_pointer_cast<HybridDiscreteFactor>(fp)) {
+  for (auto &factor : factors) {
-      dfg.push_back(ptr->inner());
+    if (auto p = boost::dynamic_pointer_cast<HybridDiscreteFactor>(factor)) {
-    } else if (auto p =
+      dfg.push_back(p->inner());
-                   boost::static_pointer_cast<HybridConditional>(fp)->inner()) {
+    } else if (auto p = boost::static_pointer_cast<HybridConditional>(factor)) {
-      dfg.push_back(boost::static_pointer_cast<DiscreteConditional>(p));
+      auto discrete_conditional =
+          boost::static_pointer_cast<DiscreteConditional>(p->inner());
+      dfg.push_back(discrete_conditional);
     } else {
       // It is an orphan wrapper
     }
   }
 
-  auto result = EliminateDiscrete(dfg, frontalKeys);
+  auto result = EliminateForMPE(dfg, frontalKeys);
 
   return {boost::make_shared<HybridConditional>(result.first),
           boost::make_shared<HybridDiscreteFactor>(result.second)};
@@ -178,6 +186,19 @@ hybridElimination(const HybridGaussianFactorGraph &factors,
   // sum out frontals, this is the factor on the separator
   GaussianMixtureFactor::Sum sum = sumFrontals(factors);
 
+  // If a tree leaf contains nullptr,
+  // convert that leaf to an empty GaussianFactorGraph.
+  // Needed since the DecisionTree will otherwise create
+  // a GFG with a single (null) factor.
+  auto emptyGaussian = [](const GaussianFactorGraph &gfg) {
+    bool hasNull =
+        std::any_of(gfg.begin(), gfg.end(),
+                    [](const GaussianFactor::shared_ptr &ptr) { return !ptr; });
+
+    return hasNull ? GaussianFactorGraph() : gfg;
+  };
+  sum = GaussianMixtureFactor::Sum(sum, emptyGaussian);
+
   using EliminationPair = GaussianFactorGraph::EliminationResult;
 
   KeyVector keysOfEliminated;  // Not the ordering
@@ -189,7 +210,10 @@ hybridElimination(const HybridGaussianFactorGraph &factors,
     if (graph.empty()) {
       return {nullptr, nullptr};
     }
-    auto result = EliminatePreferCholesky(graph, frontalKeys);
+    std::pair<boost::shared_ptr<GaussianConditional>,
+              boost::shared_ptr<GaussianFactor>>
+        result = EliminatePreferCholesky(graph, frontalKeys);
+
     if (keysOfEliminated.empty()) {
       keysOfEliminated =
           result.first->keys();  // Initialize the keysOfEliminated to be the
@@ -222,6 +246,7 @@ hybridElimination(const HybridGaussianFactorGraph &factors,
       return exp(-factor->error(empty_values));
     };
     DecisionTree<Key, double> fdt(separatorFactors, factorError);
+
     auto discreteFactor =
         boost::make_shared<DecisionTreeFactor>(discreteSeparator, fdt);
 
@@ -229,14 +254,27 @@ hybridElimination(const HybridGaussianFactorGraph &factors,
             boost::make_shared<HybridDiscreteFactor>(discreteFactor)};
 
   } else {
-    // Create a resulting DCGaussianMixture on the separator.
+    // Create a resulting GaussianMixtureFactor on the separator.
     auto factor = boost::make_shared<GaussianMixtureFactor>(
         KeyVector(continuousSeparator.begin(), continuousSeparator.end()),
         discreteSeparator, separatorFactors);
     return {boost::make_shared<HybridConditional>(conditional), factor};
   }
 }
-/* ************************************************************************ */
+/* ************************************************************************
+ * Function to eliminate variables **under the following assumptions**:
+ * 1. When the ordering is fully continuous, and the graph only contains
+ * continuous and hybrid factors
+ * 2. When the ordering is fully discrete, and the graph only contains discrete
+ * factors
+ *
+ * Any usage outside of this is considered incorrect.
+ *
+ * \warning This function is not meant to be used with arbitrary hybrid factor
+ * graphs. For example, if there exists continuous parents, and one tries to
+ * eliminate a discrete variable (as specified in the ordering), the result will
+ * be INCORRECT and there will be NO error raised.
+ */
 std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr>  //
 EliminateHybrid(const HybridGaussianFactorGraph &factors,
                 const Ordering &frontalKeys) {
@@ -366,4 +404,41 @@ void HybridGaussianFactorGraph::add(DecisionTreeFactor::shared_ptr factor) {
   FactorGraph::add(boost::make_shared<HybridDiscreteFactor>(factor));
 }
 
+/* ************************************************************************ */
+const KeySet HybridGaussianFactorGraph::getDiscreteKeys() const {
+  KeySet discrete_keys;
+  for (auto &factor : factors_) {
+    for (const DiscreteKey &k : factor->discreteKeys()) {
+      discrete_keys.insert(k.first);
+    }
+  }
+  return discrete_keys;
+}
+
+/* ************************************************************************ */
+const KeySet HybridGaussianFactorGraph::getContinuousKeys() const {
+  KeySet keys;
+  for (auto &factor : factors_) {
+    for (const Key &key : factor->continuousKeys()) {
+      keys.insert(key);
+    }
+  }
+  return keys;
+}
+
+/* ************************************************************************ */
+const Ordering HybridGaussianFactorGraph::getHybridOrdering() const {
+  KeySet discrete_keys = getDiscreteKeys();
+  for (auto &factor : factors_) {
+    for (const DiscreteKey &k : factor->discreteKeys()) {
+      discrete_keys.insert(k.first);
+    }
+  }
+
+  const VariableIndex index(factors_);
+  Ordering ordering = Ordering::ColamdConstrainedLast(
+      index, KeyVector(discrete_keys.begin(), discrete_keys.end()), true);
+  return ordering;
+}
+
 }  // namespace gtsam

gtsam/hybrid/HybridGaussianFactorGraph.h

@@ -19,9 +19,12 @@
 #pragma once
 
 #include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/hybrid/HybridFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianFactor.h>
 #include <gtsam/inference/EliminateableFactorGraph.h>
 #include <gtsam/inference/FactorGraph.h>
 #include <gtsam/inference/Ordering.h>
+#include <gtsam/linear/GaussianFactor.h>
 
 namespace gtsam {
 
@@ -53,10 +56,9 @@ struct EliminationTraits<HybridGaussianFactorGraph> {
   typedef HybridBayesNet
       BayesNetType;  ///< Type of Bayes net from sequential elimination
   typedef HybridEliminationTree
-      EliminationTreeType;                ///< Type of elimination tree
+      EliminationTreeType;                      ///< Type of elimination tree
-  typedef HybridBayesTree BayesTreeType;  ///< Type of Bayes tree
+  typedef HybridBayesTree BayesTreeType;        ///< Type of Bayes tree
-  typedef HybridJunctionTree
+  typedef HybridJunctionTree JunctionTreeType;  ///< Type of Junction tree
-      JunctionTreeType;  ///< Type of Junction tree
   /// The default dense elimination function
   static std::pair<boost::shared_ptr<ConditionalType>,
                    boost::shared_ptr<FactorType> >
@@ -72,10 +74,16 @@ struct EliminationTraits<HybridGaussianFactorGraph> {
  * Everything inside needs to be hybrid factor or hybrid conditional.
  */
 class GTSAM_EXPORT HybridGaussianFactorGraph
-    : public FactorGraph<HybridFactor>,
+    : public HybridFactorGraph,
       public EliminateableFactorGraph<HybridGaussianFactorGraph> {
+ protected:
+  /// Check if FACTOR type is derived from GaussianFactor.
+  template <typename FACTOR>
+  using IsGaussian = typename std::enable_if<
+      std::is_base_of<GaussianFactor, FACTOR>::value>::type;
+
  public:
-  using Base = FactorGraph<HybridFactor>;
+  using Base = HybridFactorGraph;
   using This = HybridGaussianFactorGraph;  ///< this class
   using BaseEliminateable =
       EliminateableFactorGraph<This>;          ///< for elimination
@@ -100,7 +108,13 @@ class GTSAM_EXPORT HybridGaussianFactorGraph
 
   /// @}
 
-  using FactorGraph::add;
+  using Base::empty;
+  using Base::reserve;
+  using Base::size;
+  using Base::operator[];
+  using Base::add;
+  using Base::push_back;
+  using Base::resize;
 
   /// Add a Jacobian factor to the factor graph.
   void add(JacobianFactor&& factor);
@@ -113,6 +127,53 @@ class GTSAM_EXPORT HybridGaussianFactorGraph
 
   /// Add a DecisionTreeFactor as a shared ptr.
   void add(boost::shared_ptr<DecisionTreeFactor> factor);
+
+  /**
+   * Add a gaussian factor *pointer* to the internal gaussian factor graph
+   * @param gaussianFactor - boost::shared_ptr to the factor to add
+   */
+  template <typename FACTOR>
+  IsGaussian<FACTOR> push_gaussian(
+      const boost::shared_ptr<FACTOR>& gaussianFactor) {
+    Base::push_back(boost::make_shared<HybridGaussianFactor>(gaussianFactor));
+  }
+
+  /// Construct a factor and add (shared pointer to it) to factor graph.
+  template <class FACTOR, class... Args>
+  IsGaussian<FACTOR> emplace_gaussian(Args&&... args) {
+    auto factor = boost::allocate_shared<FACTOR>(
+        Eigen::aligned_allocator<FACTOR>(), std::forward<Args>(args)...);
+    push_gaussian(factor);
+  }
+
+  /**
+   * @brief Add a single factor shared pointer to the hybrid factor graph.
+   * Dynamically handles the factor type and assigns it to the correct
+   * underlying container.
+   *
+   * @param sharedFactor The factor to add to this factor graph.
+   */
+  void push_back(const SharedFactor& sharedFactor) {
+    if (auto p = boost::dynamic_pointer_cast<GaussianFactor>(sharedFactor)) {
+      push_gaussian(p);
+    } else {
+      Base::push_back(sharedFactor);
+    }
+  }
+
+  /// Get all the discrete keys in the factor graph.
+  const KeySet getDiscreteKeys() const;
+
+  /// Get all the continuous keys in the factor graph.
+  const KeySet getContinuousKeys() const;
+
+  /**
+   * @brief Return a Colamd constrained ordering where the discrete keys are
+   * eliminated after the continuous keys.
+   *
+   * @return const Ordering
+   */
+  const Ordering getHybridOrdering() const;
 };
 
 }  // namespace gtsam

gtsam/hybrid/HybridGaussianISAM.cpp

@@ -41,6 +41,7 @@ HybridGaussianISAM::HybridGaussianISAM(const HybridBayesTree& bayesTree)
 void HybridGaussianISAM::updateInternal(
     const HybridGaussianFactorGraph& newFactors,
     HybridBayesTree::Cliques* orphans,
+    const boost::optional<Ordering>& ordering,
     const HybridBayesTree::Eliminate& function) {
   // Remove the contaminated part of the Bayes tree
   BayesNetType bn;
@@ -74,16 +75,21 @@ void HybridGaussianISAM::updateInternal(
   std::copy(allDiscrete.begin(), allDiscrete.end(),
             std::back_inserter(newKeysDiscreteLast));
 
-  // KeyVector new
-
   // Get an ordering where the new keys are eliminated last
   const VariableIndex index(factors);
-  const Ordering ordering = Ordering::ColamdConstrainedLast(
+  Ordering elimination_ordering;
-      index, KeyVector(newKeysDiscreteLast.begin(), newKeysDiscreteLast.end()),
+  if (ordering) {
-      true);
+    elimination_ordering = *ordering;
+  } else {
+    elimination_ordering = Ordering::ColamdConstrainedLast(
+        index,
+        KeyVector(newKeysDiscreteLast.begin(), newKeysDiscreteLast.end()),
+        true);
+  }
 
   // eliminate all factors (top, added, orphans) into a new Bayes tree
-  auto bayesTree = factors.eliminateMultifrontal(ordering, function, index);
+  HybridBayesTree::shared_ptr bayesTree =
+      factors.eliminateMultifrontal(elimination_ordering, function, index);
 
   // Re-add into Bayes tree data structures
   this->roots_.insert(this->roots_.end(), bayesTree->roots().begin(),
@@ -93,9 +99,61 @@ void HybridGaussianISAM::updateInternal(
 
 /* ************************************************************************* */
 void HybridGaussianISAM::update(const HybridGaussianFactorGraph& newFactors,
+                                const boost::optional<Ordering>& ordering,
                                 const HybridBayesTree::Eliminate& function) {
   Cliques orphans;
-  this->updateInternal(newFactors, &orphans, function);
+  this->updateInternal(newFactors, &orphans, ordering, function);
+}
+
+/* ************************************************************************* */
+/**
+ * @brief Check if `b` is a subset of `a`.
+ * Non-const since they need to be sorted.
+ *
+ * @param a KeyVector
+ * @param b KeyVector
+ * @return True if the keys of b is a subset of a, else false.
+ */
+bool IsSubset(KeyVector a, KeyVector b) {
+  std::sort(a.begin(), a.end());
+  std::sort(b.begin(), b.end());
+  return std::includes(a.begin(), a.end(), b.begin(), b.end());
+}
+
+/* ************************************************************************* */
+void HybridGaussianISAM::prune(const Key& root, const size_t maxNrLeaves) {
+  auto decisionTree = boost::dynamic_pointer_cast<DecisionTreeFactor>(
+      this->clique(root)->conditional()->inner());
+  DecisionTreeFactor prunedDiscreteFactor = decisionTree->prune(maxNrLeaves);
+  decisionTree->root_ = prunedDiscreteFactor.root_;
+
+  std::vector<gtsam::Key> prunedKeys;
+  for (auto&& clique : nodes()) {
+    // The cliques can be repeated for each frontal so we record it in
+    // prunedKeys and check if we have already pruned a particular clique.
+    if (std::find(prunedKeys.begin(), prunedKeys.end(), clique.first) !=
+        prunedKeys.end()) {
+      continue;
+    }
+
+    // Add all the keys of the current clique to be pruned to prunedKeys
+    for (auto&& key : clique.second->conditional()->frontals()) {
+      prunedKeys.push_back(key);
+    }
+
+    // Convert parents() to a KeyVector for comparison
+    KeyVector parents;
+    for (auto&& parent : clique.second->conditional()->parents()) {
+      parents.push_back(parent);
+    }
+
+    if (IsSubset(parents, decisionTree->keys())) {
+      auto gaussianMixture = boost::dynamic_pointer_cast<GaussianMixture>(
+          clique.second->conditional()->inner());
+
+      gaussianMixture->prune(prunedDiscreteFactor);
+    }
+  }
 }
 
 }  // namespace gtsam

gtsam/hybrid/HybridGaussianISAM.h

@@ -48,6 +48,7 @@ class GTSAM_EXPORT HybridGaussianISAM : public ISAM<HybridBayesTree> {
   void updateInternal(
       const HybridGaussianFactorGraph& newFactors,
       HybridBayesTree::Cliques* orphans,
+      const boost::optional<Ordering>& ordering = boost::none,
       const HybridBayesTree::Eliminate& function =
           HybridBayesTree::EliminationTraitsType::DefaultEliminate);
 
@@ -59,8 +60,17 @@ class GTSAM_EXPORT HybridGaussianISAM : public ISAM<HybridBayesTree> {
    * @param function Elimination function.
    */
   void update(const HybridGaussianFactorGraph& newFactors,
+              const boost::optional<Ordering>& ordering = boost::none,
               const HybridBayesTree::Eliminate& function =
                   HybridBayesTree::EliminationTraitsType::DefaultEliminate);
+
+  /**
+   * @brief 
+   * 
+   * @param root The root key in the discrete conditional decision tree.
+   * @param maxNumberLeaves 
+   */
+  void prune(const Key& root, const size_t maxNumberLeaves);
 };
 
 /// traits

gtsam/hybrid/HybridJunctionTree.cpp

@@ -31,9 +31,7 @@ template class EliminatableClusterTree<HybridBayesTree,
 template class JunctionTree<HybridBayesTree, HybridGaussianFactorGraph>;
 
 struct HybridConstructorTraversalData {
-  typedef
+  typedef HybridJunctionTree::Node Node;
-      typename JunctionTree<HybridBayesTree, HybridGaussianFactorGraph>::Node
-          Node;
   typedef
       typename JunctionTree<HybridBayesTree,
                             HybridGaussianFactorGraph>::sharedNode sharedNode;
@@ -62,6 +60,7 @@ struct HybridConstructorTraversalData {
     data.junctionTreeNode = boost::make_shared<Node>(node->key, node->factors);
     parentData.junctionTreeNode->addChild(data.junctionTreeNode);
 
+    // Add all the discrete keys in the hybrid factors to the current data
     for (HybridFactor::shared_ptr& f : node->factors) {
       for (auto& k : f->discreteKeys()) {
         data.discreteKeys.insert(k.first);
@@ -72,8 +71,8 @@ struct HybridConstructorTraversalData {
   }
 
   // Post-order visitor function
-  static void ConstructorTraversalVisitorPostAlg2(
+  static void ConstructorTraversalVisitorPost(
-      const boost::shared_ptr<HybridEliminationTree::Node>& ETreeNode,
+      const boost::shared_ptr<HybridEliminationTree::Node>& node,
       const HybridConstructorTraversalData& data) {
     // In this post-order visitor, we combine the symbolic elimination results
     // from the elimination tree children and symbolically eliminate the current
@@ -86,15 +85,15 @@ struct HybridConstructorTraversalData {
 
     // Do symbolic elimination for this node
     SymbolicFactors symbolicFactors;
-    symbolicFactors.reserve(ETreeNode->factors.size() +
+    symbolicFactors.reserve(node->factors.size() +
                             data.childSymbolicFactors.size());
     // Add ETree node factors
-    symbolicFactors += ETreeNode->factors;
+    symbolicFactors += node->factors;
     // Add symbolic factors passed up from children
     symbolicFactors += data.childSymbolicFactors;
 
     Ordering keyAsOrdering;
-    keyAsOrdering.push_back(ETreeNode->key);
+    keyAsOrdering.push_back(node->key);
     SymbolicConditional::shared_ptr conditional;
     SymbolicFactor::shared_ptr separatorFactor;
     boost::tie(conditional, separatorFactor) =
@@ -105,19 +104,19 @@ struct HybridConstructorTraversalData {
     data.parentData->childSymbolicFactors.push_back(separatorFactor);
     data.parentData->discreteKeys.merge(data.discreteKeys);
 
-    sharedNode node = data.junctionTreeNode;
+    sharedNode jt_node = data.junctionTreeNode;
     const FastVector<SymbolicConditional::shared_ptr>& childConditionals =
         data.childSymbolicConditionals;
-    node->problemSize_ = (int)(conditional->size() * symbolicFactors.size());
+    jt_node->problemSize_ = (int)(conditional->size() * symbolicFactors.size());
 
     // Merge our children if they are in our clique - if our conditional has
     // exactly one fewer parent than our child's conditional.
     const size_t nrParents = conditional->nrParents();
-    const size_t nrChildren = node->nrChildren();
+    const size_t nrChildren = jt_node->nrChildren();
     assert(childConditionals.size() == nrChildren);
 
     // decide which children to merge, as index into children
-    std::vector<size_t> nrChildrenFrontals = node->nrFrontalsOfChildren();
+    std::vector<size_t> nrChildrenFrontals = jt_node->nrFrontalsOfChildren();
     std::vector<bool> merge(nrChildren, false);
     size_t nrFrontals = 1;
     for (size_t i = 0; i < nrChildren; i++) {
@@ -137,7 +136,7 @@ struct HybridConstructorTraversalData {
     }
 
     // now really merge
-    node->mergeChildren(merge);
+    jt_node->mergeChildren(merge);
   }
 };
 
@@ -161,7 +160,7 @@ HybridJunctionTree::HybridJunctionTree(
                                                   // the junction tree roots
   treeTraversal::DepthFirstForest(eliminationTree, rootData,
                                   Data::ConstructorTraversalVisitorPre,
-                                  Data::ConstructorTraversalVisitorPostAlg2);
+                                  Data::ConstructorTraversalVisitorPost);
 
