Merge branch 'master' into optimize_silhouettes

author: wreise <wojciech.reise@epfl.ch> 2022-08-10 10:28:26 +0200
committer: wreise <wojciech.reise@epfl.ch> 2