   // Assign roots from the dummy node
   this->addChildrenAsRoots(rootData.junctionTreeNode);

gtsam/hybrid/HybridNonlinearFactor.cpp

@@ -0,0 +1,41 @@
+/* ----------------------------------------------------------------------------
+
+ * 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 HybridNonlinearFactor.cpp
+ *  @date May 28, 2022
+ *  @author Varun Agrawal
+ */
+
+#include <gtsam/hybrid/HybridNonlinearFactor.h>
+
+#include <boost/make_shared.hpp>
+
+namespace gtsam {
+
+/* ************************************************************************* */
+HybridNonlinearFactor::HybridNonlinearFactor(
+    const NonlinearFactor::shared_ptr &other)
+    : Base(other->keys()), inner_(other) {}
+
+/* ************************************************************************* */
+bool HybridNonlinearFactor::equals(const HybridFactor &lf, double tol) const {
+  return Base::equals(lf, tol);
+}
+
+/* ************************************************************************* */
+void HybridNonlinearFactor::print(const std::string &s,
+                                  const KeyFormatter &formatter) const {
+  HybridFactor::print(s, formatter);
+  inner_->print("\n", formatter);
+};
+
+}  // namespace gtsam

gtsam/hybrid/HybridNonlinearFactor.h

@@ -0,0 +1,62 @@
+/* ----------------------------------------------------------------------------
+
+ * 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 HybridNonlinearFactor.h
+ *  @date May 28, 2022
+ *  @author Varun Agrawal
+ */
+
+#pragma once
+
+#include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/hybrid/HybridGaussianFactor.h>
+#include <gtsam/nonlinear/NonlinearFactor.h>
+
+namespace gtsam {
+
+/**
+ * A HybridNonlinearFactor is a layer over NonlinearFactor so that we do not
+ * have a diamond inheritance.
+ */
+class HybridNonlinearFactor : public HybridFactor {
+ private:
+  NonlinearFactor::shared_ptr inner_;
+
+ public:
+  using Base = HybridFactor;
+  using This = HybridNonlinearFactor;
+  using shared_ptr = boost::shared_ptr<This>;
+
+  // Explicit conversion from a shared ptr of NonlinearFactor
+  explicit HybridNonlinearFactor(const NonlinearFactor::shared_ptr &other);
+
+  /// @name Testable
+  /// @{
+
+  /// Check equality.
+  virtual bool equals(const HybridFactor &lf, double tol) const override;
+
+  /// GTSAM print utility.
+  void print(
+      const std::string &s = "HybridNonlinearFactor\n",
+      const KeyFormatter &formatter = DefaultKeyFormatter) const override;
+
+  /// @}
+
+  NonlinearFactor::shared_ptr inner() const { return inner_; }
+
+  /// Linearize to a HybridGaussianFactor at the linearization point `c`.
+  boost::shared_ptr<HybridGaussianFactor> linearize(const Values &c) const {
+    return boost::make_shared<HybridGaussianFactor>(inner_->linearize(c));
+  }
+};
+}  // namespace gtsam

gtsam/hybrid/HybridNonlinearFactorGraph.cpp

@@ -0,0 +1,100 @@
+/* ----------------------------------------------------------------------------
+
+ * 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   HybridNonlinearFactorGraph.cpp
+ * @brief  Nonlinear hybrid factor graph that uses type erasure
+ * @author Varun Agrawal
+ * @date   May 28, 2022
+ */
+
+#include <gtsam/hybrid/HybridNonlinearFactorGraph.h>
+
+namespace gtsam {
+
+/* ************************************************************************* */
+void HybridNonlinearFactorGraph::add(
+    boost::shared_ptr<NonlinearFactor> factor) {
+  FactorGraph::add(boost::make_shared<HybridNonlinearFactor>(factor));
+}
+
+/* ************************************************************************* */
+void HybridNonlinearFactorGraph::add(
+    boost::shared_ptr<DiscreteFactor> factor) {
+  FactorGraph::add(boost::make_shared<HybridDiscreteFactor>(factor));
+}
+
+/* ************************************************************************* */
+void HybridNonlinearFactorGraph::print(const std::string& s,
+                                       const KeyFormatter& keyFormatter) const {
+  // Base::print(str, keyFormatter);
+  std::cout << (s.empty() ? "" : s + " ") << std::endl;
+  std::cout << "size: " << size() << std::endl;
+  for (size_t i = 0; i < factors_.size(); i++) {
+    std::stringstream ss;
+    ss << "factor " << i << ": ";
+    if (factors_[i]) {
+      factors_[i]->print(ss.str(), keyFormatter);
+      std::cout << std::endl;
+    }
+  }
+}
+
+/* ************************************************************************* */
+HybridGaussianFactorGraph HybridNonlinearFactorGraph::linearize(
+    const Values& continuousValues) const {
+  // create an empty linear FG
+  HybridGaussianFactorGraph linearFG;
+
+  linearFG.reserve(size());
+
+  // linearize all hybrid factors
+  for (auto&& factor : factors_) {
+    // First check if it is a valid factor
+    if (factor) {
+      // Check if the factor is a hybrid factor.
+      // It can be either a nonlinear MixtureFactor or a linear
+      // GaussianMixtureFactor.
+      if (factor->isHybrid()) {
+        // Check if it is a nonlinear mixture factor
+        if (auto nlmf = boost::dynamic_pointer_cast<MixtureFactor>(factor)) {
+          linearFG.push_back(nlmf->linearize(continuousValues));
+        } else {
+          linearFG.push_back(factor);
+        }
+
+        // Now check if the factor is a continuous only factor.
+      } else if (factor->isContinuous()) {
+        // In this case, we check if factor->inner() is nonlinear since
+        // HybridFactors wrap over continuous factors.
+        auto nlhf = boost::dynamic_pointer_cast<HybridNonlinearFactor>(factor);
+        if (auto nlf =
+                boost::dynamic_pointer_cast<NonlinearFactor>(nlhf->inner())) {
+          auto hgf = boost::make_shared<HybridGaussianFactor>(
+              nlf->linearize(continuousValues));
+          linearFG.push_back(hgf);
+        } else {
+          linearFG.push_back(factor);
+        }
+        // Finally if nothing else, we are discrete-only which doesn't need
+        // lineariztion.
+      } else {
+        linearFG.push_back(factor);
+      }
+
+    } else {
+      linearFG.push_back(GaussianFactor::shared_ptr());
+    }
+  }
+  return linearFG;
+}
+
+}  // namespace gtsam

gtsam/hybrid/HybridNonlinearFactorGraph.h

@@ -0,0 +1,137 @@
+/* ----------------------------------------------------------------------------
+
+ * 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   HybridNonlinearFactorGraph.h
+ * @brief  Nonlinear hybrid factor graph that uses type erasure
+ * @author Varun Agrawal
+ * @date   May 28, 2022
+ */
+
+#pragma once
+
+#include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/hybrid/HybridFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridNonlinearFactor.h>
+#include <gtsam/hybrid/MixtureFactor.h>
+#include <gtsam/inference/Ordering.h>
+#include <gtsam/nonlinear/NonlinearFactor.h>
+
+#include <boost/format.hpp>
+namespace gtsam {
+
+/**
+ * Nonlinear Hybrid Factor Graph
+ * -----------------------
+ * This is the non-linear version of a hybrid factor graph.
+ * Everything inside needs to be hybrid factor or hybrid conditional.
+ */
+class GTSAM_EXPORT HybridNonlinearFactorGraph : public HybridFactorGraph {
+ protected:
+  /// Check if FACTOR type is derived from NonlinearFactor.
+  template <typename FACTOR>
+  using IsNonlinear = typename std::enable_if<
+      std::is_base_of<NonlinearFactor, FACTOR>::value>::type;
+
+ public:
+  using Base = HybridFactorGraph;
+  using This = HybridNonlinearFactorGraph;     ///< this class
+  using shared_ptr = boost::shared_ptr<This>;  ///< shared_ptr to This
+
+  using Values = gtsam::Values;  ///< backwards compatibility
+  using Indices = KeyVector;     ///> map from keys to values
+
+  /// @name Constructors
+  /// @{
+
+  HybridNonlinearFactorGraph() = default;
+
+  /**
+   * Implicit copy/downcast constructor to override explicit template container
+   * constructor. In BayesTree this is used for:
+   * `cachedSeparatorMarginal_.reset(*separatorMarginal)`
+   * */
+  template <class DERIVEDFACTOR>
+  HybridNonlinearFactorGraph(const FactorGraph<DERIVEDFACTOR>& graph)
+      : Base(graph) {}
+
+  /// @}
+
+  // Allow use of selected FactorGraph methods:
+  using Base::empty;
+  using Base::reserve;
+  using Base::size;
+  using Base::operator[];
+  using Base::add;
+  using Base::resize;
+
+  /**
+   * Add a nonlinear factor *pointer* to the internal nonlinear factor graph
+   * @param nonlinearFactor - boost::shared_ptr to the factor to add
+   */
+  template <typename FACTOR>
+  IsNonlinear<FACTOR> push_nonlinear(
+      const boost::shared_ptr<FACTOR>& nonlinearFactor) {
+    Base::push_back(boost::make_shared<HybridNonlinearFactor>(nonlinearFactor));
+  }
+
+  /// Construct a factor and add (shared pointer to it) to factor graph.
+  template <class FACTOR, class... Args>
+  IsNonlinear<FACTOR> emplace_nonlinear(Args&&... args) {
+    auto factor = boost::allocate_shared<FACTOR>(
+        Eigen::aligned_allocator<FACTOR>(), std::forward<Args>(args)...);
+    push_nonlinear(factor);
+  }
+
+  /**
+   * @brief Add a single factor shared pointer to the hybrid factor graph.
+   * Dynamically handles the factor type and assigns it to the correct
+   * underlying container.
+   *
+   * @tparam FACTOR The factor type template
+   * @param sharedFactor The factor to add to this factor graph.
+   */
+  template <typename FACTOR>
+  void push_back(const boost::shared_ptr<FACTOR>& sharedFactor) {
+    if (auto p = boost::dynamic_pointer_cast<NonlinearFactor>(sharedFactor)) {
+      push_nonlinear(p);
+    } else {
+      Base::push_back(sharedFactor);
+    }
+  }
+
+  /// Add a nonlinear factor as a shared ptr.
+  void add(boost::shared_ptr<NonlinearFactor> factor);
+
+  /// Add a discrete factor as a shared ptr.
+  void add(boost::shared_ptr<DiscreteFactor> factor);
+
+  /// Print the factor graph.
+  void print(
+      const std::string& s = "HybridNonlinearFactorGraph",
+      const KeyFormatter& keyFormatter = DefaultKeyFormatter) const override;
+
+  /**
+   * @brief Linearize all the continuous factors in the
+   * HybridNonlinearFactorGraph.
+   *
+   * @param continuousValues: Dictionary of continuous values.
+   * @return HybridGaussianFactorGraph::shared_ptr
+   */
+  HybridGaussianFactorGraph linearize(const Values& continuousValues) const;
+};
+
+template <>
+struct traits<HybridNonlinearFactorGraph>
+    : public Testable<HybridNonlinearFactorGraph> {};
+
+}  // namespace gtsam

gtsam/hybrid/HybridValues.h

@@ -0,0 +1,145 @@
+/* ----------------------------------------------------------------------------
+
+ * 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 HybridValues.h
+ *  @date Jul 28, 2022
+ *  @author Shangjie Xue
+ */
+
+#pragma once
+
+#include <gtsam/discrete/Assignment.h>
+#include <gtsam/discrete/DiscreteKey.h>
+#include <gtsam/discrete/DiscreteValues.h>
+#include <gtsam/inference/Key.h>
+#include <gtsam/linear/VectorValues.h>
+#include <gtsam/nonlinear/Values.h>
+
+#include <map>
+#include <string>
+#include <vector>
+
+namespace gtsam {
+
+/**
+ * HybridValues represents a collection of DiscreteValues and VectorValues.
+ * It is typically used to store the variables of a HybridGaussianFactorGraph.
+ * Optimizing a HybridGaussianBayesNet returns this class.
+ */
+class GTSAM_EXPORT HybridValues {
+ private:
+  // DiscreteValue stored the discrete components of the HybridValues.
+  DiscreteValues discrete_;
+
+  // VectorValue stored the continuous components of the HybridValues.
+  VectorValues continuous_;
+
+ public:
+  /// @name Standard Constructors
+  /// @{
+
+  /// Default constructor creates an empty HybridValues.
+  HybridValues() = default;
+
+  /// Construct from DiscreteValues and VectorValues.
+  HybridValues(const DiscreteValues& dv, const VectorValues& cv)
+      : discrete_(dv), continuous_(cv){};
+
+  /// @}
+  /// @name Testable
+  /// @{
+
+  /// print required by Testable for unit testing
+  void print(const std::string& s = "HybridValues",
+             const KeyFormatter& keyFormatter = DefaultKeyFormatter) const {
+    std::cout << s << ": \n";
+    discrete_.print("  Discrete", keyFormatter);  // print discrete components
+    continuous_.print("  Continuous",
+                      keyFormatter);  // print continuous components
+  };
+
+  /// equals required by Testable for unit testing
+  bool equals(const HybridValues& other, double tol = 1e-9) const {
+    return discrete_.equals(other.discrete_, tol) &&
+           continuous_.equals(other.continuous_, tol);
+  }
+
+  /// @}
+  /// @name Interface
+  /// @{
+
+  /// Return the discrete MPE assignment
+  DiscreteValues discrete() const { return discrete_; }
+
+  /// Return the delta update for the continuous vectors
+  VectorValues continuous() const { return continuous_; }
+
+  /// Check whether a variable with key \c j exists in DiscreteValue.
+  bool existsDiscrete(Key j) { return (discrete_.find(j) != discrete_.end()); };
+
+  /// Check whether a variable with key \c j exists in VectorValue.
+  bool existsVector(Key j) { return continuous_.exists(j); };
+
+  /// Check whether a variable with key \c j exists.
+  bool exists(Key j) { return existsDiscrete(j) || existsVector(j); };
+
+  /** Insert a discrete \c value with key \c j.  Replaces the existing value if
+   * the key \c j is already used.
+   * @param value The vector to be inserted.
+   * @param j The index with which the value will be associated. */
+  void insert(Key j, int value) { discrete_[j] = value; };
+
+  /** Insert a vector \c value with key \c j.  Throws an invalid_argument
+   * exception if the key \c j is already used.
+   * @param value The vector to be inserted.
+   * @param j The index with which the value will be associated. */
+  void insert(Key j, const Vector& value) { continuous_.insert(j, value); }
+
+  // TODO(Shangjie)- update() and insert_or_assign() , similar to Values.h
+
+  /**
+   * Read/write access to the discrete value with key \c j, throws
+   * std::out_of_range if \c j does not exist.
+   */
+  size_t& atDiscrete(Key j) { return discrete_.at(j); };
+
+  /**
+   * Read/write access to the vector value with key \c j, throws
+   * std::out_of_range if \c j does not exist.
+   */
+  Vector& at(Key j) { return continuous_.at(j); };
+
+  /// @name Wrapper support
+  /// @{
+
+  /**
+   * @brief Output as a html table.
+   *
+   * @param keyFormatter function that formats keys.
+   * @return string html output.
+   */
+  std::string html(
+      const KeyFormatter& keyFormatter = DefaultKeyFormatter) const {
+    std::stringstream ss;
+    ss << this->discrete_.html(keyFormatter);
+    ss << this->continuous_.html(keyFormatter);
+    return ss.str();
+  };
+
+  /// @}
+};
+
+// traits
+template <>
+struct traits<HybridValues> : public Testable<HybridValues> {};
+
+}  // namespace gtsam

gtsam/hybrid/MixtureFactor.h

@@ -0,0 +1,256 @@
+/* ----------------------------------------------------------------------------
+
+ * 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   MixtureFactor.h
+ * @brief  Nonlinear Mixture factor of continuous and discrete.
+ * @author Kevin Doherty, kdoherty@mit.edu
+ * @author Varun Agrawal
+ * @date   December 2021
+ */
+
+#pragma once
+
+#include <gtsam/discrete/DiscreteValues.h>
+#include <gtsam/hybrid/GaussianMixtureFactor.h>
+#include <gtsam/hybrid/HybridNonlinearFactor.h>
+#include <gtsam/nonlinear/NonlinearFactor.h>
+#include <gtsam/nonlinear/Symbol.h>
+
+#include <algorithm>
+#include <boost/format.hpp>
+#include <cmath>
+#include <limits>
+#include <vector>
+
+namespace gtsam {
+
+/**
+ * @brief Implementation of a discrete conditional mixture factor.
+ *
+ * Implements a joint discrete-continuous factor where the discrete variable
+ * serves to "select" a mixture component corresponding to a NonlinearFactor
+ * type of measurement.
+ *
+ * This class stores all factors as HybridFactors which can then be typecast to
+ * one of (NonlinearFactor, GaussianFactor) which can then be checked to perform
+ * the correct operation.
+ */
+class MixtureFactor : public HybridFactor {
+ public:
+  using Base = HybridFactor;
+  using This = MixtureFactor;
+  using shared_ptr = boost::shared_ptr<MixtureFactor>;
+  using sharedFactor = boost::shared_ptr<NonlinearFactor>;
+
+  /**
+   * @brief typedef for DecisionTree which has Keys as node labels and
+   * NonlinearFactor as leaf nodes.
+   */
+  using Factors = DecisionTree<Key, sharedFactor>;
+
+ private:
+  /// Decision tree of Gaussian factors indexed by discrete keys.
+  Factors factors_;
+  bool normalized_;
+
+ public:
+  MixtureFactor() = default;
+
+  /**
+   * @brief Construct from Decision tree.
+   *
+   * @param keys Vector of keys for continuous factors.
+   * @param discreteKeys Vector of discrete keys.
+   * @param factors Decision tree with of shared factors.
+   * @param normalized Flag indicating if the factor error is already
+   * normalized.
+   */
+  MixtureFactor(const KeyVector& keys, const DiscreteKeys& discreteKeys,
+                const Factors& factors, bool normalized = false)
+      : Base(keys, discreteKeys), factors_(factors), normalized_(normalized) {}
+
+  /**
+   * @brief Convenience constructor that generates the underlying factor
+   * decision tree for us.
+   *
+   * Here it is important that the vector of factors has the correct number of
+   * elements based on the number of discrete keys and the cardinality of the
+   * keys, so that the decision tree is constructed appropriately.
+   *
+   * @tparam FACTOR The type of the factor shared pointers being passed in. Will
+   * be typecast to NonlinearFactor shared pointers.
+   * @param keys Vector of keys for continuous factors.
+   * @param discreteKeys Vector of discrete keys.
+   * @param factors Vector of shared pointers to factors.
+   * @param normalized Flag indicating if the factor error is already
+   * normalized.
+   */
+  template <typename FACTOR>
+  MixtureFactor(const KeyVector& keys, const DiscreteKeys& discreteKeys,
+                const std::vector<boost::shared_ptr<FACTOR>>& factors,
+                bool normalized = false)
+      : Base(keys, discreteKeys), normalized_(normalized) {
+    std::vector<NonlinearFactor::shared_ptr> nonlinear_factors;
+    KeySet continuous_keys_set(keys.begin(), keys.end());
+    KeySet factor_keys_set;
+    for (auto&& f : factors) {
+      // Insert all factor continuous keys in the continuous keys set.
+      std::copy(f->keys().begin(), f->keys().end(),
+                std::inserter(factor_keys_set, factor_keys_set.end()));
+
+      nonlinear_factors.push_back(
+          boost::dynamic_pointer_cast<NonlinearFactor>(f));
+    }
+    factors_ = Factors(discreteKeys, nonlinear_factors);
+
+    if (continuous_keys_set != factor_keys_set) {
+      throw std::runtime_error(
+          "The specified continuous keys and the keys in the factors don't "
+          "match!");
+    }
+  }
+
+  ~MixtureFactor() = default;
+
+  /**
+   * @brief Compute error of factor given both continuous and discrete values.
+   *
+   * @param continuousVals The continuous Values.
+   * @param discreteVals The discrete Values.
+   * @return double The error of this factor.
+   */
+  double error(const Values& continuousVals,
+               const DiscreteValues& discreteVals) const {
+    // Retrieve the factor corresponding to the assignment in discreteVals.
+    auto factor = factors_(discreteVals);
+    // Compute the error for the selected factor
+    const double factorError = factor->error(continuousVals);
+    if (normalized_) return factorError;
+    return factorError +
+           this->nonlinearFactorLogNormalizingConstant(factor, continuousVals);
+  }
+
+  size_t dim() const {
+    // TODO(Varun)
+    throw std::runtime_error("MixtureFactor::dim not implemented.");
+  }
+
+  /// Testable
+  /// @{
+
+  /// print to stdout
+  void print(
+      const std::string& s = "MixtureFactor",
+      const KeyFormatter& keyFormatter = DefaultKeyFormatter) const override {
+    std::cout << (s.empty() ? "" : s + " ");
+    Base::print("", keyFormatter);
+    std::cout << "\nMixtureFactor\n";
+    auto valueFormatter = [](const sharedFactor& v) {
+      if (v) {
+        return (boost::format("Nonlinear factor on %d keys") % v->size()).str();
+      } else {
+        return std::string("nullptr");
+      }
+    };
+    factors_.print("", keyFormatter, valueFormatter);
+  }
+
+  /// Check equality
+  bool equals(const HybridFactor& other, double tol = 1e-9) const override {
+    // We attempt a dynamic cast from HybridFactor to MixtureFactor. If it
+    // fails, return false.
+    if (!dynamic_cast<const MixtureFactor*>(&other)) return false;
+
+    // If the cast is successful, we'll properly construct a MixtureFactor
+    // object from `other`
+    const MixtureFactor& f(static_cast<const MixtureFactor&>(other));
+
+    // Ensure that this MixtureFactor and `f` have the same `factors_`.
+    auto compare = [tol](const sharedFactor& a, const sharedFactor& b) {
+      return traits<NonlinearFactor>::Equals(*a, *b, tol);
+    };
+    if (!factors_.equals(f.factors_, compare)) return false;
+
+    // If everything above passes, and the keys_, discreteKeys_ and normalized_
+    // member variables are identical, return true.
+    return (std::equal(keys_.begin(), keys_.end(), f.keys().begin()) &&
+            (discreteKeys_ == f.discreteKeys_) &&
+            (normalized_ == f.normalized_));
+  }
+
+  /// @}
+
+  /// Linearize specific nonlinear factors based on the assignment in
+  /// discreteValues.
+  GaussianFactor::shared_ptr linearize(
+      const Values& continuousVals, const DiscreteValues& discreteVals) const {
+    auto factor = factors_(discreteVals);
+    return factor->linearize(continuousVals);
+  }
+
+  /// Linearize all the continuous factors to get a GaussianMixtureFactor.
+  boost::shared_ptr<GaussianMixtureFactor> linearize(
+      const Values& continuousVals) const {
+    // functional to linearize each factor in the decision tree
+    auto linearizeDT = [continuousVals](const sharedFactor& factor) {
+      return factor->linearize(continuousVals);
+    };
+
+    DecisionTree<Key, GaussianFactor::shared_ptr> linearized_factors(
+        factors_, linearizeDT);
+
+    return boost::make_shared<GaussianMixtureFactor>(
+        continuousKeys_, discreteKeys_, linearized_factors);
+  }
+
+  /**
+   * If the component factors are not already normalized, we want to compute
+   * their normalizing constants so that the resulting joint distribution is
+   * appropriately computed. Remember, this is the _negative_ normalizing
+   * constant for the measurement likelihood (since we are minimizing the
+   * _negative_ log-likelihood).
+   */
+  double nonlinearFactorLogNormalizingConstant(const sharedFactor& factor,
+                                               const Values& values) const {
+    // Information matrix (inverse covariance matrix) for the factor.
+    Matrix infoMat;
+
+    // If this is a NoiseModelFactor, we'll use its noiseModel to
+    // otherwise noiseModelFactor will be nullptr
+    if (auto noiseModelFactor =
+            boost::dynamic_pointer_cast<NoiseModelFactor>(factor)) {
+      // If dynamic cast to NoiseModelFactor succeeded, see if the noise model
+      // is Gaussian
+      auto noiseModel = noiseModelFactor->noiseModel();
+
+      auto gaussianNoiseModel =
+          boost::dynamic_pointer_cast<noiseModel::Gaussian>(noiseModel);
+      if (gaussianNoiseModel) {
+        // If the noise model is Gaussian, retrieve the information matrix
+        infoMat = gaussianNoiseModel->information();
+      } else {
+        // If the factor is not a Gaussian factor, we'll linearize it to get
+        // something with a normalized noise model
+        // TODO(kevin): does this make sense to do? I think maybe not in
+        // general? Should we just yell at the user?
+        auto gaussianFactor = factor->linearize(values);
+        infoMat = gaussianFactor->information();
+      }
+    }
+
+    // Compute the (negative) log of the normalizing constant
+    return -(factor->dim() * log(2.0 * M_PI) / 2.0) -
+           (log(infoMat.determinant()) / 2.0);
+  }
+};
+
+}  // namespace gtsam

gtsam/hybrid/hybrid.i

@@ -4,6 +4,22 @@
 
 namespace gtsam {
 
+#include <gtsam/hybrid/HybridValues.h>
+class HybridValues {
+  gtsam::DiscreteValues discrete() const;
+  gtsam::VectorValues continuous() const;
+  HybridValues();
+  HybridValues(const gtsam::DiscreteValues &dv, const gtsam::VectorValues &cv);
+  void print(string s = "HybridValues",
+             const gtsam::KeyFormatter& keyFormatter =
+                 gtsam::DefaultKeyFormatter) const;
+  bool equals(const gtsam::HybridValues& other, double tol) const;
+  void insert(gtsam::Key j, int value);
+  void insert(gtsam::Key j, const gtsam::Vector& value);
+  size_t& atDiscrete(gtsam::Key j);
+  gtsam::Vector& at(gtsam::Key j);
+};
+
 #include <gtsam/hybrid/HybridFactor.h>
 virtual class HybridFactor {
   void print(string s = "HybridFactor\n",
@@ -23,7 +39,17 @@ virtual class HybridConditional {
   bool equals(const gtsam::HybridConditional& other, double tol = 1e-9) const;
   size_t nrFrontals() const;
   size_t nrParents() const;
-  Factor* inner();
+  gtsam::Factor* inner();
+};
+
+#include <gtsam/hybrid/HybridDiscreteFactor.h>
+virtual class HybridDiscreteFactor {
+  HybridDiscreteFactor(gtsam::DecisionTreeFactor dtf);
+  void print(string s = "HybridDiscreteFactor\n",
+             const gtsam::KeyFormatter& keyFormatter =
+                 gtsam::DefaultKeyFormatter) const;
+  bool equals(const gtsam::HybridDiscreteFactor& other, double tol = 1e-9) const;
+  gtsam::Factor* inner();
 };
 
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
@@ -73,6 +99,8 @@ class HybridBayesTree {
   bool empty() const;
   const HybridBayesTreeClique* operator[](size_t j) const;
 
+  gtsam::HybridValues optimize() const;
+
   string dot(const gtsam::KeyFormatter& keyFormatter =
                  gtsam::DefaultKeyFormatter) const;
 };
@@ -84,6 +112,7 @@ class HybridBayesNet {
   size_t size() const;
   gtsam::KeySet keys() const;
   const gtsam::HybridConditional* at(size_t i) const;
+  gtsam::HybridValues optimize() const;
   void print(string s = "HybridBayesNet\n",
              const gtsam::KeyFormatter& keyFormatter =
                  gtsam::DefaultKeyFormatter) const;
@@ -115,6 +144,7 @@ class HybridGaussianFactorGraph {
   void add(gtsam::JacobianFactor* factor);
 
   bool empty() const;
+  void remove(size_t i);
   size_t size() const;
   gtsam::KeySet keys() const;
   const gtsam::HybridFactor* at(size_t i) const;
@@ -142,4 +172,50 @@ class HybridGaussianFactorGraph {
       const gtsam::DotWriter& writer = gtsam::DotWriter()) const;
 };
 
+#include <gtsam/hybrid/HybridNonlinearFactorGraph.h>
+class HybridNonlinearFactorGraph {
+  HybridNonlinearFactorGraph();
+  HybridNonlinearFactorGraph(const gtsam::HybridNonlinearFactorGraph& graph);
+  void push_back(gtsam::HybridFactor* factor);
+  void push_back(gtsam::NonlinearFactor* factor);
+  void push_back(gtsam::HybridDiscreteFactor* factor);
+  void add(gtsam::NonlinearFactor* factor);
+  void add(gtsam::DiscreteFactor* factor);
+  gtsam::HybridGaussianFactorGraph linearize(const gtsam::Values& continuousValues) const;
+
+  bool empty() const;
+  void remove(size_t i);
+  size_t size() const;
+  gtsam::KeySet keys() const;
+  const gtsam::HybridFactor* at(size_t i) const;
+
+  void print(string s = "HybridNonlinearFactorGraph\n",
+       const gtsam::KeyFormatter& keyFormatter =
+       gtsam::DefaultKeyFormatter) const;
+};
+
+#include <gtsam/hybrid/MixtureFactor.h>
+class MixtureFactor : gtsam::HybridFactor {
+  MixtureFactor(const gtsam::KeyVector& keys, const gtsam::DiscreteKeys& discreteKeys,
+                const gtsam::DecisionTree<gtsam::Key, gtsam::NonlinearFactor*>& factors, bool normalized = false);
+
+  template <FACTOR = {gtsam::NonlinearFactor}>
+  MixtureFactor(const gtsam::KeyVector& keys, const gtsam::DiscreteKeys& discreteKeys,
+                const std::vector<FACTOR*>& factors,
+                bool normalized = false);
+
+  double error(const gtsam::Values& continuousVals,
+               const gtsam::DiscreteValues& discreteVals) const;
+
+  double nonlinearFactorLogNormalizingConstant(const gtsam::NonlinearFactor* factor,
+                                               const gtsam::Values& values) const;
+
+  GaussianMixtureFactor* linearize(
+      const gtsam::Values& continuousVals) const;
+
+  void print(string s = "MixtureFactor\n",
+             const gtsam::KeyFormatter& keyFormatter =
+                 gtsam::DefaultKeyFormatter) const;
+};
+
 }  // namespace gtsam

gtsam/hybrid/tests/Switching.h

@@ -18,20 +18,39 @@
 
 #include <gtsam/base/Matrix.h>
 #include <gtsam/discrete/DecisionTreeFactor.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
 #include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridNonlinearFactorGraph.h>
+#include <gtsam/hybrid/MixtureFactor.h>
 #include <gtsam/inference/Symbol.h>
 #include <gtsam/linear/JacobianFactor.h>
+#include <gtsam/linear/NoiseModel.h>
+#include <gtsam/nonlinear/PriorFactor.h>
+#include <gtsam/slam/BetweenFactor.h>
+
+#include <vector>
 
 #pragma once
 
-using gtsam::symbol_shorthand::C;
-using gtsam::symbol_shorthand::X;
-
 namespace gtsam {
+
+using symbol_shorthand::C;
+using symbol_shorthand::M;
+using symbol_shorthand::X;
+
+/**
+ * @brief Create a switching system chain. A switching system is a continuous
+ * system which depends on a discrete mode at each time step of the chain.
+ *
+ * @param n The number of chain elements.
+ * @param keyFunc The functional to help specify the continuous key.
+ * @param dKeyFunc The functional to help specify the discrete key.
+ * @return HybridGaussianFactorGraph::shared_ptr
+ */
 inline HybridGaussianFactorGraph::shared_ptr makeSwitchingChain(
     size_t n, std::function<Key(int)> keyFunc = X,
-    std::function<Key(int)> dKeyFunc = C) {
+    std::function<Key(int)> dKeyFunc = M) {
   HybridGaussianFactorGraph hfg;
 
   hfg.add(JacobianFactor(keyFunc(1), I_3x3, Z_3x1));
@@ -54,9 +73,19 @@ inline HybridGaussianFactorGraph::shared_ptr makeSwitchingChain(
   return boost::make_shared<HybridGaussianFactorGraph>(std::move(hfg));
 }
 
+/**
+ * @brief Return the ordering as a binary tree such that all parent nodes are
+ * above their children.
+ *
+ * This will result in a nested dissection Bayes tree after elimination.
+ *
+ * @param input The original ordering.
+ * @return std::pair<KeyVector, std::vector<int>>
+ */
 inline std::pair<KeyVector, std::vector<int>> makeBinaryOrdering(
     std::vector<Key> &input) {
   KeyVector new_order;
+
   std::vector<int> levels(input.size());
   std::function<void(std::vector<Key>::iterator, std::vector<Key>::iterator,
                      int)>
@@ -79,8 +108,101 @@ inline std::pair<KeyVector, std::vector<int>> makeBinaryOrdering(
 
   bsg(input.begin(), input.end(), 0);
   std::reverse(new_order.begin(), new_order.end());
-  // std::reverse(levels.begin(), levels.end());
+
   return {new_order, levels};
 }
 
+/* ***************************************************************************
+ */
+using MotionModel = BetweenFactor<double>;
+// using MotionMixture = MixtureFactor<MotionModel>;
+
+// Test fixture with switching network.
+struct Switching {
+  size_t K;
+  DiscreteKeys modes;
+  HybridNonlinearFactorGraph nonlinearFactorGraph;
+  HybridGaussianFactorGraph linearizedFactorGraph;
+  Values linearizationPoint;
+
+  /// Create with given number of time steps.
+  Switching(size_t K, double between_sigma = 1.0, double prior_sigma = 0.1)
+      : K(K) {
+    // Create DiscreteKeys for binary K modes, modes[0] will not be used.
+    for (size_t k = 0; k <= K; k++) {
+      modes.emplace_back(M(k), 2);
+    }
+
+    // Create hybrid factor graph.
+    // Add a prior on X(1).
+    auto prior = boost::make_shared<PriorFactor<double>>(
+        X(1), 0, noiseModel::Isotropic::Sigma(1, prior_sigma));
+    nonlinearFactorGraph.push_nonlinear(prior);
+
+    // Add "motion models".
+    for (size_t k = 1; k < K; k++) {
+      KeyVector keys = {X(k), X(k + 1)};
+      auto motion_models = motionModels(k, between_sigma);
+      std::vector<NonlinearFactor::shared_ptr> components;
+      for (auto &&f : motion_models) {
+        components.push_back(boost::dynamic_pointer_cast<NonlinearFactor>(f));
+      }
+      nonlinearFactorGraph.emplace_hybrid<MixtureFactor>(
+          keys, DiscreteKeys{modes[k]}, components);
+    }
+
+    // Add measurement factors
+    auto measurement_noise = noiseModel::Isotropic::Sigma(1, prior_sigma);
+    for (size_t k = 2; k <= K; k++) {
+      nonlinearFactorGraph.emplace_nonlinear<PriorFactor<double>>(
+          X(k), 1.0 * (k - 1), measurement_noise);
+    }
+
+    // Add "mode chain"
+    addModeChain(&nonlinearFactorGraph);
+
+    // Create the linearization point.
+    for (size_t k = 1; k <= K; k++) {
+      linearizationPoint.insert<double>(X(k), static_cast<double>(k));
+    }
+
+    linearizedFactorGraph = nonlinearFactorGraph.linearize(linearizationPoint);
+  }
+
+  // Create motion models for a given time step
+  static std::vector<MotionModel::shared_ptr> motionModels(size_t k,
+                                                           double sigma = 1.0) {
+    auto noise_model = noiseModel::Isotropic::Sigma(1, sigma);
+    auto still =
+             boost::make_shared<MotionModel>(X(k), X(k + 1), 0.0, noise_model),
+         moving =
+             boost::make_shared<MotionModel>(X(k), X(k + 1), 1.0, noise_model);
+    return {still, moving};
+  }
+
+  // Add "mode chain" to HybridNonlinearFactorGraph
+  void addModeChain(HybridNonlinearFactorGraph *fg) {
+    auto prior = boost::make_shared<DiscreteDistribution>(modes[1], "1/1");
+    fg->push_discrete(prior);
+    for (size_t k = 1; k < K - 1; k++) {
+      auto parents = {modes[k]};
+      auto conditional = boost::make_shared<DiscreteConditional>(
+          modes[k + 1], parents, "1/2 3/2");
+      fg->push_discrete(conditional);
+    }
+  }
+
+  // Add "mode chain" to HybridGaussianFactorGraph
+  void addModeChain(HybridGaussianFactorGraph *fg) {
+    auto prior = boost::make_shared<DiscreteDistribution>(modes[1], "1/1");
+    fg->push_discrete(prior);
+    for (size_t k = 1; k < K - 1; k++) {
+      auto parents = {modes[k]};
+      auto conditional = boost::make_shared<DiscreteConditional>(
+          modes[k + 1], parents, "1/2 3/2");
+      fg->push_discrete(conditional);
+    }
+  }
+};
+
 }  // namespace gtsam

gtsam/hybrid/tests/testGaussianHybridFactorGraph.cpp

@@ -17,6 +17,7 @@
 
 #include <CppUnitLite/Test.h>
 #include <CppUnitLite/TestHarness.h>
+#include <gtsam/base/TestableAssertions.h>
 #include <gtsam/discrete/DecisionTreeFactor.h>
 #include <gtsam/discrete/DiscreteKey.h>
 #include <gtsam/discrete/DiscreteValues.h>
@@ -30,6 +31,7 @@
 #include <gtsam/hybrid/HybridGaussianFactor.h>
 #include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/hybrid/HybridGaussianISAM.h>
+#include <gtsam/hybrid/HybridValues.h>
 #include <gtsam/inference/BayesNet.h>
 #include <gtsam/inference/DotWriter.h>
 #include <gtsam/inference/Key.h>
@@ -52,32 +54,36 @@ using namespace boost::assign;
 using namespace std;
 using namespace gtsam;
 
-using gtsam::symbol_shorthand::C;
 using gtsam::symbol_shorthand::D;
+using gtsam::symbol_shorthand::M;
 using gtsam::symbol_shorthand::X;
 using gtsam::symbol_shorthand::Y;
 
 /* ************************************************************************* */
-TEST(HybridGaussianFactorGraph, creation) {
+TEST(HybridGaussianFactorGraph, Creation) {
-  HybridConditional test;
+  HybridConditional conditional;
 
   HybridGaussianFactorGraph hfg;
 
-  hfg.add(HybridGaussianFactor(JacobianFactor(0, I_3x3, Z_3x1)));
+  hfg.add(HybridGaussianFactor(JacobianFactor(X(0), I_3x3, Z_3x1)));
 
-  GaussianMixture clgc(
+  // Define a gaussian mixture conditional P(x0|x1, c0) and add it to the factor
-      {X(0)}, {X(1)}, DiscreteKeys(DiscreteKey{C(0), 2}),
+  // graph
-      GaussianMixture::Conditionals(
+  GaussianMixture gm({X(0)}, {X(1)}, DiscreteKeys(DiscreteKey{M(0), 2}),
-          C(0),
+                     GaussianMixture::Conditionals(
-          boost::make_shared<GaussianConditional>(X(0), Z_3x1, I_3x3, X(1),
+                         M(0),
-                                                  I_3x3),
+                         boost::make_shared<GaussianConditional>(
-          boost::make_shared<GaussianConditional>(X(0), Vector3::Ones(), I_3x3,
+                             X(0), Z_3x1, I_3x3, X(1), I_3x3),
-                                                  X(1), I_3x3)));
+                         boost::make_shared<GaussianConditional>(
-  GTSAM_PRINT(clgc);
+                             X(0), Vector3::Ones(), I_3x3, X(1), I_3x3)));
+  hfg.add(gm);
+
+  EXPECT_LONGS_EQUAL(2, hfg.size());
 }
 
 /* ************************************************************************* */
-TEST(HybridGaussianFactorGraph, eliminate) {
+TEST(HybridGaussianFactorGraph, EliminateSequential) {
+  // Test elimination of a single variable.
   HybridGaussianFactorGraph hfg;
 
   hfg.add(HybridGaussianFactor(JacobianFactor(0, I_3x3, Z_3x1)));
@@ -88,13 +94,15 @@ TEST(HybridGaussianFactorGraph, eliminate) {
 }
 
 /* ************************************************************************* */
-TEST(HybridGaussianFactorGraph, eliminateMultifrontal) {
+TEST(HybridGaussianFactorGraph, EliminateMultifrontal) {
+  // Test multifrontal elimination
   HybridGaussianFactorGraph hfg;
 
-  DiscreteKey c(C(1), 2);
+  DiscreteKey m(M(1), 2);
 
+  // Add priors on x0 and c1
   hfg.add(JacobianFactor(X(0), I_3x3, Z_3x1));
-  hfg.add(HybridDiscreteFactor(DecisionTreeFactor(c, {2, 8})));
+  hfg.add(HybridDiscreteFactor(DecisionTreeFactor(m, {2, 8})));
 
   Ordering ordering;
   ordering.push_back(X(0));
@@ -108,117 +116,111 @@ TEST(HybridGaussianFactorGraph, eliminateMultifrontal) {
 TEST(HybridGaussianFactorGraph, eliminateFullSequentialEqualChance) {
   HybridGaussianFactorGraph hfg;
 
-  DiscreteKey c1(C(1), 2);
+  DiscreteKey m1(M(1), 2);
 
+  // Add prior on x0
   hfg.add(JacobianFactor(X(0), I_3x3, Z_3x1));
+  // Add factor between x0 and x1
   hfg.add(JacobianFactor(X(0), I_3x3, X(1), -I_3x3, Z_3x1));
 
+  // Add a gaussian mixture factor ϕ(x1, c1)
   DecisionTree<Key, GaussianFactor::shared_ptr> dt(
-      C(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
+      M(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
       boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones()));
 
-  hfg.add(GaussianMixtureFactor({X(1)}, {c1}, dt));
+  hfg.add(GaussianMixtureFactor({X(1)}, {m1}, dt));
 
   auto result =
-      hfg.eliminateSequential(Ordering::ColamdConstrainedLast(hfg, {C(1)}));
+      hfg.eliminateSequential(Ordering::ColamdConstrainedLast(hfg, {M(1)}));
 
   auto dc = result->at(2)->asDiscreteConditional();
   DiscreteValues dv;
-  dv[C(1)] = 0;
+  dv[M(1)] = 0;
-  EXPECT_DOUBLES_EQUAL(0.6225, dc->operator()(dv), 1e-3);
+  EXPECT_DOUBLES_EQUAL(1, dc->operator()(dv), 1e-3);
 }
 
 /* ************************************************************************* */
 TEST(HybridGaussianFactorGraph, eliminateFullSequentialSimple) {
   HybridGaussianFactorGraph hfg;
 
-  DiscreteKey c1(C(1), 2);
+  DiscreteKey m1(M(1), 2);
 
+  // Add prior on x0
   hfg.add(JacobianFactor(X(0), I_3x3, Z_3x1));
+  // Add factor between x0 and x1
   hfg.add(JacobianFactor(X(0), I_3x3, X(1), -I_3x3, Z_3x1));
 
-  DecisionTree<Key, GaussianFactor::shared_ptr> dt(
+  std::vector<GaussianFactor::shared_ptr> factors = {
-      C(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
+      boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
-      boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones()));
+      boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones())};
+  hfg.add(GaussianMixtureFactor({X(1)}, {m1}, factors));
 
-  hfg.add(GaussianMixtureFactor({X(1)}, {c1}, dt));
+  // Discrete probability table for c1
-  // hfg.add(GaussianMixtureFactor({X(0)}, {c1}, dt));
+  hfg.add(DecisionTreeFactor(m1, {2, 8}));
-  hfg.add(HybridDiscreteFactor(DecisionTreeFactor(c1, {2, 8})));
+  // Joint discrete probability table for c1, c2
-  hfg.add(HybridDiscreteFactor(
+  hfg.add(DecisionTreeFactor({{M(1), 2}, {M(2), 2}}, "1 2 3 4"));
-      DecisionTreeFactor({{C(1), 2}, {C(2), 2}}, "1 2 3 4")));
-  // hfg.add(HybridDiscreteFactor(DecisionTreeFactor({{C(2), 2}, {C(3), 2}}, "1
-  // 2 3 4"))); hfg.add(HybridDiscreteFactor(DecisionTreeFactor({{C(3), 2},
-  // {C(1), 2}}, "1 2 2 1")));
 
-  auto result = hfg.eliminateSequential(
+  HybridBayesNet::shared_ptr result = hfg.eliminateSequential(
-      Ordering::ColamdConstrainedLast(hfg, {C(1), C(2)}));
+      Ordering::ColamdConstrainedLast(hfg, {M(1), M(2)}));
 
-  GTSAM_PRINT(*result);
+  // There are 4 variables (2 continuous + 2 discrete) in the bayes net.
+  EXPECT_LONGS_EQUAL(4, result->size());
 }
 
 /* ************************************************************************* */
 TEST(HybridGaussianFactorGraph, eliminateFullMultifrontalSimple) {
   HybridGaussianFactorGraph hfg;
 
-  DiscreteKey c1(C(1), 2);
+  DiscreteKey m1(M(1), 2);
 
   hfg.add(JacobianFactor(X(0), I_3x3, Z_3x1));
   hfg.add(JacobianFactor(X(0), I_3x3, X(1), -I_3x3, Z_3x1));
 
-  // DecisionTree<Key, GaussianFactor::shared_ptr> dt(
-  //     C(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
-  //     boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones()));
-
-  // hfg.add(GaussianMixtureFactor({X(1)}, {c1}, dt));
   hfg.add(GaussianMixtureFactor::FromFactors(
-      {X(1)}, {{C(1), 2}},
+      {X(1)}, {{M(1), 2}},
       {boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
        boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones())}));
 
-  // hfg.add(GaussianMixtureFactor({X(0)}, {c1}, dt));
+  hfg.add(DecisionTreeFactor(m1, {2, 8}));
-  hfg.add(DecisionTreeFactor(c1, {2, 8}));
+  hfg.add(DecisionTreeFactor({{M(1), 2}, {M(2), 2}}, "1 2 3 4"));
-  hfg.add(DecisionTreeFactor({{C(1), 2}, {C(2), 2}}, "1 2 3 4"));
-  // hfg.add(HybridDiscreteFactor(DecisionTreeFactor({{C(2), 2}, {C(3), 2}}, "1
-  // 2 3 4"))); hfg.add(HybridDiscreteFactor(DecisionTreeFactor({{C(3), 2},
-  // {C(1), 2}}, "1 2 2 1")));
 
-  auto result = hfg.eliminateMultifrontal(
+  HybridBayesTree::shared_ptr result =
-      Ordering::ColamdConstrainedLast(hfg, {C(1), C(2)}));
+      hfg.eliminateMultifrontal(hfg.getHybridOrdering());
 
-  GTSAM_PRINT(*result);
+  // The bayes tree should have 3 cliques
-  GTSAM_PRINT(*result->marginalFactor(C(2)));
+  EXPECT_LONGS_EQUAL(3, result->size());
+  // GTSAM_PRINT(*result);
+  // GTSAM_PRINT(*result->marginalFactor(M(2)));
 }
 
 /* ************************************************************************* */
 TEST(HybridGaussianFactorGraph, eliminateFullMultifrontalCLG) {
   HybridGaussianFactorGraph hfg;
 
-  DiscreteKey c(C(1), 2);
+  DiscreteKey m(M(1), 2);
 
+  // Prior on x0
   hfg.add(JacobianFactor(X(0), I_3x3, Z_3x1));
+  // Factor between x0-x1
   hfg.add(JacobianFactor(X(0), I_3x3, X(1), -I_3x3, Z_3x1));
 
+  // Decision tree with different modes on x1
   DecisionTree<Key, GaussianFactor::shared_ptr> dt(
-      C(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
+      M(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
       boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones()));
 
-  hfg.add(GaussianMixtureFactor({X(1)}, {c}, dt));
+  // Hybrid factor P(x1|c1)
-  hfg.add(HybridDiscreteFactor(DecisionTreeFactor(c, {2, 8})));
+  hfg.add(GaussianMixtureFactor({X(1)}, {m}, dt));
-  //  hfg.add(HybridDiscreteFactor(DecisionTreeFactor({{C(1), 2}, {C(2), 2}}, "1
+  // Prior factor on c1
-  //  2 3 4")));
+  hfg.add(HybridDiscreteFactor(DecisionTreeFactor(m, {2, 8})));
 
-  auto ordering_full = Ordering::ColamdConstrainedLast(hfg, {C(1)});
+  // Get a constrained ordering keeping c1 last
+  auto ordering_full = hfg.getHybridOrdering();
 
+  // Returns a Hybrid Bayes Tree with distribution P(x0|x1)P(x1|c1)P(c1)
   HybridBayesTree::shared_ptr hbt = hfg.eliminateMultifrontal(ordering_full);
 
-  GTSAM_PRINT(*hbt);
+  EXPECT_LONGS_EQUAL(3, hbt->size());
-  /*
-  Explanation: the Junction tree will need to reeliminate to get to the marginal
-  on X(1), which is not possible because it involves eliminating discrete before
-  continuous. The solution to this, however, is in Murphy02. TLDR is that this
-  is 1. expensive and 2. inexact. neverless it is doable. And I believe that we
-  should do this.
-  */
 }
 
 /* ************************************************************************* */
@@ -233,66 +235,72 @@ TEST(HybridGaussianFactorGraph, eliminateFullMultifrontalTwoClique) {
   hfg.add(JacobianFactor(X(1), I_3x3, X(2), -I_3x3, Z_3x1));
 
   {
-    // DecisionTree<Key, GaussianFactor::shared_ptr> dt(
-    //     C(0), boost::make_shared<JacobianFactor>(X(0), I_3x3, Z_3x1),
-    //     boost::make_shared<JacobianFactor>(X(0), I_3x3, Vector3::Ones()));
-
     hfg.add(GaussianMixtureFactor::FromFactors(
-        {X(0)}, {{C(0), 2}},
+        {X(0)}, {{M(0), 2}},
         {boost::make_shared<JacobianFactor>(X(0), I_3x3, Z_3x1),
          boost::make_shared<JacobianFactor>(X(0), I_3x3, Vector3::Ones())}));
 
     DecisionTree<Key, GaussianFactor::shared_ptr> dt1(
-        C(1), boost::make_shared<JacobianFactor>(X(2), I_3x3, Z_3x1),
+        M(1), boost::make_shared<JacobianFactor>(X(2), I_3x3, Z_3x1),
         boost::make_shared<JacobianFactor>(X(2), I_3x3, Vector3::Ones()));
 
-    hfg.add(GaussianMixtureFactor({X(2)}, {{C(1), 2}}, dt1));
+    hfg.add(GaussianMixtureFactor({X(2)}, {{M(1), 2}}, dt1));
   }
 
-  // hfg.add(HybridDiscreteFactor(DecisionTreeFactor(c, {2, 8})));
   hfg.add(HybridDiscreteFactor(
-      DecisionTreeFactor({{C(1), 2}, {C(2), 2}}, "1 2 3 4")));
+      DecisionTreeFactor({{M(1), 2}, {M(2), 2}}, "1 2 3 4")));
 
   hfg.add(JacobianFactor(X(3), I_3x3, X(4), -I_3x3, Z_3x1));
   hfg.add(JacobianFactor(X(4), I_3x3, X(5), -I_3x3, Z_3x1));
 
   {
     DecisionTree<Key, GaussianFactor::shared_ptr> dt(
-        C(3), boost::make_shared<JacobianFactor>(X(3), I_3x3, Z_3x1),
+        M(3), boost::make_shared<JacobianFactor>(X(3), I_3x3, Z_3x1),
         boost::make_shared<JacobianFactor>(X(3), I_3x3, Vector3::Ones()));
 
-    hfg.add(GaussianMixtureFactor({X(3)}, {{C(3), 2}}, dt));
+    hfg.add(GaussianMixtureFactor({X(3)}, {{M(3), 2}}, dt));
 
     DecisionTree<Key, GaussianFactor::shared_ptr> dt1(
-        C(2), boost::make_shared<JacobianFactor>(X(5), I_3x3, Z_3x1),
+        M(2), boost::make_shared<JacobianFactor>(X(5), I_3x3, Z_3x1),
         boost::make_shared<JacobianFactor>(X(5), I_3x3, Vector3::Ones()));
 
-    hfg.add(GaussianMixtureFactor({X(5)}, {{C(2), 2}}, dt1));
+    hfg.add(GaussianMixtureFactor({X(5)}, {{M(2), 2}}, dt1));
   }
 
   auto ordering_full =
-      Ordering::ColamdConstrainedLast(hfg, {C(0), C(1), C(2), C(3)});
+      Ordering::ColamdConstrainedLast(hfg, {M(0), M(1), M(2), M(3)});
-
-  GTSAM_PRINT(ordering_full);
 
   HybridBayesTree::shared_ptr hbt;
   HybridGaussianFactorGraph::shared_ptr remaining;
   std::tie(hbt, remaining) = hfg.eliminatePartialMultifrontal(ordering_full);
 
-  GTSAM_PRINT(*hbt);
+  // 9 cliques in the bayes tree and 0 remaining variables to eliminate.
+  EXPECT_LONGS_EQUAL(9, hbt->size());
+  EXPECT_LONGS_EQUAL(0, remaining->size());
 
-  GTSAM_PRINT(*remaining);
-
-  hbt->dot(std::cout);
   /*
-  Explanation: the Junction tree will need to reeliminate to get to the marginal
+  (Fan) Explanation: the Junction tree will need to reeliminate to get to the
-  on X(1), which is not possible because it involves eliminating discrete before
+  marginal on X(1), which is not possible because it involves eliminating
-  continuous. The solution to this, however, is in Murphy02. TLDR is that this
+  discrete before continuous. The solution to this, however, is in Murphy02.
-  is 1. expensive and 2. inexact. neverless it is doable. And I believe that we
+  TLDR is that this is 1. expensive and 2. inexact. nevertheless it is doable.
-  should do this.
+  And I believe that we should do this.
   */
 }
 
+void dotPrint(const HybridGaussianFactorGraph::shared_ptr &hfg,
+              const HybridBayesTree::shared_ptr &hbt,
+              const Ordering &ordering) {
+  DotWriter dw;
+  dw.positionHints['c'] = 2;
+  dw.positionHints['x'] = 1;
+  std::cout << hfg->dot(DefaultKeyFormatter, dw);
+  std::cout << "\n";
+  hbt->dot(std::cout);
+
+  std::cout << "\n";
+  std::cout << hfg->eliminateSequential(ordering)->dot(DefaultKeyFormatter, dw);
+}
+
 /* ************************************************************************* */
 // TODO(fan): make a graph like Varun's paper one
 TEST(HybridGaussianFactorGraph, Switching) {
@@ -303,13 +311,13 @@ TEST(HybridGaussianFactorGraph, Switching) {
   // X(3), X(7)
   // X(2), X(8)
   // X(1), X(4), X(6), X(9)
-  // C(5) will be the center, C(1-4), C(6-8)
+  // M(5) will be the center, M(1-4), M(6-8)
-  // C(3), C(7)
+  // M(3), M(7)
-  // C(1), C(4), C(2), C(6), C(8)
+  // M(1), M(4), M(2), M(6), M(8)
   // auto ordering_full =
   //     Ordering(KeyVector{X(1), X(4), X(2), X(6), X(9), X(8), X(3), X(7),
   //     X(5),
-  //                        C(1), C(4), C(2), C(6), C(8), C(3), C(7), C(5)});
+  //                        M(1), M(4), M(2), M(6), M(8), M(3), M(7), M(5)});
   KeyVector ordering;
 
   {
@@ -326,79 +334,32 @@ TEST(HybridGaussianFactorGraph, Switching) {
     for (auto &l : lvls) {
       l = -l;
     }
-    std::copy(lvls.begin(), lvls.end(),
-              std::ostream_iterator<int>(std::cout, ","));
-    std::cout << "\n";
   }
   {
     std::vector<int> naturalC(N - 1);
     std::iota(naturalC.begin(), naturalC.end(), 1);
     std::vector<Key> ordC;
     std::transform(naturalC.begin(), naturalC.end(), std::back_inserter(ordC),
-                   [](int x) { return C(x); });
+                   [](int x) { return M(x); });
     KeyVector ndC;
     std::vector<int> lvls;
 
     // std::copy(ordC.begin(), ordC.end(), std::back_inserter(ordering));
     std::tie(ndC, lvls) = makeBinaryOrdering(ordC);
     std::copy(ndC.begin(), ndC.end(), std::back_inserter(ordering));
-    std::copy(lvls.begin(), lvls.end(),
-              std::ostream_iterator<int>(std::cout, ","));
   }
   auto ordering_full = Ordering(ordering);
 
-  // auto ordering_full =
-  //     Ordering();
-
-  // for (int i = 1; i <= 9; i++) {
-  //   ordering_full.push_back(X(i));
-  // }
-
-  // for (int i = 1; i < 9; i++) {
-  //   ordering_full.push_back(C(i));
-  // }
-
-  // auto ordering_full =
-  //     Ordering(KeyVector{X(1), X(4), X(2), X(6), X(9), X(8), X(3), X(7),
-  //     X(5),
-  //                        C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8)});
-
   // GTSAM_PRINT(*hfg);
-  GTSAM_PRINT(ordering_full);
+  // GTSAM_PRINT(ordering_full);
 
   HybridBayesTree::shared_ptr hbt;
   HybridGaussianFactorGraph::shared_ptr remaining;
   std::tie(hbt, remaining) = hfg->eliminatePartialMultifrontal(ordering_full);
 
-  // GTSAM_PRINT(*hbt);
+  // 12 cliques in the bayes tree and 0 remaining variables to eliminate.
-
+  EXPECT_LONGS_EQUAL(12, hbt->size());
-  // GTSAM_PRINT(*remaining);
+  EXPECT_LONGS_EQUAL(0, remaining->size());
-
-  {
-    DotWriter dw;
-    dw.positionHints['c'] = 2;
-    dw.positionHints['x'] = 1;
-    std::cout << hfg->dot(DefaultKeyFormatter, dw);
-    std::cout << "\n";
-    hbt->dot(std::cout);
-  }
-
-  {
-    DotWriter dw;
-    // dw.positionHints['c'] = 2;
-    // dw.positionHints['x'] = 1;
-    std::cout << "\n";
-    std::cout << hfg->eliminateSequential(ordering_full)
-                     ->dot(DefaultKeyFormatter, dw);
-  }
-  /*
-  Explanation: the Junction tree will need to reeliminate to get to the marginal
-  on X(1), which is not possible because it involves eliminating discrete before
-  continuous. The solution to this, however, is in Murphy02. TLDR is that this
-  is 1. expensive and 2. inexact. neverless it is doable. And I believe that we
-  should do this.
-  */
-  hbt->marginalFactor(C(11))->print("HBT: ");
 }
 
 /* ************************************************************************* */
@@ -411,13 +372,13 @@ TEST(HybridGaussianFactorGraph, SwitchingISAM) {
   // X(3), X(7)
   // X(2), X(8)
   // X(1), X(4), X(6), X(9)
-  // C(5) will be the center, C(1-4), C(6-8)
+  // M(5) will be the center, M(1-4), M(6-8)
-  // C(3), C(7)
+  // M(3), M(7)
-  // C(1), C(4), C(2), C(6), C(8)
+  // M(1), M(4), M(2), M(6), M(8)
   // auto ordering_full =
   //     Ordering(KeyVector{X(1), X(4), X(2), X(6), X(9), X(8), X(3), X(7),
   //     X(5),
-  //                        C(1), C(4), C(2), C(6), C(8), C(3), C(7), C(5)});
+  //                        M(1), M(4), M(2), M(6), M(8), M(3), M(7), M(5)});
   KeyVector ordering;
 
   {
@@ -434,67 +395,37 @@ TEST(HybridGaussianFactorGraph, SwitchingISAM) {
     for (auto &l : lvls) {
       l = -l;
     }
-    std::copy(lvls.begin(), lvls.end(),
-              std::ostream_iterator<int>(std::cout, ","));
-    std::cout << "\n";
   }
   {
     std::vector<int> naturalC(N - 1);
     std::iota(naturalC.begin(), naturalC.end(), 1);
     std::vector<Key> ordC;
     std::transform(naturalC.begin(), naturalC.end(), std::back_inserter(ordC),
-                   [](int x) { return C(x); });
+                   [](int x) { return M(x); });
     KeyVector ndC;
     std::vector<int> lvls;
 
     // std::copy(ordC.begin(), ordC.end(), std::back_inserter(ordering));
     std::tie(ndC, lvls) = makeBinaryOrdering(ordC);
     std::copy(ndC.begin(), ndC.end(), std::back_inserter(ordering));
-    std::copy(lvls.begin(), lvls.end(),
-              std::ostream_iterator<int>(std::cout, ","));
   }
   auto ordering_full = Ordering(ordering);
 
-  // GTSAM_PRINT(*hfg);
-  GTSAM_PRINT(ordering_full);
-
   HybridBayesTree::shared_ptr hbt;
   HybridGaussianFactorGraph::shared_ptr remaining;
   std::tie(hbt, remaining) = hfg->eliminatePartialMultifrontal(ordering_full);
 
-  // GTSAM_PRINT(*hbt);
-
-  // GTSAM_PRINT(*remaining);
-
-  {
-    DotWriter dw;
-    dw.positionHints['c'] = 2;
-    dw.positionHints['x'] = 1;
-    std::cout << hfg->dot(DefaultKeyFormatter, dw);
-    std::cout << "\n";
-    hbt->dot(std::cout);
-  }
-
-  {
-    DotWriter dw;
-    // dw.positionHints['c'] = 2;
-    // dw.positionHints['x'] = 1;
-    std::cout << "\n";
-    std::cout << hfg->eliminateSequential(ordering_full)
-                     ->dot(DefaultKeyFormatter, dw);
-  }
-
   auto new_fg = makeSwitchingChain(12);
   auto isam = HybridGaussianISAM(*hbt);
 
-  {
+  // Run an ISAM update.
-    HybridGaussianFactorGraph factorGraph;
+  HybridGaussianFactorGraph factorGraph;
-    factorGraph.push_back(new_fg->at(new_fg->size() - 2));
+  factorGraph.push_back(new_fg->at(new_fg->size() - 2));
-    factorGraph.push_back(new_fg->at(new_fg->size() - 1));
+  factorGraph.push_back(new_fg->at(new_fg->size() - 1));
-    isam.update(factorGraph);
+  isam.update(factorGraph);
-    std::cout << isam.dot();
+
-    isam.marginalFactor(C(11))->print();
+  // ISAM should have 12 factors after the last update
-  }
+  EXPECT_LONGS_EQUAL(12, isam.size());
 }
 
 /* ************************************************************************* */
@@ -517,23 +448,8 @@ TEST(HybridGaussianFactorGraph, SwitchingTwoVar) {
     ordX.emplace_back(Y(i));
   }
 
-  // {
-  //   KeyVector ndX;
-  //   std::vector<int> lvls;
-  //   std::tie(ndX, lvls) = makeBinaryOrdering(naturalX);
-  //   std::copy(ndX.begin(), ndX.end(), std::back_inserter(ordering));
-  //   std::copy(lvls.begin(), lvls.end(),
-  //             std::ostream_iterator<int>(std::cout, ","));
-  //   std::cout << "\n";
-
-  //   for (size_t i = 0; i < N; i++) {
-  //     ordX.emplace_back(X(ndX[i]));
-  //     ordX.emplace_back(Y(ndX[i]));
-  //   }
-  // }
-
   for (size_t i = 1; i <= N - 1; i++) {
-    ordX.emplace_back(C(i));
+    ordX.emplace_back(M(i));
   }
   for (size_t i = 1; i <= N - 1; i++) {
     ordX.emplace_back(D(i));
@@ -545,8 +461,8 @@ TEST(HybridGaussianFactorGraph, SwitchingTwoVar) {
     dw.positionHints['c'] = 0;
     dw.positionHints['d'] = 3;
     dw.positionHints['y'] = 2;
-    std::cout << hfg->dot(DefaultKeyFormatter, dw);
+    // std::cout << hfg->dot(DefaultKeyFormatter, dw);
-    std::cout << "\n";
+    // std::cout << "\n";
   }
 
   {
@@ -555,10 +471,10 @@ TEST(HybridGaussianFactorGraph, SwitchingTwoVar) {
     // dw.positionHints['c'] = 0;
     // dw.positionHints['d'] = 3;
     dw.positionHints['x'] = 1;
-    std::cout << "\n";
+    // std::cout << "\n";
     // std::cout << hfg->eliminateSequential(Ordering(ordX))
     //                  ->dot(DefaultKeyFormatter, dw);
-    hfg->eliminateMultifrontal(Ordering(ordX))->dot(std::cout);
+    // hfg->eliminateMultifrontal(Ordering(ordX))->dot(std::cout);
   }
 
   Ordering ordering_partial;
@@ -566,25 +482,45 @@ TEST(HybridGaussianFactorGraph, SwitchingTwoVar) {
     ordering_partial.emplace_back(X(i));
     ordering_partial.emplace_back(Y(i));
   }
-  {
+  HybridBayesNet::shared_ptr hbn;
-    HybridBayesNet::shared_ptr hbn;
+  HybridGaussianFactorGraph::shared_ptr remaining;
-    HybridGaussianFactorGraph::shared_ptr remaining;
+  std::tie(hbn, remaining) = hfg->eliminatePartialSequential(ordering_partial);
-    std::tie(hbn, remaining) =
-        hfg->eliminatePartialSequential(ordering_partial);
 
-    // remaining->print();
+  EXPECT_LONGS_EQUAL(14, hbn->size());
-    {
+  EXPECT_LONGS_EQUAL(11, remaining->size());
-      DotWriter dw;
+
-      dw.positionHints['x'] = 1;
+  {
-      dw.positionHints['c'] = 0;
+    DotWriter dw;
-      dw.positionHints['d'] = 3;
+    dw.positionHints['x'] = 1;
-      dw.positionHints['y'] = 2;
+    dw.positionHints['c'] = 0;
-      std::cout << remaining->dot(DefaultKeyFormatter, dw);
+    dw.positionHints['d'] = 3;
-      std::cout << "\n";
+    dw.positionHints['y'] = 2;
-    }
+    // std::cout << remaining->dot(DefaultKeyFormatter, dw);
+    // std::cout << "\n";
   }
 }
 
+TEST(HybridGaussianFactorGraph, optimize) {
+  HybridGaussianFactorGraph hfg;
+
+  DiscreteKey c1(C(1), 2);
+
+  hfg.add(JacobianFactor(X(0), I_3x3, Z_3x1));
+  hfg.add(JacobianFactor(X(0), I_3x3, X(1), -I_3x3, Z_3x1));
+
+  DecisionTree<Key, GaussianFactor::shared_ptr> dt(
+      C(1), boost::make_shared<JacobianFactor>(X(1), I_3x3, Z_3x1),
+      boost::make_shared<JacobianFactor>(X(1), I_3x3, Vector3::Ones()));
+
+  hfg.add(GaussianMixtureFactor({X(1)}, {c1}, dt));
+
+  auto result =
+      hfg.eliminateSequential(Ordering::ColamdConstrainedLast(hfg, {C(1)}));
+
+  HybridValues hv = result->optimize();
+
+  EXPECT(assert_equal(hv.atDiscrete(C(1)), int(0)));
+}
 /* ************************************************************************* */
 int main() {
   TestResult tr;

gtsam/hybrid/tests/testGaussianMixtureFactor.cpp

@@ -74,7 +74,7 @@ TEST(GaussianMixtureFactor, Sum) {
   // Check that number of keys is 3
   EXPECT_LONGS_EQUAL(3, mixtureFactorA.keys().size());
 
-  // Check that number of discrete keys is 1 // TODO(Frank): should not exist?
+  // Check that number of discrete keys is 1
   EXPECT_LONGS_EQUAL(1, mixtureFactorA.discreteKeys().size());
 
   // Create sum of two mixture factors: it will be a decision tree now on both
@@ -104,7 +104,7 @@ TEST(GaussianMixtureFactor, Printing) {
   GaussianMixtureFactor mixtureFactor({X(1), X(2)}, {m1}, factors);
 
   std::string expected =
-      R"(Hybrid x1 x2; 1 ]{
+      R"(Hybrid [x1 x2; 1]{
  Choice(1) 
  0 Leaf :
   A[x1] = [

gtsam/hybrid/tests/testHybridBayesNet.cpp

@@ -0,0 +1,189 @@
+/* ----------------------------------------------------------------------------
+
+ * 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    testHybridBayesNet.cpp
+ * @brief   Unit tests for HybridBayesNet
+ * @author  Varun Agrawal
+ * @author  Fan Jiang
+ * @author  Frank Dellaert
+ * @date    December 2021
+ */
+
+#include <gtsam/base/serializationTestHelpers.h>
+#include <gtsam/hybrid/HybridBayesNet.h>
+#include <gtsam/hybrid/HybridBayesTree.h>
+#include <gtsam/nonlinear/NonlinearFactorGraph.h>
+
+#include "Switching.h"
+
+// Include for test suite
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+using namespace gtsam::serializationTestHelpers;
+
+using noiseModel::Isotropic;
+using symbol_shorthand::M;
+using symbol_shorthand::X;
+
+static const DiscreteKey Asia(0, 2);
+
+/* ****************************************************************************/
+// Test creation
+TEST(HybridBayesNet, Creation) {
+  HybridBayesNet bayesNet;
+
+  bayesNet.add(Asia, "99/1");
+
+  DiscreteConditional expected(Asia, "99/1");
+
+  CHECK(bayesNet.atDiscrete(0));
+  auto& df = *bayesNet.atDiscrete(0);
+  EXPECT(df.equals(expected));
+}
+
+/* ****************************************************************************/
+// Test choosing an assignment of conditionals
+TEST(HybridBayesNet, Choose) {
+  Switching s(4);
+
+  Ordering ordering;
+  for (auto&& kvp : s.linearizationPoint) {
+    ordering += kvp.key;
+  }
+
+  HybridBayesNet::shared_ptr hybridBayesNet;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      s.linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+  DiscreteValues assignment;
+  assignment[M(1)] = 1;
+  assignment[M(2)] = 1;
+  assignment[M(3)] = 0;
+
+  GaussianBayesNet gbn = hybridBayesNet->choose(assignment);
+
+  EXPECT_LONGS_EQUAL(4, gbn.size());
+
+  EXPECT(assert_equal(*(*boost::dynamic_pointer_cast<GaussianMixture>(
+                          hybridBayesNet->atMixture(0)))(assignment),
+                      *gbn.at(0)));
+  EXPECT(assert_equal(*(*boost::dynamic_pointer_cast<GaussianMixture>(
+                          hybridBayesNet->atMixture(1)))(assignment),
+                      *gbn.at(1)));
+  EXPECT(assert_equal(*(*boost::dynamic_pointer_cast<GaussianMixture>(
+                          hybridBayesNet->atMixture(2)))(assignment),
+                      *gbn.at(2)));
+  EXPECT(assert_equal(*(*boost::dynamic_pointer_cast<GaussianMixture>(
+                          hybridBayesNet->atMixture(3)))(assignment),
+                      *gbn.at(3)));
+}
+
+/* ****************************************************************************/
+// Test bayes net optimize
+TEST(HybridBayesNet, OptimizeAssignment) {
+  Switching s(4);
+
+  Ordering ordering;
+  for (auto&& kvp : s.linearizationPoint) {
+    ordering += kvp.key;
+  }
+
+  HybridBayesNet::shared_ptr hybridBayesNet;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      s.linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+  DiscreteValues assignment;
+  assignment[M(1)] = 1;
+  assignment[M(2)] = 1;
+  assignment[M(3)] = 1;
+
+  VectorValues delta = hybridBayesNet->optimize(assignment);
+
+  // The linearization point has the same value as the key index,
+  // e.g. X(1) = 1, X(2) = 2,
+  // but the factors specify X(k) = k-1, so delta should be -1.
+  VectorValues expected_delta;
+  expected_delta.insert(make_pair(X(1), -Vector1::Ones()));
+  expected_delta.insert(make_pair(X(2), -Vector1::Ones()));
+  expected_delta.insert(make_pair(X(3), -Vector1::Ones()));
+  expected_delta.insert(make_pair(X(4), -Vector1::Ones()));
+
+  EXPECT(assert_equal(expected_delta, delta));
+}
+
+/* ****************************************************************************/
+// Test bayes net optimize
+TEST(HybridBayesNet, Optimize) {
+  Switching s(4);
+
+  Ordering hybridOrdering = s.linearizedFactorGraph.getHybridOrdering();
+  HybridBayesNet::shared_ptr hybridBayesNet =
+      s.linearizedFactorGraph.eliminateSequential(hybridOrdering);
+
+  HybridValues delta = hybridBayesNet->optimize();
+
+  DiscreteValues expectedAssignment;
+  expectedAssignment[M(1)] = 1;
+  expectedAssignment[M(2)] = 0;
+  expectedAssignment[M(3)] = 1;
+  EXPECT(assert_equal(expectedAssignment, delta.discrete()));
+
+  VectorValues expectedValues;
+  expectedValues.insert(X(1), -0.999904 * Vector1::Ones());
+  expectedValues.insert(X(2), -0.99029 * Vector1::Ones());
+  expectedValues.insert(X(3), -1.00971 * Vector1::Ones());
+  expectedValues.insert(X(4), -1.0001 * Vector1::Ones());
+
+  EXPECT(assert_equal(expectedValues, delta.continuous(), 1e-5));
+}
+
+/* ****************************************************************************/
+// Test bayes net multifrontal optimize
+TEST(HybridBayesNet, OptimizeMultifrontal) {
+  Switching s(4);
+
+  Ordering hybridOrdering = s.linearizedFactorGraph.getHybridOrdering();
+  HybridBayesTree::shared_ptr hybridBayesTree =
+      s.linearizedFactorGraph.eliminateMultifrontal(hybridOrdering);
+  HybridValues delta = hybridBayesTree->optimize();
+
+  VectorValues expectedValues;
+  expectedValues.insert(X(1), -0.999904 * Vector1::Ones());
+  expectedValues.insert(X(2), -0.99029 * Vector1::Ones());
+  expectedValues.insert(X(3), -1.00971 * Vector1::Ones());
+  expectedValues.insert(X(4), -1.0001 * Vector1::Ones());
+
+  EXPECT(assert_equal(expectedValues, delta.continuous(), 1e-5));
+}
+
+/* ****************************************************************************/
+// Test HybridBayesNet serialization.
+TEST(HybridBayesNet, Serialization) {
+  Switching s(4);
+  Ordering ordering = s.linearizedFactorGraph.getHybridOrdering();
+  HybridBayesNet hbn = *(s.linearizedFactorGraph.eliminateSequential(ordering));
+
+  EXPECT(equalsObj<HybridBayesNet>(hbn));
+  EXPECT(equalsXML<HybridBayesNet>(hbn));
+  EXPECT(equalsBinary<HybridBayesNet>(hbn));
+}
+
+/* ************************************************************************* */
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}
+/* ************************************************************************* */

gtsam/hybrid/tests/testHybridBayesTree.cpp

@@ -0,0 +1,166 @@
+/* ----------------------------------------------------------------------------
+
+ * 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    testHybridBayesTree.cpp
+ * @brief   Unit tests for HybridBayesTree
+ * @author  Varun Agrawal
+ * @date    August 2022
+ */
+
+#include <gtsam/base/serializationTestHelpers.h>
+#include <gtsam/discrete/DiscreteFactorGraph.h>
+#include <gtsam/hybrid/HybridBayesTree.h>
+#include <gtsam/hybrid/HybridGaussianISAM.h>
+
+#include "Switching.h"
+
+// Include for test suite
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+using noiseModel::Isotropic;
+using symbol_shorthand::M;
+using symbol_shorthand::X;
+
+/* ****************************************************************************/
+// Test for optimizing a HybridBayesTree with a given assignment.
+TEST(HybridBayesTree, OptimizeAssignment) {
+  Switching s(4);
+
+  HybridGaussianISAM isam;
+  HybridGaussianFactorGraph graph1;
+
+  // Add the 3 hybrid factors, x1-x2, x2-x3, x3-x4
+  for (size_t i = 1; i < 4; i++) {
+    graph1.push_back(s.linearizedFactorGraph.at(i));
+  }
+
+  // Add the Gaussian factors, 1 prior on X(1),
+  // 3 measurements on X(2), X(3), X(4)
+  graph1.push_back(s.linearizedFactorGraph.at(0));
+  for (size_t i = 4; i <= 7; i++) {
+    graph1.push_back(s.linearizedFactorGraph.at(i));
+  }
+
+  // Add the discrete factors
+  for (size_t i = 7; i <= 9; i++) {
+    graph1.push_back(s.linearizedFactorGraph.at(i));
+  }
+
+  isam.update(graph1);
+
+  DiscreteValues assignment;
+  assignment[M(1)] = 1;
+  assignment[M(2)] = 1;
+  assignment[M(3)] = 1;
+
+  VectorValues delta = isam.optimize(assignment);
+
+  // The linearization point has the same value as the key index,
+  // e.g. X(1) = 1, X(2) = 2,
+  // but the factors specify X(k) = k-1, so delta should be -1.
+  VectorValues expected_delta;
+  expected_delta.insert(make_pair(X(1), -Vector1::Ones()));
+  expected_delta.insert(make_pair(X(2), -Vector1::Ones()));
+  expected_delta.insert(make_pair(X(3), -Vector1::Ones()));
+  expected_delta.insert(make_pair(X(4), -Vector1::Ones()));
+
+  EXPECT(assert_equal(expected_delta, delta));
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t k = 1; k <= s.K; k++) ordering += X(k);
+
+  HybridBayesNet::shared_ptr hybridBayesNet;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      s.linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+  GaussianBayesNet gbn = hybridBayesNet->choose(assignment);
+  VectorValues expected = gbn.optimize();
+
+  EXPECT(assert_equal(expected, delta));
+}
+
+/* ****************************************************************************/
+// Test for optimizing a HybridBayesTree.
+TEST(HybridBayesTree, Optimize) {
+  Switching s(4);
+
+  HybridGaussianISAM isam;
+  HybridGaussianFactorGraph graph1;
+
+  // Add the 3 hybrid factors, x1-x2, x2-x3, x3-x4
+  for (size_t i = 1; i < 4; i++) {
+    graph1.push_back(s.linearizedFactorGraph.at(i));
+  }
+
+  // Add the Gaussian factors, 1 prior on X(1),
+  // 3 measurements on X(2), X(3), X(4)
+  graph1.push_back(s.linearizedFactorGraph.at(0));
+  for (size_t i = 4; i <= 6; i++) {
+    graph1.push_back(s.linearizedFactorGraph.at(i));
+  }
+
+  // Add the discrete factors
+  for (size_t i = 7; i <= 9; i++) {
+    graph1.push_back(s.linearizedFactorGraph.at(i));
+  }
+
+  isam.update(graph1);
+
+  HybridValues delta = isam.optimize();
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t k = 1; k <= s.K; k++) ordering += X(k);
+
+  HybridBayesNet::shared_ptr hybridBayesNet;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      s.linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+  DiscreteFactorGraph dfg;
+  for (auto&& f : *remainingFactorGraph) {
+    auto factor = dynamic_pointer_cast<HybridDiscreteFactor>(f);
+    dfg.push_back(
+        boost::dynamic_pointer_cast<DecisionTreeFactor>(factor->inner()));
+  }
+
+  DiscreteValues expectedMPE = dfg.optimize();
+  VectorValues expectedValues = hybridBayesNet->optimize(expectedMPE);
+
+  EXPECT(assert_equal(expectedMPE, delta.discrete()));
+  EXPECT(assert_equal(expectedValues, delta.continuous()));
+}
+
+/* ****************************************************************************/
+// Test HybridBayesTree serialization.
+TEST(HybridBayesTree, Serialization) {
+  Switching s(4);
+  Ordering ordering = s.linearizedFactorGraph.getHybridOrdering();
+  HybridBayesTree hbt =
+      *(s.linearizedFactorGraph.eliminateMultifrontal(ordering));
+
+  using namespace gtsam::serializationTestHelpers;
+  EXPECT(equalsObj<HybridBayesTree>(hbt));
+  EXPECT(equalsXML<HybridBayesTree>(hbt));
+  EXPECT(equalsBinary<HybridBayesTree>(hbt));
+}
+
+/* ************************************************************************* */
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}
+/* ************************************************************************* */

gtsam/hybrid/tests/testHybridFactorGraph.cpp

@@ -0,0 +1,45 @@
+/* ----------------------------------------------------------------------------
+ * 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    testHybridFactorGraph.cpp
+ * @brief   Unit tests for HybridFactorGraph
+ * @author  Varun Agrawal
+ * @date    May 2021
+ */
+
+#include <CppUnitLite/Test.h>
+#include <CppUnitLite/TestHarness.h>
+#include <gtsam/base/TestableAssertions.h>
+#include <gtsam/base/utilities.h>
+#include <gtsam/hybrid/HybridFactorGraph.h>
+#include <gtsam/inference/Symbol.h>
+#include <gtsam/nonlinear/PriorFactor.h>
+
+using namespace std;
+using namespace gtsam;
+using noiseModel::Isotropic;
+using symbol_shorthand::L;
+using symbol_shorthand::M;
+using symbol_shorthand::X;
+
+/* ****************************************************************************
+ * Test that any linearizedFactorGraph gaussian factors are appended to the
+ * existing gaussian factor graph in the hybrid factor graph.
+ */
+TEST(HybridFactorGraph, Constructor) {
+  // Initialize the hybrid factor graph
+  HybridFactorGraph fg;
+}
+
+/* ************************************************************************* */
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}
+/* ************************************************************************* */

gtsam/hybrid/tests/testHybridIncremental.cpp

@@ -0,0 +1,563 @@
+/* ----------------------------------------------------------------------------
+
+ * 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    testHybridIncremental.cpp
+ * @brief   Unit tests for incremental inference
+ * @author  Fan Jiang, Varun Agrawal, Frank Dellaert
+ * @date    Jan 2021
+ */
+
+#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 <numeric>
+
+#include "Switching.h"
+
+// Include for test suite
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+using noiseModel::Isotropic;
+using symbol_shorthand::L;
+using symbol_shorthand::M;
+using symbol_shorthand::W;
+using symbol_shorthand::X;
+using symbol_shorthand::Y;
+using symbol_shorthand::Z;
+
+/* ****************************************************************************/
+// Test if we can perform elimination incrementally.
+TEST(HybridGaussianElimination, IncrementalElimination) {
+  Switching switching(3);
+  HybridGaussianISAM isam;
+  HybridGaussianFactorGraph graph1;
+
+  // Create initial factor graph
+  //  *        *      *
+  //  |        |      |
+  //  X1  -*-  X2 -*- X3
+  //   \*-M1-*/
+  graph1.push_back(switching.linearizedFactorGraph.at(0));  // P(X1)
+  graph1.push_back(switching.linearizedFactorGraph.at(1));  // P(X1, X2 | M1)
+  graph1.push_back(switching.linearizedFactorGraph.at(2));  // P(X2, X3 | M2)
+  graph1.push_back(switching.linearizedFactorGraph.at(5));  // P(M1)
+
+  // Run update step
+  isam.update(graph1);
+
+  // Check that after update we have 3 hybrid Bayes net nodes:
+  // P(X1 | X2, M1) and P(X2, X3 | M1, M2), P(M1, M2)
+  EXPECT_LONGS_EQUAL(3, isam.size());
+  EXPECT(isam[X(1)]->conditional()->frontals() == KeyVector{X(1)});
+  EXPECT(isam[X(1)]->conditional()->parents() == KeyVector({X(2), M(1)}));
+  EXPECT(isam[X(2)]->conditional()->frontals() == KeyVector({X(2), X(3)}));
+  EXPECT(isam[X(2)]->conditional()->parents() == KeyVector({M(1), M(2)}));
+
+  /********************************************************/
+  // New factor graph for incremental update.
+  HybridGaussianFactorGraph graph2;
+
+  graph1.push_back(switching.linearizedFactorGraph.at(3));  // P(X2)
+  graph2.push_back(switching.linearizedFactorGraph.at(4));  // P(X3)
+  graph2.push_back(switching.linearizedFactorGraph.at(6));  // P(M1, M2)
+
+  isam.update(graph2);
+
+  // Check that after the second update we have
+  // 1 additional hybrid Bayes net node:
+  // P(X2, X3 | M1, M2)
+  EXPECT_LONGS_EQUAL(3, isam.size());
+  EXPECT(isam[X(3)]->conditional()->frontals() == KeyVector({X(2), X(3)}));
+  EXPECT(isam[X(3)]->conditional()->parents() == KeyVector({M(1), M(2)}));
+}
+
+/* ****************************************************************************/
+// Test if we can incrementally do the inference
+TEST(HybridGaussianElimination, IncrementalInference) {
+  Switching switching(3);
+  HybridGaussianISAM isam;
+  HybridGaussianFactorGraph graph1;
+
+  // Create initial factor graph
+  //    *        *        *
+  //    |        |        |
+  //    X1  -*-  X2  -*-  X3
+  //         |        |
+  //      *-M1 - * - M2
+  graph1.push_back(switching.linearizedFactorGraph.at(0));  // P(X1)
+  graph1.push_back(switching.linearizedFactorGraph.at(1));  // P(X1, X2 | M1)
+  graph1.push_back(switching.linearizedFactorGraph.at(3));  // P(X2)
+  graph1.push_back(switching.linearizedFactorGraph.at(5));  // P(M1)
+
+  // Run update step
+  isam.update(graph1);
+
+  auto discreteConditional_m1 =
+      isam[M(1)]->conditional()->asDiscreteConditional();
+  EXPECT(discreteConditional_m1->keys() == KeyVector({M(1)}));
+
+  /********************************************************/
+  // New factor graph for incremental update.
+  HybridGaussianFactorGraph graph2;
+
+  graph2.push_back(switching.linearizedFactorGraph.at(2));  // P(X2, X3 | M2)
+  graph2.push_back(switching.linearizedFactorGraph.at(4));  // P(X3)
+  graph2.push_back(switching.linearizedFactorGraph.at(6));  // P(M1, M2)
+
+  isam.update(graph2);
+
+  /********************************************************/
+  // Run batch elimination so we can compare results.
+  Ordering ordering;
+  ordering += X(1);
+  ordering += X(2);
+  ordering += X(3);
+
+  // Now we calculate the actual factors using full elimination
+  HybridBayesTree::shared_ptr expectedHybridBayesTree;
+  HybridGaussianFactorGraph::shared_ptr expectedRemainingGraph;
+  std::tie(expectedHybridBayesTree, expectedRemainingGraph) =
+      switching.linearizedFactorGraph.eliminatePartialMultifrontal(ordering);
+
+  // The densities on X(1) should be the same
+  auto x1_conditional =
+      dynamic_pointer_cast<GaussianMixture>(isam[X(1)]->conditional()->inner());
+  auto actual_x1_conditional = dynamic_pointer_cast<GaussianMixture>(
+      (*expectedHybridBayesTree)[X(1)]->conditional()->inner());
+  EXPECT(assert_equal(*x1_conditional, *actual_x1_conditional));
+
+  // The densities on X(2) should be the same
+  auto x2_conditional =
+      dynamic_pointer_cast<GaussianMixture>(isam[X(2)]->conditional()->inner());
+  auto actual_x2_conditional = dynamic_pointer_cast<GaussianMixture>(
+      (*expectedHybridBayesTree)[X(2)]->conditional()->inner());
+  EXPECT(assert_equal(*x2_conditional, *actual_x2_conditional));
+
+  // The densities on X(3) should be the same
+  auto x3_conditional =
+      dynamic_pointer_cast<GaussianMixture>(isam[X(3)]->conditional()->inner());
+  auto actual_x3_conditional = dynamic_pointer_cast<GaussianMixture>(
+      (*expectedHybridBayesTree)[X(2)]->conditional()->inner());
+  EXPECT(assert_equal(*x3_conditional, *actual_x3_conditional));
+
+  // We only perform manual continuous elimination for 0,0.
+  // The other discrete probabilities on M(2) are calculated the same way
+  Ordering discrete_ordering;
+  discrete_ordering += M(1);
+  discrete_ordering += M(2);
+  HybridBayesTree::shared_ptr discreteBayesTree =
+      expectedRemainingGraph->eliminateMultifrontal(discrete_ordering);
+
+  DiscreteValues m00;
+  m00[M(1)] = 0, m00[M(2)] = 0;
+  DiscreteConditional decisionTree =
+      *(*discreteBayesTree)[M(2)]->conditional()->asDiscreteConditional();
+  double m00_prob = decisionTree(m00);
+
+  auto discreteConditional = isam[M(2)]->conditional()->asDiscreteConditional();
+
+  // Test if the probability values are as expected with regression tests.
+  DiscreteValues assignment;
+  EXPECT(assert_equal(m00_prob, 0.0619233, 1e-5));
+  assignment[M(1)] = 0;
+  assignment[M(2)] = 0;
+  EXPECT(assert_equal(m00_prob, (*discreteConditional)(assignment), 1e-5));
+  assignment[M(1)] = 1;
+  assignment[M(2)] = 0;
+  EXPECT(assert_equal(0.183743, (*discreteConditional)(assignment), 1e-5));
+  assignment[M(1)] = 0;
+  assignment[M(2)] = 1;
+  EXPECT(assert_equal(0.204159, (*discreteConditional)(assignment), 1e-5));
+  assignment[M(1)] = 1;
+  assignment[M(2)] = 1;
+  EXPECT(assert_equal(0.2, (*discreteConditional)(assignment), 1e-5));
+
+  // Check if the clique conditional generated from incremental elimination
+  // matches that of batch elimination.
+  auto expectedChordal = expectedRemainingGraph->eliminateMultifrontal();
+  auto expectedConditional = dynamic_pointer_cast<DecisionTreeFactor>(
+      (*expectedChordal)[M(2)]->conditional()->inner());
+  auto actualConditional = dynamic_pointer_cast<DecisionTreeFactor>(
+      isam[M(2)]->conditional()->inner());
+  EXPECT(assert_equal(*actualConditional, *expectedConditional, 1e-6));
+}
+
+/* ****************************************************************************/
+// Test if we can approximately do the inference
+TEST(HybridGaussianElimination, Approx_inference) {
+  Switching switching(4);
+  HybridGaussianISAM incrementalHybrid;
+  HybridGaussianFactorGraph graph1;
+
+  // Add the 3 hybrid factors, x1-x2, x2-x3, x3-x4
+  for (size_t i = 1; i < 4; i++) {
+    graph1.push_back(switching.linearizedFactorGraph.at(i));
+  }
+
+  // Add the Gaussian factors, 1 prior on X(1),
+  // 3 measurements on X(2), X(3), X(4)
+  graph1.push_back(switching.linearizedFactorGraph.at(0));
+  for (size_t i = 4; i <= 7; i++) {
+    graph1.push_back(switching.linearizedFactorGraph.at(i));
+  }
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t j = 1; j <= 4; j++) {
+    ordering += X(j);
+  }
+
+  // Now we calculate the actual factors using full elimination
+  HybridBayesTree::shared_ptr unprunedHybridBayesTree;
+  HybridGaussianFactorGraph::shared_ptr unprunedRemainingGraph;
+  std::tie(unprunedHybridBayesTree, unprunedRemainingGraph) =
+      switching.linearizedFactorGraph.eliminatePartialMultifrontal(ordering);
+
+  size_t maxNrLeaves = 5;
+  incrementalHybrid.update(graph1);
+
+  incrementalHybrid.prune(M(3), 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_m1 = *dynamic_pointer_cast<DiscreteConditional>(
+      incrementalHybrid[M(1)]->conditional()->inner());
+  EXPECT(discreteConditional_m1.keys() == KeyVector({M(1), M(2), M(3)}));
+
+  // 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_m1.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<GaussianMixture>(
+      unprunedHybridBayesTree->clique(X(4))->conditional()->inner());
+  auto &lastDensity = *dynamic_pointer_cast<GaussianMixture>(
+      incrementalHybrid[X(4)]->conditional()->inner());
+
+  std::vector<std::pair<DiscreteValues, double>> assignments =
+      discreteConditional_m1.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(HybridGaussianElimination, Incremental_approximate) {
+  Switching switching(5);
+  HybridGaussianISAM incrementalHybrid;
+  HybridGaussianFactorGraph graph1;
+
+  /***** Run Round 1 *****/
+  // Add the 3 hybrid factors, x1-x2, x2-x3, x3-x4
+  for (size_t i = 1; i < 4; i++) {
+    graph1.push_back(switching.linearizedFactorGraph.at(i));
+  }
+
+  // Add the Gaussian factors, 1 prior on X(1),
+  // 3 measurements on X(2), X(3), X(4)
+  graph1.push_back(switching.linearizedFactorGraph.at(0));
+  for (size_t i = 5; i <= 7; i++) {
+    graph1.push_back(switching.linearizedFactorGraph.at(i));
+  }
+
+  // Run update with pruning
+  size_t maxComponents = 5;
+  incrementalHybrid.update(graph1);
+  incrementalHybrid.prune(M(3), maxComponents);
+
+  // Check if we have a bayes tree with 4 hybrid nodes,
+  // each with 2, 4, 8, and 5 (pruned) leaves respetively.
+  EXPECT_LONGS_EQUAL(4, incrementalHybrid.size());
+  EXPECT_LONGS_EQUAL(
+      2, incrementalHybrid[X(1)]->conditional()->asMixture()->nrComponents());
+  EXPECT_LONGS_EQUAL(
+      4, incrementalHybrid[X(2)]->conditional()->asMixture()->nrComponents());
+  EXPECT_LONGS_EQUAL(
+      5, incrementalHybrid[X(3)]->conditional()->asMixture()->nrComponents());
+  EXPECT_LONGS_EQUAL(
+      5, incrementalHybrid[X(4)]->conditional()->asMixture()->nrComponents());
+
+  /***** Run Round 2 *****/
+  HybridGaussianFactorGraph graph2;
+  graph2.push_back(switching.linearizedFactorGraph.at(4));
+  graph2.push_back(switching.linearizedFactorGraph.at(8));
+
+  // Run update with pruning a second time.
+  incrementalHybrid.update(graph2);
+  incrementalHybrid.prune(M(4), 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(4)]->conditional()->asMixture()->nrComponents());
+  EXPECT_LONGS_EQUAL(
+      5, incrementalHybrid[X(5)]->conditional()->asMixture()->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 x1 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_nonlinear<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_nonlinear<BetweenFactor<Pose2>>(X(0), Y(0), Pose2(0, 1.0, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(Y(0), Z(0), Pose2(0, 1.0, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<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);
+  KeyVector contKeys = {W(0), W(1)};
+  auto noise_model = noiseModel::Isotropic::Sigma(3, 1.0);
+  auto still = boost::make_shared<PlanarMotionModel>(W(0), W(1), Pose2(0, 0, 0),
+                                                     noise_model),
+       moving = boost::make_shared<PlanarMotionModel>(W(0), W(1), odometry,
+                                                      noise_model);
+  std::vector<PlanarMotionModel::shared_ptr> components = {moving, still};
+  auto mixtureFactor = boost::make_shared<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(1), 2)}, components);
+  fg.push_back(mixtureFactor);
+
+  // Add equivalent of ImuFactor
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(X(0), X(1), Pose2(1.0, 0.0, 0),
+                                             poseNoise);
+  // PoseFactors-like at k=1
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(X(1), Y(1), Pose2(0, 1, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(Y(1), Z(1), Pose2(0, 1, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<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.
+  contKeys = {W(1), W(2)};
+  still = boost::make_shared<PlanarMotionModel>(W(1), W(2), Pose2(0, 0, 0),
+                                                noise_model);
+  moving =
+      boost::make_shared<PlanarMotionModel>(W(1), W(2), odometry, noise_model);
+  components = {moving, still};
+  mixtureFactor = boost::make_shared<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(2), 2)}, components);
+  fg.push_back(mixtureFactor);
+
+  // Add equivalent of ImuFactor
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(X(1), X(2), Pose2(1.0, 0.0, 0),
+                                             poseNoise);
+  // PoseFactors-like at k=1
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(X(2), Y(2), Pose2(0, 1, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(Y(2), Z(2), Pose2(0, 1, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<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(M(2), 2);
+
+  /*************** Run Round 4 ***************/
+  // Add odometry factor with discrete modes.
+  contKeys = {W(2), W(3)};
+  still = boost::make_shared<PlanarMotionModel>(W(2), W(3), Pose2(0, 0, 0),
+                                                noise_model);
+  moving =
+      boost::make_shared<PlanarMotionModel>(W(2), W(3), odometry, noise_model);
+  components = {moving, still};
+  mixtureFactor = boost::make_shared<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(3), 2)}, components);
+  fg.push_back(mixtureFactor);
+
+  // Add equivalent of ImuFactor
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(X(2), X(3), Pose2(1.0, 0.0, 0),
+                                             poseNoise);
+  // PoseFactors-like at k=3
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(X(3), Y(3), Pose2(0, 1, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<BetweenFactor<Pose2>>(Y(3), Z(3), Pose2(0, 1, 0),
+                                             poseNoise);
+  fg.emplace_nonlinear<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);
+  inc.prune(M(3), 3);
+
+  // The final discrete graph should not be empty since we have eliminated
+  // all continuous variables.
+  auto discreteTree = inc[M(3)]->conditional()->asDiscreteConditional();
+  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()->asMixture();
+  EXPECT_LONGS_EQUAL(3, lastConditional->nrComponents());
+}
+
+/* ************************************************************************* */
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}

gtsam/hybrid/tests/testHybridNonlinearFactorGraph.cpp

@@ -0,0 +1,737 @@
+/* ----------------------------------------------------------------------------
+ * 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    testHybridNonlinearFactorGraph.cpp
+ * @brief   Unit tests for HybridNonlinearFactorGraph
+ * @author  Varun Agrawal
+ * @author  Fan Jiang
+ * @author  Frank Dellaert
+ * @date    December 2021
+ */
+
+#include <gtsam/base/TestableAssertions.h>
+#include <gtsam/base/utilities.h>
+#include <gtsam/discrete/DiscreteBayesNet.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
+#include <gtsam/discrete/DiscreteFactorGraph.h>
+#include <gtsam/geometry/Pose2.h>
+#include <gtsam/hybrid/HybridEliminationTree.h>
+#include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/hybrid/HybridNonlinearFactorGraph.h>
+#include <gtsam/hybrid/MixtureFactor.h>
+#include <gtsam/linear/GaussianBayesNet.h>
+#include <gtsam/linear/GaussianFactorGraph.h>
+#include <gtsam/nonlinear/NonlinearFactorGraph.h>
+#include <gtsam/nonlinear/PriorFactor.h>
+#include <gtsam/sam/BearingRangeFactor.h>
+#include <gtsam/slam/BetweenFactor.h>
+
+#include <numeric>
+
+#include "Switching.h"
+
+// Include for test suite
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+using noiseModel::Isotropic;
+using symbol_shorthand::L;
+using symbol_shorthand::M;
+using symbol_shorthand::X;
+
+/* ****************************************************************************
+ * Test that any linearizedFactorGraph gaussian factors are appended to the
+ * existing gaussian factor graph in the hybrid factor graph.
+ */
+TEST(HybridFactorGraph, GaussianFactorGraph) {
+  HybridNonlinearFactorGraph fg;
+
+  // Add a simple prior factor to the nonlinear factor graph
+  fg.emplace_nonlinear<PriorFactor<double>>(X(0), 0, Isotropic::Sigma(1, 0.1));
+
+  // Linearization point
+  Values linearizationPoint;
+  linearizationPoint.insert<double>(X(0), 0);
+
+  HybridGaussianFactorGraph ghfg = fg.linearize(linearizationPoint);
+
+  // Add a factor to the GaussianFactorGraph
+  ghfg.add(JacobianFactor(X(0), I_1x1, Vector1(5)));
+
+  EXPECT_LONGS_EQUAL(2, ghfg.size());
+}
+
+/***************************************************************************
+ * Test equality for Hybrid Nonlinear Factor Graph.
+ */
+TEST(HybridNonlinearFactorGraph, Equals) {
+  HybridNonlinearFactorGraph graph1;
+  HybridNonlinearFactorGraph graph2;
+
+  // Test empty factor graphs
+  EXPECT(assert_equal(graph1, graph2));
+
+  auto f0 = boost::make_shared<PriorFactor<Pose2>>(
+      1, Pose2(), noiseModel::Isotropic::Sigma(3, 0.001));
+  graph1.push_back(f0);
+  graph2.push_back(f0);
+
+  auto f1 = boost::make_shared<BetweenFactor<Pose2>>(
+      1, 2, Pose2(), noiseModel::Isotropic::Sigma(3, 0.1));
+  graph1.push_back(f1);
+  graph2.push_back(f1);
+
+  // Test non-empty graphs
+  EXPECT(assert_equal(graph1, graph2));
+}
+
+/***************************************************************************
+ * Test that the resize method works correctly for a HybridNonlinearFactorGraph.
+ */
+TEST(HybridNonlinearFactorGraph, Resize) {
+  HybridNonlinearFactorGraph fg;
+  auto nonlinearFactor = boost::make_shared<BetweenFactor<double>>();
+  fg.push_back(nonlinearFactor);
+
+  auto discreteFactor = boost::make_shared<DecisionTreeFactor>();
+  fg.push_back(discreteFactor);
+
+  auto dcFactor = boost::make_shared<MixtureFactor>();
+  fg.push_back(dcFactor);
+
+  EXPECT_LONGS_EQUAL(fg.size(), 3);
+
+  fg.resize(0);
+  EXPECT_LONGS_EQUAL(fg.size(), 0);
+}
+
+/***************************************************************************
+ * Test that the resize method works correctly for a
+ * HybridGaussianFactorGraph.
+ */
+TEST(HybridGaussianFactorGraph, Resize) {
+  HybridNonlinearFactorGraph nhfg;
+  auto nonlinearFactor = boost::make_shared<BetweenFactor<double>>(
+      X(0), X(1), 0.0, Isotropic::Sigma(1, 0.1));
+  nhfg.push_back(nonlinearFactor);
+  auto discreteFactor = boost::make_shared<DecisionTreeFactor>();
+  nhfg.push_back(discreteFactor);
+
+  KeyVector contKeys = {X(0), X(1)};
+  auto noise_model = noiseModel::Isotropic::Sigma(1, 1.0);
+  auto still = boost::make_shared<MotionModel>(X(0), X(1), 0.0, noise_model),
+       moving = boost::make_shared<MotionModel>(X(0), X(1), 1.0, noise_model);
+
+  std::vector<MotionModel::shared_ptr> components = {still, moving};
+  auto dcFactor = boost::make_shared<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(1), 2)}, components);
+  nhfg.push_back(dcFactor);
+
+  Values linearizationPoint;
+  linearizationPoint.insert<double>(X(0), 0);
+  linearizationPoint.insert<double>(X(1), 1);
+
+  // Generate `HybridGaussianFactorGraph` by linearizing
+  HybridGaussianFactorGraph gfg = nhfg.linearize(linearizationPoint);
+
+  EXPECT_LONGS_EQUAL(gfg.size(), 3);
+
+  gfg.resize(0);
+  EXPECT_LONGS_EQUAL(gfg.size(), 0);
+}
+
+/***************************************************************************
+ * Test that the MixtureFactor reports correctly if the number of continuous
+ * keys provided do not match the keys in the factors.
+ */
+TEST(HybridGaussianFactorGraph, MixtureFactor) {
+  auto nonlinearFactor = boost::make_shared<BetweenFactor<double>>(
+      X(0), X(1), 0.0, Isotropic::Sigma(1, 0.1));
+  auto discreteFactor = boost::make_shared<DecisionTreeFactor>();
+
+  auto noise_model = noiseModel::Isotropic::Sigma(1, 1.0);
+  auto still = boost::make_shared<MotionModel>(X(0), X(1), 0.0, noise_model),
+       moving = boost::make_shared<MotionModel>(X(0), X(1), 1.0, noise_model);
+
+  std::vector<MotionModel::shared_ptr> components = {still, moving};
+
+  // Check for exception when number of continuous keys are under-specified.
+  KeyVector contKeys = {X(0)};
+  THROWS_EXCEPTION(boost::make_shared<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(1), 2)}, components));
+
+  // Check for exception when number of continuous keys are too many.
+  contKeys = {X(0), X(1), X(2)};
+  THROWS_EXCEPTION(boost::make_shared<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(1), 2)}, components));
+}
+
+/*****************************************************************************
+ * Test push_back on HFG makes the correct distinction.
+ */
+TEST(HybridFactorGraph, PushBack) {
+  HybridNonlinearFactorGraph fg;
+
+  auto nonlinearFactor = boost::make_shared<BetweenFactor<double>>();
+  fg.push_back(nonlinearFactor);
+
+  EXPECT_LONGS_EQUAL(fg.size(), 1);
+
+  fg = HybridNonlinearFactorGraph();
+
+  auto discreteFactor = boost::make_shared<DecisionTreeFactor>();
+  fg.push_back(discreteFactor);
+
+  EXPECT_LONGS_EQUAL(fg.size(), 1);
+
+  fg = HybridNonlinearFactorGraph();
+
+  auto dcFactor = boost::make_shared<MixtureFactor>();
+  fg.push_back(dcFactor);
+
+  EXPECT_LONGS_EQUAL(fg.size(), 1);
+
+  // Now do the same with HybridGaussianFactorGraph
+  HybridGaussianFactorGraph ghfg;
+
+  auto gaussianFactor = boost::make_shared<JacobianFactor>();
+  ghfg.push_back(gaussianFactor);
+
+  EXPECT_LONGS_EQUAL(ghfg.size(), 1);
+
+  ghfg = HybridGaussianFactorGraph();
+  ghfg.push_back(discreteFactor);
+
+  EXPECT_LONGS_EQUAL(ghfg.size(), 1);
+
+  ghfg = HybridGaussianFactorGraph();
+  ghfg.push_back(dcFactor);
+
+  HybridGaussianFactorGraph hgfg2;
+  hgfg2.push_back(ghfg.begin(), ghfg.end());
+
+  EXPECT_LONGS_EQUAL(ghfg.size(), 1);
+
+  HybridNonlinearFactorGraph hnfg;
+  NonlinearFactorGraph factors;
+  auto noise = noiseModel::Isotropic::Sigma(3, 1.0);
+  factors.emplace_shared<PriorFactor<Pose2>>(0, Pose2(0, 0, 0), noise);
+  factors.emplace_shared<PriorFactor<Pose2>>(1, Pose2(1, 0, 0), noise);
+  factors.emplace_shared<PriorFactor<Pose2>>(2, Pose2(2, 0, 0), noise);
+  // TODO(Varun) This does not currently work. It should work once HybridFactor
+  // becomes a base class of NonlinearFactor.
+  // hnfg.push_back(factors.begin(), factors.end());
+
+  // EXPECT_LONGS_EQUAL(3, hnfg.size());
+}
+
+/****************************************************************************
+ * Test construction of switching-like hybrid factor graph.
+ */
+TEST(HybridFactorGraph, Switching) {
+  Switching self(3);
+
+  EXPECT_LONGS_EQUAL(7, self.nonlinearFactorGraph.size());
+  EXPECT_LONGS_EQUAL(7, self.linearizedFactorGraph.size());
+}
+
+/****************************************************************************
+ * Test linearization on a switching-like hybrid factor graph.
+ */
+TEST(HybridFactorGraph, Linearization) {
+  Switching self(3);
+
+  // Linearize here:
+  HybridGaussianFactorGraph actualLinearized =
+      self.nonlinearFactorGraph.linearize(self.linearizationPoint);
+
+  EXPECT_LONGS_EQUAL(7, actualLinearized.size());
+}
+
+/****************************************************************************
+ * Test elimination tree construction
+ */
+TEST(HybridFactorGraph, EliminationTree) {
+  Switching self(3);
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t k = 1; k <= self.K; k++) ordering += X(k);
+
+  // Create elimination tree.
+  HybridEliminationTree etree(self.linearizedFactorGraph, ordering);
+  EXPECT_LONGS_EQUAL(1, etree.roots().size())
+}
+
+/****************************************************************************
+ *Test elimination function by eliminating x1 in *-x1-*-x2 graph.
+ */
+TEST(GaussianElimination, Eliminate_x1) {
+  Switching self(3);
+
+  // Gather factors on x1, has a simple Gaussian and a mixture factor.
+  HybridGaussianFactorGraph factors;
+  // Add gaussian prior
+  factors.push_back(self.linearizedFactorGraph[0]);
+  // Add first hybrid factor
+  factors.push_back(self.linearizedFactorGraph[1]);
+
+  // Eliminate x1
+  Ordering ordering;
+  ordering += X(1);
+
+  auto result = EliminateHybrid(factors, ordering);
+  CHECK(result.first);
+  EXPECT_LONGS_EQUAL(1, result.first->nrFrontals());
+  CHECK(result.second);
+  // Has two keys, x2 and m1
+  EXPECT_LONGS_EQUAL(2, result.second->size());
+}
+
+/****************************************************************************
+ * Test elimination function by eliminating x2 in x1-*-x2-*-x3 chain.
+ *                                                m1/      \m2
+ */
+TEST(HybridsGaussianElimination, Eliminate_x2) {
+  Switching self(3);
+
+  // Gather factors on x2, will be two mixture factors (with x1 and x3, resp.).
+  HybridGaussianFactorGraph factors;
+  factors.push_back(self.linearizedFactorGraph[1]);  // involves m1
+  factors.push_back(self.linearizedFactorGraph[2]);  // involves m2
+
+  // Eliminate x2
+  Ordering ordering;
+  ordering += X(2);
+
+  std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr> result =
+      EliminateHybrid(factors, ordering);
+  CHECK(result.first);
+  EXPECT_LONGS_EQUAL(1, result.first->nrFrontals());
+  CHECK(result.second);
+  // Note: separator keys should include m1, m2.
+  EXPECT_LONGS_EQUAL(4, result.second->size());
+}
+
+/****************************************************************************
+ * Helper method to generate gaussian factor graphs with a specific mode.
+ */
+GaussianFactorGraph::shared_ptr batchGFG(double between,
+                                         Values linearizationPoint) {
+  NonlinearFactorGraph graph;
+  graph.addPrior<double>(X(1), 0, Isotropic::Sigma(1, 0.1));
+
+  auto between_x1_x2 = boost::make_shared<MotionModel>(
+      X(1), X(2), between, Isotropic::Sigma(1, 1.0));
+
+  graph.push_back(between_x1_x2);
+
+  return graph.linearize(linearizationPoint);
+}
+
+/****************************************************************************
+ * Test elimination function by eliminating x1 and x2 in graph.
+ */
+TEST(HybridGaussianElimination, EliminateHybrid_2_Variable) {
+  Switching self(2, 1.0, 0.1);
+
+  auto factors = self.linearizedFactorGraph;
+
+  // Eliminate x1
+  Ordering ordering;
+  ordering += X(1);
+  ordering += X(2);
+
+  HybridConditional::shared_ptr hybridConditionalMixture;
+  HybridFactor::shared_ptr factorOnModes;
+
+  std::tie(hybridConditionalMixture, factorOnModes) =
+      EliminateHybrid(factors, ordering);
+
+  auto gaussianConditionalMixture =
+      dynamic_pointer_cast<GaussianMixture>(hybridConditionalMixture->inner());
+
+  CHECK(gaussianConditionalMixture);
+  // Frontals = [x1, x2]
+  EXPECT_LONGS_EQUAL(2, gaussianConditionalMixture->nrFrontals());
+  // 1 parent, which is the mode
+  EXPECT_LONGS_EQUAL(1, gaussianConditionalMixture->nrParents());
+
+  // This is now a HybridDiscreteFactor
+  auto hybridDiscreteFactor =
+      dynamic_pointer_cast<HybridDiscreteFactor>(factorOnModes);
+  // Access the type-erased inner object and convert to DecisionTreeFactor
+  auto discreteFactor =
+      dynamic_pointer_cast<DecisionTreeFactor>(hybridDiscreteFactor->inner());
+  CHECK(discreteFactor);
+  EXPECT_LONGS_EQUAL(1, discreteFactor->discreteKeys().size());
+  EXPECT(discreteFactor->root_->isLeaf() == false);
+
+  // TODO(Varun) Test emplace_discrete
+}
+
+/****************************************************************************
+ * Test partial elimination
+ */
+TEST(HybridFactorGraph, Partial_Elimination) {
+  Switching self(3);
+
+  auto linearizedFactorGraph = self.linearizedFactorGraph;
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t k = 1; k <= self.K; k++) ordering += X(k);
+
+  // Eliminate partially.
+  HybridBayesNet::shared_ptr hybridBayesNet;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+  CHECK(hybridBayesNet);
+  EXPECT_LONGS_EQUAL(3, hybridBayesNet->size());
+  EXPECT(hybridBayesNet->at(0)->frontals() == KeyVector{X(1)});
+  EXPECT(hybridBayesNet->at(0)->parents() == KeyVector({X(2), M(1)}));
+  EXPECT(hybridBayesNet->at(1)->frontals() == KeyVector{X(2)});
+  EXPECT(hybridBayesNet->at(1)->parents() == KeyVector({X(3), M(1), M(2)}));
+  EXPECT(hybridBayesNet->at(2)->frontals() == KeyVector{X(3)});
+  EXPECT(hybridBayesNet->at(2)->parents() == KeyVector({M(1), M(2)}));
+
+  CHECK(remainingFactorGraph);
+  EXPECT_LONGS_EQUAL(3, remainingFactorGraph->size());
+  EXPECT(remainingFactorGraph->at(0)->keys() == KeyVector({M(1)}));
+  EXPECT(remainingFactorGraph->at(1)->keys() == KeyVector({M(2), M(1)}));
+  EXPECT(remainingFactorGraph->at(2)->keys() == KeyVector({M(1), M(2)}));
+}
+
+/****************************************************************************
+ * Test full elimination
+ */
+TEST(HybridFactorGraph, Full_Elimination) {
+  Switching self(3);
+
+  auto linearizedFactorGraph = self.linearizedFactorGraph;
+
+  // We first do a partial elimination
+  HybridBayesNet::shared_ptr hybridBayesNet_partial;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph_partial;
+  DiscreteBayesNet discreteBayesNet;
+
+  {
+    // Create ordering.
+    Ordering ordering;
+    for (size_t k = 1; k <= self.K; k++) ordering += X(k);
+
+    // Eliminate partially.
+    std::tie(hybridBayesNet_partial, remainingFactorGraph_partial) =
+        linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+    DiscreteFactorGraph discrete_fg;
+    // TODO(Varun) Make this a function of HybridGaussianFactorGraph?
+    for (HybridFactor::shared_ptr& factor : (*remainingFactorGraph_partial)) {
+      auto df = dynamic_pointer_cast<HybridDiscreteFactor>(factor);
+      discrete_fg.push_back(df->inner());
+    }
+    ordering.clear();
+    for (size_t k = 1; k < self.K; k++) ordering += M(k);
+    discreteBayesNet =
+        *discrete_fg.eliminateSequential(ordering, EliminateForMPE);
+  }
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t k = 1; k <= self.K; k++) ordering += X(k);
+  for (size_t k = 1; k < self.K; k++) ordering += M(k);
+
+  // Eliminate partially.
+  HybridBayesNet::shared_ptr hybridBayesNet =
+      linearizedFactorGraph.eliminateSequential(ordering);
+
+  CHECK(hybridBayesNet);
+  EXPECT_LONGS_EQUAL(5, hybridBayesNet->size());
+  // p(x1 | x2, m1)
+  EXPECT(hybridBayesNet->at(0)->frontals() == KeyVector{X(1)});
+  EXPECT(hybridBayesNet->at(0)->parents() == KeyVector({X(2), M(1)}));
+  // p(x2 | x3, m1, m2)
+  EXPECT(hybridBayesNet->at(1)->frontals() == KeyVector{X(2)});
+  EXPECT(hybridBayesNet->at(1)->parents() == KeyVector({X(3), M(1), M(2)}));
+  // p(x3 | m1, m2)
+  EXPECT(hybridBayesNet->at(2)->frontals() == KeyVector{X(3)});
+  EXPECT(hybridBayesNet->at(2)->parents() == KeyVector({M(1), M(2)}));
+  // P(m1 | m2)
+  EXPECT(hybridBayesNet->at(3)->frontals() == KeyVector{M(1)});
+  EXPECT(hybridBayesNet->at(3)->parents() == KeyVector({M(2)}));
+  EXPECT(
+      dynamic_pointer_cast<DiscreteConditional>(hybridBayesNet->at(3)->inner())
+          ->equals(*discreteBayesNet.at(0)));
+  // P(m2)
+  EXPECT(hybridBayesNet->at(4)->frontals() == KeyVector{M(2)});
+  EXPECT_LONGS_EQUAL(0, hybridBayesNet->at(4)->nrParents());
+  EXPECT(
+      dynamic_pointer_cast<DiscreteConditional>(hybridBayesNet->at(4)->inner())
+          ->equals(*discreteBayesNet.at(1)));
+}
+
+/****************************************************************************
+ * Test printing
+ */
+TEST(HybridFactorGraph, Printing) {
+  Switching self(3);
+
+  auto linearizedFactorGraph = self.linearizedFactorGraph;
+
+  // Create ordering.
+  Ordering ordering;
+  for (size_t k = 1; k <= self.K; k++) ordering += X(k);
+
+  // Eliminate partially.
+  HybridBayesNet::shared_ptr hybridBayesNet;
+  HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      linearizedFactorGraph.eliminatePartialSequential(ordering);
+
+  string expected_hybridFactorGraph = R"(
+size: 7
+factor 0: Continuous [x1]
+
+  A[x1] = [
+	10
+]
+  b = [ -10 ]
+  No noise model
+factor 1: Hybrid [x1 x2; m1]{
+ Choice(m1) 
+ 0 Leaf :
+  A[x1] = [
+	-1
+]
+  A[x2] = [
+	1
+]
+  b = [ -1 ]
+  No noise model
+
+ 1 Leaf :
+  A[x1] = [
+	-1
+]
+  A[x2] = [
+	1
+]
+  b = [ -0 ]
+  No noise model
+
+}
+factor 2: Hybrid [x2 x3; m2]{
+ Choice(m2) 
+ 0 Leaf :
+  A[x2] = [
+	-1
+]
+  A[x3] = [
+	1
+]
+  b = [ -1 ]
+  No noise model
+
+ 1 Leaf :
+  A[x2] = [
+	-1
+]
+  A[x3] = [
+	1
+]
+  b = [ -0 ]
+  No noise model
+
+}
+factor 3: Continuous [x2]
+
+  A[x2] = [
+	10
+]
+  b = [ -10 ]
+  No noise model
+factor 4: Continuous [x3]
+
+  A[x3] = [
+	10
+]
+  b = [ -10 ]
+  No noise model
+factor 5: Discrete [m1]
+ P( m1 ):
+ Leaf  0.5
+
+factor 6: Discrete [m2 m1]
+ P( m2 | m1 ):
+ Choice(m2) 
+ 0 Choice(m1) 
+ 0 0 Leaf 0.33333333
+ 0 1 Leaf  0.6
+ 1 Choice(m1) 
+ 1 0 Leaf 0.66666667
+ 1 1 Leaf  0.4
+
+)";
+  EXPECT(assert_print_equal(expected_hybridFactorGraph, linearizedFactorGraph));
+
+  // Expected output for hybridBayesNet.
+  string expected_hybridBayesNet = R"(
+size: 3
+factor 0: Hybrid  P( x1 | x2 m1)
+ Discrete Keys = (m1, 2), 
+ Choice(m1) 
+ 0 Leaf  p(x1 | x2)
+  R = [ 10.0499 ]
+  S[x2] = [ -0.0995037 ]
+  d = [ -9.85087 ]
+  No noise model
+
+ 1 Leaf  p(x1 | x2)
+  R = [ 10.0499 ]
+  S[x2] = [ -0.0995037 ]
+  d = [ -9.95037 ]
+  No noise model
+
+factor 1: Hybrid  P( x2 | x3 m1 m2)
+ Discrete Keys = (m1, 2), (m2, 2), 
+ Choice(m2) 
+ 0 Choice(m1) 
+ 0 0 Leaf  p(x2 | x3)
+  R = [ 10.099 ]
+  S[x3] = [ -0.0990196 ]
+  d = [ -9.99901 ]
+  No noise model
+
+ 0 1 Leaf  p(x2 | x3)
+  R = [ 10.099 ]
+  S[x3] = [ -0.0990196 ]
+  d = [ -9.90098 ]
+  No noise model
+
+ 1 Choice(m1) 
+ 1 0 Leaf  p(x2 | x3)
+  R = [ 10.099 ]
+  S[x3] = [ -0.0990196 ]
+  d = [ -10.098 ]
+  No noise model
+
+ 1 1 Leaf  p(x2 | x3)
+  R = [ 10.099 ]
+  S[x3] = [ -0.0990196 ]
+  d = [ -10 ]
+  No noise model
+
+factor 2: Hybrid  P( x3 | m1 m2)
+ Discrete Keys = (m1, 2), (m2, 2), 
+ Choice(m2) 
+ 0 Choice(m1) 
+ 0 0 Leaf  p(x3)
+  R = [ 10.0494 ]
+  d = [ -10.1489 ]
+  No noise model
+
+ 0 1 Leaf  p(x3)
+  R = [ 10.0494 ]
+  d = [ -10.1479 ]
+  No noise model
+
+ 1 Choice(m1) 
+ 1 0 Leaf  p(x3)
+  R = [ 10.0494 ]
+  d = [ -10.0504 ]
+  No noise model
+
+ 1 1 Leaf  p(x3)
+  R = [ 10.0494 ]
+  d = [ -10.0494 ]
+  No noise model
+
+)";
+  EXPECT(assert_print_equal(expected_hybridBayesNet, *hybridBayesNet));
+}
+
+/****************************************************************************
+ * Simple PlanarSLAM example test with 2 poses and 2 landmarks (each pose
+ * connects to 1 landmark) to expose issue with default decision tree creation
+ * in hybrid elimination. The hybrid factor is between the poses X0 and X1.
+ * The issue arises if we eliminate a landmark variable first since it is not
+ * connected to a HybridFactor.
+ */
+TEST(HybridFactorGraph, DefaultDecisionTree) {
+  HybridNonlinearFactorGraph fg;
+
+  // Add a prior on pose x1 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_nonlinear<PriorFactor<Pose2>>(X(0), prior, priorNoise);
+
+  using PlanarMotionModel = BetweenFactor<Pose2>;
+
+  // Add odometry factor
+  Pose2 odometry(2.0, 0.0, 0.0);
+  KeyVector contKeys = {X(0), X(1)};
+  auto noise_model = noiseModel::Isotropic::Sigma(3, 1.0);
+  auto still = boost::make_shared<PlanarMotionModel>(X(0), X(1), Pose2(0, 0, 0),
+                                                     noise_model),
+       moving = boost::make_shared<PlanarMotionModel>(X(0), X(1), odometry,
+                                                      noise_model);
+  std::vector<PlanarMotionModel::shared_ptr> motion_models = {still, moving};
+  fg.emplace_hybrid<MixtureFactor>(
+      contKeys, DiscreteKeys{gtsam::DiscreteKey(M(1), 2)}, motion_models);
+
+  // Add Range-Bearing measurements to from X0 to L0 and X1 to L1.
+  // create a noise model for the landmark measurements
+  auto measurementNoise = noiseModel::Diagonal::Sigmas(
+      Vector2(0.1, 0.2));  // 0.1 rad std on bearing, 20cm on range
+  // create the measurement values - indices are (pose id, landmark id)
+  Rot2 bearing11 = Rot2::fromDegrees(45), bearing22 = Rot2::fromDegrees(90);
+  double range11 = std::sqrt(4.0 + 4.0), range22 = 2.0;
+
+  // Add Bearing-Range factors
+  fg.emplace_nonlinear<BearingRangeFactor<Pose2, Point2>>(
+      X(0), L(0), bearing11, range11, measurementNoise);
+  fg.emplace_nonlinear<BearingRangeFactor<Pose2, Point2>>(
+      X(1), L(1), bearing22, range22, measurementNoise);
+
+  // Create (deliberately inaccurate) initial estimate
+  Values initialEstimate;
+  initialEstimate.insert(X(0), Pose2(0.5, 0.0, 0.2));
+  initialEstimate.insert(X(1), Pose2(2.3, 0.1, -0.2));
+  initialEstimate.insert(L(0), Point2(1.8, 2.1));
+  initialEstimate.insert(L(1), Point2(4.1, 1.8));
+
+  // We want to eliminate variables not connected to DCFactors first.
+  Ordering ordering;
+  ordering += L(0);
+  ordering += L(1);
+  ordering += X(0);
+  ordering += X(1);
+
+  HybridGaussianFactorGraph linearized = fg.linearize(initialEstimate);
+  gtsam::HybridBayesNet::shared_ptr hybridBayesNet;
+  gtsam::HybridGaussianFactorGraph::shared_ptr remainingFactorGraph;
+
+  // This should NOT fail
+  std::tie(hybridBayesNet, remainingFactorGraph) =
+      linearized.eliminatePartialSequential(ordering);
+  EXPECT_LONGS_EQUAL(4, hybridBayesNet->size());
+  EXPECT_LONGS_EQUAL(1, remainingFactorGraph->size());
+}
+
+/* ************************************************************************* */
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}
+/* ************************************************************************* */

gtsam/hybrid/tests/testHybridValues.cpp

@@ -0,0 +1,58 @@
+/* ----------------------------------------------------------------------------
+
+ * 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 testHybridValues.cpp
+ *  @date Jul 28, 2022
+ *  @author Shangjie Xue
+ */
+
+#include <gtsam/base/Testable.h>
+#include <gtsam/base/TestableAssertions.h>
+#include <gtsam/discrete/Assignment.h>
+#include <gtsam/discrete/DiscreteKey.h>
+#include <gtsam/discrete/DiscreteValues.h>
+#include <gtsam/hybrid/HybridValues.h>
+#include <gtsam/inference/Key.h>
+#include <gtsam/inference/Symbol.h>
+#include <gtsam/linear/VectorValues.h>
+#include <gtsam/nonlinear/Values.h>
+
+// Include for test suite
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+
+TEST(HybridValues, basics) {
+  HybridValues values;
+  values.insert(99, Vector2(2, 3));
+  values.insert(100, 3);
+  EXPECT(assert_equal(values.at(99), Vector2(2, 3)));
+  EXPECT(assert_equal(values.atDiscrete(100), int(3)));
+
+  values.print();
+
+  HybridValues values2;
+  values2.insert(100, 3);
+  values2.insert(99, Vector2(2, 3));
+  EXPECT(assert_equal(values2, values));
+
+  values2.insert(98, Vector2(2, 3));
+  EXPECT(!assert_equal(values2, values));
+}
+
+/* ************************************************************************* */
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}
+/* ************************************************************************* */

gtsam/inference/FactorGraph.h

@@ -116,7 +116,7 @@ class FactorGraph {
   using HasDerivedValueType = typename std::enable_if<
       std::is_base_of<FactorType, typename T::value_type>::value>::type;
 
-  /// Check if T has a value_type derived from FactorType.
+  /// Check if T has a pointer type derived from FactorType.
   template <typename T>
   using HasDerivedElementType = typename std::enable_if<std::is_base_of<
       FactorType, typename T::value_type::element_type>::value>::type;

gtsam/inference/JunctionTree-inst.h

@@ -33,7 +33,7 @@ struct ConstructorTraversalData {
   typedef typename JunctionTree<BAYESTREE, GRAPH>::sharedNode sharedNode;
 
   ConstructorTraversalData* const parentData;
-  sharedNode myJTNode;
+  sharedNode junctionTreeNode;
   FastVector<SymbolicConditional::shared_ptr> childSymbolicConditionals;
   FastVector<SymbolicFactor::shared_ptr> childSymbolicFactors;
 
@@ -53,8 +53,9 @@ struct ConstructorTraversalData {
     // a traversal data structure with its own JT node, and create a child
     // pointer in its parent.
     ConstructorTraversalData myData = ConstructorTraversalData(&parentData);
-    myData.myJTNode = boost::make_shared<Node>(node->key, node->factors);
+    myData.junctionTreeNode =
-    parentData.myJTNode->addChild(myData.myJTNode);
+        boost::make_shared<Node>(node->key, node->factors);
+    parentData.junctionTreeNode->addChild(myData.junctionTreeNode);
     return myData;
   }
 
@@ -91,7 +92,7 @@ struct ConstructorTraversalData {
     myData.parentData->childSymbolicConditionals.push_back(myConditional);
     myData.parentData->childSymbolicFactors.push_back(mySeparatorFactor);
 
-    sharedNode node = myData.myJTNode;
+    sharedNode node = myData.junctionTreeNode;
     const FastVector<SymbolicConditional::shared_ptr>& childConditionals =
         myData.childSymbolicConditionals;
     node->problemSize_ = (int) (myConditional->size() * symbolicFactors.size());
@@ -138,14 +139,14 @@ JunctionTree<BAYESTREE, GRAPH>::JunctionTree(
   typedef typename EliminationTree<ETREE_BAYESNET, ETREE_GRAPH>::Node ETreeNode;
   typedef ConstructorTraversalData<BAYESTREE, GRAPH, ETreeNode> Data;
   Data rootData(0);
-  rootData.myJTNode = boost::make_shared<typename Base::Node>(); // Make a dummy node to gather
+  // Make a dummy node to gather the junction tree roots
-                                                                 // the junction tree roots
+  rootData.junctionTreeNode = boost::make_shared<typename Base::Node>();
   treeTraversal::DepthFirstForest(eliminationTree, rootData,
       Data::ConstructorTraversalVisitorPre,
       Data::ConstructorTraversalVisitorPostAlg2);
 
   // Assign roots from the dummy node
-  this->addChildrenAsRoots(rootData.myJTNode);
+  this->addChildrenAsRoots(rootData.junctionTreeNode);
 
   // Transfer remaining factors from elimination tree
   Base::remainingFactors_ = eliminationTree.remainingFactors();

gtsam/linear/GaussianISAM.h

@@ -10,7 +10,7 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file SymbolicISAM.h
+ * @file GaussianISAM.h
  * @date July 29, 2013
  * @author Frank Dellaert
  * @author Richard Roberts

gtsam/linear/tests/testSerializationLinear.cpp

@@ -198,6 +198,33 @@ TEST (Serialization, gaussian_factor_graph) {
   EXPECT(equalsBinary(graph));
 }
 
+/* ****************************************************************************/
+TEST(Serialization, gaussian_bayes_net) {
+  // Create an arbitrary Bayes Net
+  GaussianBayesNet gbn;
+  gbn += GaussianConditional::shared_ptr(new GaussianConditional(
+      0, Vector2(1.0, 2.0), (Matrix2() << 3.0, 4.0, 0.0, 6.0).finished(), 3,
+      (Matrix2() << 7.0, 8.0, 9.0, 10.0).finished(), 4,
+      (Matrix2() << 11.0, 12.0, 13.0, 14.0).finished()));
+  gbn += GaussianConditional::shared_ptr(new GaussianConditional(
+      1, Vector2(15.0, 16.0), (Matrix2() << 17.0, 18.0, 0.0, 20.0).finished(),
+      2, (Matrix2() << 21.0, 22.0, 23.0, 24.0).finished(), 4,
+      (Matrix2() << 25.0, 26.0, 27.0, 28.0).finished()));
+  gbn += GaussianConditional::shared_ptr(new GaussianConditional(
+      2, Vector2(29.0, 30.0), (Matrix2() << 31.0, 32.0, 0.0, 34.0).finished(),
+      3, (Matrix2() << 35.0, 36.0, 37.0, 38.0).finished()));
+  gbn += GaussianConditional::shared_ptr(new GaussianConditional(
+      3, Vector2(39.0, 40.0), (Matrix2() << 41.0, 42.0, 0.0, 44.0).finished(),
+      4, (Matrix2() << 45.0, 46.0, 47.0, 48.0).finished()));
+  gbn += GaussianConditional::shared_ptr(new GaussianConditional(
+      4, Vector2(49.0, 50.0), (Matrix2() << 51.0, 52.0, 0.0, 54.0).finished()));
+
+  std::string serialized = serialize(gbn);
+  GaussianBayesNet actual;
+  deserialize(serialized, actual);
+  EXPECT(assert_equal(gbn, actual));
+}
+
 /* ************************************************************************* */
 TEST (Serialization, gaussian_bayes_tree) {
   const Key x1=1, x2=2, x3=3, x4=4;

gtsam/navigation/CombinedImuFactor.cpp

@@ -93,9 +93,14 @@ void PreintegratedCombinedMeasurements::resetIntegration() {
 //------------------------------------------------------------------------------
 void PreintegratedCombinedMeasurements::integrateMeasurement(
     const Vector3& measuredAcc, const Vector3& measuredOmega, double dt) {
+  if (dt <= 0) {
+    throw std::runtime_error(
+        "PreintegratedCombinedMeasurements::integrateMeasurement: dt <=0");
+  }
+
   // Update preintegrated measurements.
-  Matrix9 A; // overall Jacobian wrt preintegrated measurements (df/dx)
+  Matrix9 A; // Jacobian wrt preintegrated measurements without bias (df/dx)
-  Matrix93 B, C;
+  Matrix93 B, C;  // Jacobian of state wrpt accel bias and omega bias respectively.
   PreintegrationType::update(measuredAcc, measuredOmega, dt, &A, &B, &C);
 
   // Update preintegrated measurements covariance: as in [2] we consider a first
@@ -105,47 +110,78 @@ void PreintegratedCombinedMeasurements::integrateMeasurement(
   // and preintegrated measurements
 
   // Single Jacobians to propagate covariance
-  // TODO(frank): should we not also account for bias on position?
+  Matrix3 theta_H_biasOmega = C.topRows<3>();
-  Matrix3 theta_H_biasOmega = -C.topRows<3>();
+  Matrix3 pos_H_biasAcc = B.middleRows<3>(3);
-  Matrix3 vel_H_biasAcc = -B.bottomRows<3>();
+  Matrix3 vel_H_biasAcc = B.bottomRows<3>();
+
+  Matrix3 theta_H_biasOmegaInit = -theta_H_biasOmega;
+  Matrix3 pos_H_biasAccInit = -pos_H_biasAcc;
+  Matrix3 vel_H_biasAccInit = -vel_H_biasAcc;
 
   // overall Jacobian wrt preintegrated measurements (df/dx)
   Eigen::Matrix<double, 15, 15> F;
   F.setZero();
   F.block<9, 9>(0, 0) = A;
   F.block<3, 3>(0, 12) = theta_H_biasOmega;
+  F.block<3, 3>(3, 9) = pos_H_biasAcc;
   F.block<3, 3>(6, 9) = vel_H_biasAcc;
   F.block<6, 6>(9, 9) = I_6x6;
 
+  // Update the uncertainty on the state (matrix F in [4]).
+  preintMeasCov_ = F * preintMeasCov_ * F.transpose();
+
   // propagate uncertainty
   // TODO(frank): use noiseModel routine so we can have arbitrary noise models.
   const Matrix3& aCov = p().accelerometerCovariance;
   const Matrix3& wCov = p().gyroscopeCovariance;
   const Matrix3& iCov = p().integrationCovariance;
+  const Matrix6& bInitCov = p().biasAccOmegaInt;
 
   // first order uncertainty propagation
-  // Optimized matrix multiplication   (1/dt) * G * measurementCovariance *
+  // Optimized matrix mult: (1/dt) * G * measurementCovariance * G.transpose()
-  // G.transpose()
   Eigen::Matrix<double, 15, 15> G_measCov_Gt;
   G_measCov_Gt.setZero(15, 15);
 
+  const Matrix3& bInitCov11 = bInitCov.block<3, 3>(0, 0) / dt;
+  const Matrix3& bInitCov12 = bInitCov.block<3, 3>(0, 3) / dt;
+  const Matrix3& bInitCov21 = bInitCov.block<3, 3>(3, 0) / dt;
+  const Matrix3& bInitCov22 = bInitCov.block<3, 3>(3, 3) / dt;
+
   // BLOCK DIAGONAL TERMS
-  D_t_t(&G_measCov_Gt) = dt * iCov;
+  D_R_R(&G_measCov_Gt) =
-  D_v_v(&G_measCov_Gt) = (1 / dt) * vel_H_biasAcc
+      (theta_H_biasOmega * (wCov / dt) * theta_H_biasOmega.transpose())  //
-      * (aCov + p().biasAccOmegaInt.block<3, 3>(0, 0))
+      +
-      * (vel_H_biasAcc.transpose());
+      (theta_H_biasOmegaInit * bInitCov22 * theta_H_biasOmegaInit.transpose());
-  D_R_R(&G_measCov_Gt) = (1 / dt) * theta_H_biasOmega
+
-      * (wCov + p().biasAccOmegaInt.block<3, 3>(3, 3))
+  D_t_t(&G_measCov_Gt) =
-      * (theta_H_biasOmega.transpose());
+      (pos_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose())           //
+      + (pos_H_biasAccInit * bInitCov11 * pos_H_biasAccInit.transpose())  //
+      + (dt * iCov);
+
+  D_v_v(&G_measCov_Gt) =
+      (vel_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose())  //
+      + (vel_H_biasAccInit * bInitCov11 * vel_H_biasAccInit.transpose());
+
   D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance;
   D_g_g(&G_measCov_Gt) = dt * p().biasOmegaCovariance;
 
   // OFF BLOCK DIAGONAL TERMS
-  Matrix3 temp = vel_H_biasAcc * p().biasAccOmegaInt.block<3, 3>(3, 0)
+  D_R_t(&G_measCov_Gt) =
-      * theta_H_biasOmega.transpose();
+      theta_H_biasOmegaInit * bInitCov21 * pos_H_biasAccInit.transpose();
-  D_v_R(&G_measCov_Gt) = temp;
+  D_R_v(&G_measCov_Gt) =
-  D_R_v(&G_measCov_Gt) = temp.transpose();
+      theta_H_biasOmegaInit * bInitCov21 * vel_H_biasAccInit.transpose();
-  preintMeasCov_ = F * preintMeasCov_ * F.transpose() + G_measCov_Gt;
+  D_t_R(&G_measCov_Gt) =
+      pos_H_biasAccInit * bInitCov12 * theta_H_biasOmegaInit.transpose();
+  D_t_v(&G_measCov_Gt) =
+      (pos_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose()) +
+      (pos_H_biasAccInit * bInitCov11 * vel_H_biasAccInit.transpose());
+  D_v_R(&G_measCov_Gt) =
+      vel_H_biasAccInit * bInitCov12 * theta_H_biasOmegaInit.transpose();
+  D_v_t(&G_measCov_Gt) =
+      (vel_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose()) +
+      (vel_H_biasAccInit * bInitCov11 * pos_H_biasAccInit.transpose());
+
+  preintMeasCov_.noalias() += G_measCov_Gt;
 }
 
 //------------------------------------------------------------------------------
@@ -253,6 +289,5 @@ std::ostream& operator<<(std::ostream& os, const CombinedImuFactor& f) {
   os << "  noise model sigmas: " << f.noiseModel_->sigmas().transpose();
   return os;
 }
-}
- /// namespace gtsam
 
+}  // namespace gtsam

gtsam/navigation/CombinedImuFactor.h

@@ -51,6 +51,7 @@ typedef ManifoldPreintegration PreintegrationType;
  *     TRO, 28(1):61-76, 2012.
  * [3] L. Carlone, S. Williams, R. Roberts, "Preintegrated IMU factor:
  *     Computation of the Jacobian Matrices", Tech. Report, 2013.
+ *     Available in this repo as "PreintegratedIMUJacobians.pdf".
  * [4] C. Forster, L. Carlone, F. Dellaert, D. Scaramuzza, IMU Preintegration on
  *     Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation,
  *     Robotics: Science and Systems (RSS), 2015.
@@ -61,7 +62,7 @@ typedef ManifoldPreintegration PreintegrationType;
 struct GTSAM_EXPORT PreintegrationCombinedParams : PreintegrationParams {
   Matrix3 biasAccCovariance;    ///< continuous-time "Covariance" describing accelerometer bias random walk
   Matrix3 biasOmegaCovariance;  ///< continuous-time "Covariance" describing gyroscope bias random walk
-  Matrix6 biasAccOmegaInt;     ///< covariance of bias used for pre-integration
+  Matrix6 biasAccOmegaInt;     ///< covariance of bias used as initial estimate.
 
   /// Default constructor makes uninitialized params struct.
   /// Used for serialization.
@@ -92,11 +93,11 @@ struct GTSAM_EXPORT PreintegrationCombinedParams : PreintegrationParams {
 
   void setBiasAccCovariance(const Matrix3& cov) { biasAccCovariance=cov; }
   void setBiasOmegaCovariance(const Matrix3& cov) { biasOmegaCovariance=cov; }
-  void setBiasAccOmegaInt(const Matrix6& cov) { biasAccOmegaInt=cov; }
+  void setBiasAccOmegaInit(const Matrix6& cov) { biasAccOmegaInt=cov; }
   
   const Matrix3& getBiasAccCovariance() const { return biasAccCovariance; }
   const Matrix3& getBiasOmegaCovariance() const { return biasOmegaCovariance; }
-  const Matrix6& getBiasAccOmegaInt() const { return biasAccOmegaInt; }
+  const Matrix6& getBiasAccOmegaInit() const { return biasAccOmegaInt; }
   
 private:
 

gtsam/navigation/ImuBias.h

@@ -105,7 +105,7 @@ public:
   /// @{
 
   /** identity for group operation */
-  static ConstantBias identity() {
+  static ConstantBias Identity() {
     return ConstantBias();
   }
 

gtsam/navigation/ImuFactor.cpp

@@ -59,7 +59,7 @@ void PreintegratedImuMeasurements::integrateMeasurement(
 
   // Update preintegrated measurements (also get Jacobian)
   Matrix9 A;  // overall Jacobian wrt preintegrated measurements (df/dx)
-  Matrix93 B, C;
+  Matrix93 B, C;  // Jacobian of state wrpt accel bias and omega bias respectively.
   PreintegrationType::update(measuredAcc, measuredOmega, dt, &A, &B, &C);
 
   // first order covariance propagation:
@@ -73,11 +73,13 @@ void PreintegratedImuMeasurements::integrateMeasurement(
   const Matrix3& iCov = p().integrationCovariance;
 
   // (1/dt) allows to pass from continuous time noise to discrete time noise
+  // Update the uncertainty on the state (matrix A in [4]).
   preintMeasCov_ = A * preintMeasCov_ * A.transpose();
+  // These 2 updates account for uncertainty on the IMU measurement (matrix B in [4]).
   preintMeasCov_.noalias() += B * (aCov / dt) * B.transpose();
   preintMeasCov_.noalias() += C * (wCov / dt) * C.transpose();
 
-  // NOTE(frank): (Gi*dt)*(C/dt)*(Gi'*dt), with Gi << Z_3x3, I_3x3, Z_3x3
+  // NOTE(frank): (Gi*dt)*(C/dt)*(Gi'*dt), with Gi << Z_3x3, I_3x3, Z_3x3 (9x3 matrix)
   preintMeasCov_.block<3, 3>(3, 3).noalias() += iCov * dt;
 }
 

gtsam/navigation/ImuFactor.h

@@ -53,6 +53,7 @@ typedef ManifoldPreintegration PreintegrationType;
  *     TRO, 28(1):61-76, 2012.
  * [3] L. Carlone, S. Williams, R. Roberts, "Preintegrated IMU factor:
  *     Computation of the Jacobian Matrices", Tech. Report, 2013.
+ *     Available in this repo as "PreintegratedIMUJacobians.pdf".
  * [4] C. Forster, L. Carlone, F. Dellaert, D. Scaramuzza, "IMU Preintegration on
  *     Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation",
  *     Robotics: Science and Systems (RSS), 2015.

gtsam/navigation/PreintegrationBase.cpp

@@ -157,9 +157,9 @@ Vector9 PreintegrationBase::computeError(const NavState& state_i,
       state_j.localCoordinates(predictedState_j, H2 ? &D_error_state_j : 0,
                                H1 || H3 ? &D_error_predict : 0);
 
-  if (H1) *H1 << D_error_predict* D_predict_state_i;
+  if (H1) *H1 << D_error_predict * D_predict_state_i;
   if (H2) *H2 << D_error_state_j;
-  if (H3) *H3 << D_error_predict* D_predict_bias_i;
+  if (H3) *H3 << D_error_predict * D_predict_bias_i;
 
   return error;
 }

gtsam/navigation/ScenarioRunner.cpp

@@ -15,8 +15,8 @@
  * @author  Frank Dellaert
  */
 
-#include <gtsam/navigation/ScenarioRunner.h>
 #include <gtsam/base/timing.h>
+#include <gtsam/navigation/ScenarioRunner.h>
 
 #include <boost/assign.hpp>
 #include <cmath>
@@ -105,4 +105,62 @@ Matrix6 ScenarioRunner::estimateNoiseCovariance(size_t N) const {
   return Q / (N - 1);
 }
 
+PreintegratedCombinedMeasurements CombinedScenarioRunner::integrate(
+    double T, const Bias& estimatedBias, bool corrupted) const {
+  gttic_(integrate);
+  PreintegratedCombinedMeasurements pim(p_, estimatedBias);
+
+  const double dt = imuSampleTime();
+  const size_t nrSteps = T / dt;
+  double t = 0;
+  for (size_t k = 0; k < nrSteps; k++, t += dt) {
+    Vector3 measuredOmega =
+        corrupted ? measuredAngularVelocity(t) : actualAngularVelocity(t);
+    Vector3 measuredAcc =
+        corrupted ? measuredSpecificForce(t) : actualSpecificForce(t);
+    pim.integrateMeasurement(measuredAcc, measuredOmega, dt);
+  }
+
+  return pim;
+}
+
+NavState CombinedScenarioRunner::predict(
+    const PreintegratedCombinedMeasurements& pim,
+    const Bias& estimatedBias) const {
+  const NavState state_i(scenario().pose(0), scenario().velocity_n(0));
+  return pim.predict(state_i, estimatedBias);
+}
+
+Eigen::Matrix<double, 15, 15> CombinedScenarioRunner::estimateCovariance(
+    double T, size_t N, const Bias& estimatedBias) const {
+  gttic_(estimateCovariance);
+
+  // Get predict prediction from ground truth measurements
+  NavState prediction = predict(integrate(T));
+
+  // Sample !
+  Matrix samples(15, N);
+  Vector15 sum = Vector15::Zero();
+  for (size_t i = 0; i < N; i++) {
+    auto pim = integrate(T, estimatedBias, true);
+    NavState sampled = predict(pim);
+    Vector15 xi = Vector15::Zero();
+    xi << sampled.localCoordinates(prediction),
+        (estimatedBias_.vector() - estimatedBias.vector());
+    samples.col(i) = xi;
+    sum += xi;
+  }
+
+  // Compute MC covariance
+  Vector15 sampleMean = sum / N;
+  Eigen::Matrix<double, 15, 15> Q;
+  Q.setZero();
+  for (size_t i = 0; i < N; i++) {
+    Vector15 xi = samples.col(i) - sampleMean;
+    Q += xi * xi.transpose();
+  }
+
+  return Q / (N - 1);
+}
+
 }  // namespace gtsam

gtsam/navigation/ScenarioRunner.h

@@ -16,9 +16,10 @@
  */
 
 #pragma once
+#include <gtsam/linear/Sampler.h>
+#include <gtsam/navigation/CombinedImuFactor.h>
 #include <gtsam/navigation/ImuFactor.h>
 #include <gtsam/navigation/Scenario.h>
-#include <gtsam/linear/Sampler.h>
 
 namespace gtsam {
 
@@ -66,10 +67,10 @@ class GTSAM_EXPORT ScenarioRunner {
   // also, uses g=10 for easy debugging
   const Vector3& gravity_n() const { return p_->n_gravity; }
 
+  const Scenario& scenario() const { return scenario_; }
+
   // A gyro simply measures angular velocity in body frame
-  Vector3 actualAngularVelocity(double t) const {
+  Vector3 actualAngularVelocity(double t) const { return scenario_.omega_b(t); }
-    return scenario_.omega_b(t);
-  }
 
   // An accelerometer measures acceleration in body, but not gravity
   Vector3 actualSpecificForce(double t) const {
@@ -106,4 +107,39 @@ class GTSAM_EXPORT ScenarioRunner {
   Matrix6 estimateNoiseCovariance(size_t N = 1000) const;
 };
 
+/*
+ *  Simple class to test navigation scenarios with CombinedImuMeasurements.
+ *  Takes a trajectory scenario as input, and can generate IMU measurements
+ */
+class GTSAM_EXPORT CombinedScenarioRunner : public ScenarioRunner {
+ public:
+  typedef boost::shared_ptr<PreintegrationCombinedParams> SharedParams;
+
+ private:
+  const SharedParams p_;
+  const Bias estimatedBias_;
+
+ public:
+  CombinedScenarioRunner(const Scenario& scenario, const SharedParams& p,
+                         double imuSampleTime = 1.0 / 100.0,
+                         const Bias& bias = Bias())
+      : ScenarioRunner(scenario, static_cast<ScenarioRunner::SharedParams>(p),
+                       imuSampleTime, bias),
+        p_(p),
+        estimatedBias_(bias) {}
+
+  /// Integrate measurements for T seconds into a PIM
+  PreintegratedCombinedMeasurements integrate(
+      double T, const Bias& estimatedBias = Bias(),
+      bool corrupted = false) const;
+
+  /// Predict predict given a PIM
+  NavState predict(const PreintegratedCombinedMeasurements& pim,
+                   const Bias& estimatedBias = Bias()) const;
+
+  /// Compute a Monte Carlo estimate of the predict covariance using N samples
+  Eigen::Matrix<double, 15, 15> estimateCovariance(
+      double T, size_t N = 1000, const Bias& estimatedBias = Bias()) const;
+};
+
 }  // namespace gtsam

gtsam/navigation/navigation.i

@@ -17,7 +17,7 @@ class ConstantBias {
   bool equals(const gtsam::imuBias::ConstantBias& expected, double tol) const;
 
   // Group
-  static gtsam::imuBias::ConstantBias identity();
+  static gtsam::imuBias::ConstantBias Identity();
 
   // Operator Overloads
   gtsam::imuBias::ConstantBias operator-() const;
@@ -165,11 +165,11 @@ virtual class PreintegrationCombinedParams : gtsam::PreintegrationParams {
 
   void setBiasAccCovariance(Matrix cov);
   void setBiasOmegaCovariance(Matrix cov);
-  void setBiasAccOmegaInt(Matrix cov);
+  void setBiasAccOmegaInit(Matrix cov);
   
   Matrix getBiasAccCovariance() const ;
   Matrix getBiasOmegaCovariance() const ;
-  Matrix getBiasAccOmegaInt() const;
+  Matrix getBiasAccOmegaInit() const;
  
 };
 

gtsam/navigation/tests/testCombinedImuFactor.cpp

@@ -16,18 +16,19 @@
  * @author  Frank Dellaert
  * @author  Richard Roberts
  * @author  Stephen Williams
+ * @author  Varun Agrawal
  */
 
-#include <gtsam/navigation/ImuFactor.h>
+#include <CppUnitLite/TestHarness.h>
-#include <gtsam/navigation/CombinedImuFactor.h>
-#include <gtsam/navigation/ImuBias.h>
-#include <gtsam/geometry/Pose3.h>
-#include <gtsam/nonlinear/Values.h>
-#include <gtsam/inference/Symbol.h>
 #include <gtsam/base/TestableAssertions.h>
 #include <gtsam/base/numericalDerivative.h>
-
+#include <gtsam/geometry/Pose3.h>
-#include <CppUnitLite/TestHarness.h>
+#include <gtsam/inference/Symbol.h>
+#include <gtsam/navigation/CombinedImuFactor.h>
+#include <gtsam/navigation/ImuBias.h>
+#include <gtsam/navigation/ImuFactor.h>
+#include <gtsam/navigation/ScenarioRunner.h>
+#include <gtsam/nonlinear/Values.h>
 
 #include <list>
 
@@ -40,12 +41,15 @@ static boost::shared_ptr<PreintegratedCombinedMeasurements::Params> Params() {
   p->gyroscopeCovariance = kGyroSigma * kGyroSigma * I_3x3;
   p->accelerometerCovariance = kAccelSigma * kAccelSigma * I_3x3;
   p->integrationCovariance = 0.0001 * I_3x3;
+  p->biasAccCovariance = Z_3x3;
+  p->biasOmegaCovariance = Z_3x3;
+  p->biasAccOmegaInt = Z_6x6;
   return p;
 }
-}
+}  // namespace testing
 
 /* ************************************************************************* */
-TEST( CombinedImuFactor, PreintegratedMeasurements ) {
+TEST(CombinedImuFactor, PreintegratedMeasurements ) {
   // Linearization point
   Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); ///< Current estimate of acceleration and angular rate biases
 
@@ -71,8 +75,9 @@ TEST( CombinedImuFactor, PreintegratedMeasurements ) {
   DOUBLES_EQUAL(expected1.deltaTij(), actual1.deltaTij(), tol);
 }
 
+
 /* ************************************************************************* */
-TEST( CombinedImuFactor, ErrorWithBiases ) {
+TEST(CombinedImuFactor, ErrorWithBiases ) {
   Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); // Biases (acc, rot)
   Bias bias2(Vector3(0.2, 0.2, 0), Vector3(1, 0, 0.3)); // Biases (acc, rot)
   Pose3 x1(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0)), Point3(5.0, 1.0, -50.0));
@@ -203,6 +208,114 @@ TEST(CombinedImuFactor, PredictRotation) {
   EXPECT(assert_equal(expectedPose, actual.pose(), tol));
 }
 
+/* ************************************************************************* */
+// Testing covariance to check if all the jacobians are accounted for.
+TEST(CombinedImuFactor, CheckCovariance) {
+  auto params = PreintegrationCombinedParams::MakeSharedU(9.81);
+
+  params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3);
+  params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3);
+  params->setIntegrationCovariance(pow(0.0, 2) * I_3x3);
+  params->setOmegaCoriolis(Vector3::Zero());
+
+  imuBias::ConstantBias currentBias;
+
+  PreintegratedCombinedMeasurements actual(params, currentBias);
+
+  // Measurements
+  Vector3 measuredAcc(0.1577, -0.8251, 9.6111);
+  Vector3 measuredOmega(-0.0210, 0.0311, 0.0145);
+  double deltaT = 0.01;
+
+  actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
+
+  Eigen::Matrix<double, 15, 15> expected;
+  expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,          //
+      0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,                  //
+      0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,                  //
+      0, 0, 0, 2.50025e-07, 0, 0, 5.0005e-05, 0, 0, 0, 0, 0, 0, 0, 0,  //
+      0, 0, 0, 0, 2.50025e-07, 0, 0, 5.0005e-05, 0, 0, 0, 0, 0, 0, 0,  //
+      0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 5.0005e-05, 0, 0, 0, 0, 0, 0,  //
+      0, 0, 0, 5.0005e-05, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0,     //
+      0, 0, 0, 0, 5.0005e-05, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0,     //
+      0, 0, 0, 0, 0, 5.0005e-05, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0,     //
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0,                  //
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0,                  //
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0,                  //
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0,                  //
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0,                  //
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01;
+
+  // regression
+  EXPECT(assert_equal(expected, actual.preintMeasCov()));
+}
+
+// Test that the covariance values for the ImuFactor and the CombinedImuFactor
+// (top-left 9x9) are the same
+TEST(CombinedImuFactor, SameCovariance) {
+  // IMU measurements and time delta
+  Vector3 accMeas(0.1577, -0.8251, 9.6111);
+  Vector3 omegaMeas(-0.0210, 0.0311, 0.0145);
+  double deltaT = 0.01;
+
+  // Assume zero bias
+  imuBias::ConstantBias currentBias;
+
+  // Define params for ImuFactor
+  auto params = PreintegrationParams::MakeSharedU();
+  params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3);
+  params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3);
+  params->setIntegrationCovariance(pow(0, 2) * I_3x3);
+  params->setOmegaCoriolis(Vector3::Zero());
+
+  // The IMU preintegration object for ImuFactor
+  PreintegratedImuMeasurements pim(params, currentBias);
+  pim.integrateMeasurement(accMeas, omegaMeas, deltaT);
+
+  // Define params for CombinedImuFactor
+  auto combined_params = PreintegrationCombinedParams::MakeSharedU();
+  combined_params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3);
+  combined_params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3);
+  // Set bias integration covariance explicitly to zero
+  combined_params->setIntegrationCovariance(Z_3x3);
+  combined_params->setOmegaCoriolis(Z_3x1);
+  // Set bias initial covariance explicitly to zero
+  combined_params->setBiasAccOmegaInit(Z_6x6);
+
+  // The IMU preintegration object for CombinedImuFactor
+  PreintegratedCombinedMeasurements cpim(combined_params, currentBias);
+  cpim.integrateMeasurement(accMeas, omegaMeas, deltaT);
+
+  // Assert if the noise covariance
+  EXPECT(assert_equal(pim.preintMeasCov(),
+                      cpim.preintMeasCov().block(0, 0, 9, 9)));
+}
+
+/* ************************************************************************* */
+TEST(CombinedImuFactor, Accelerating) {
+  const double a = 0.2, v = 50;
+
+  // Set up body pointing towards y axis, and start at 10,20,0 with velocity
+  // going in X The body itself has Z axis pointing down
+  const Rot3 nRb(Point3(0, 1, 0), Point3(1, 0, 0), Point3(0, 0, -1));
+  const Point3 initial_position(10, 20, 0);
+  const Vector3 initial_velocity(v, 0, 0);
+
+  const AcceleratingScenario scenario(nRb, initial_position, initial_velocity,
+                                      Vector3(a, 0, 0));
+
+  const double T = 3.0;  // seconds
+
+  CombinedScenarioRunner runner(scenario, testing::Params(), T / 10);
+
+  PreintegratedCombinedMeasurements pim = runner.integrate(T);
+  EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
+
+  auto estimatedCov = runner.estimateCovariance(T, 100);
+  Eigen::Matrix<double, 15, 15> expected = pim.preintMeasCov();
+  EXPECT(assert_equal(estimatedCov, expected, 0.1));
+}
+
 /* ************************************************************************* */
 int main() {
   TestResult tr;

gtsam/nonlinear/CustomFactor.h

@@ -19,8 +19,6 @@
 
 #include <gtsam/nonlinear/NonlinearFactor.h>
 
-using namespace gtsam;
-
 namespace gtsam {
 
 using JacobianVector = std::vector<Matrix>;

gtsam/nonlinear/GncOptimizer.h

@@ -42,7 +42,7 @@ static double Chi2inv(const double alpha, const size_t dofs) {
 
 /* ************************************************************************* */
 template<class GncParameters>
-class GTSAM_EXPORT GncOptimizer {
+class GncOptimizer {
  public:
   /// For each parameter, specify the corresponding optimizer: e.g., GaussNewtonParams -> GaussNewtonOptimizer.
   typedef typename GncParameters::OptimizerType BaseOptimizer;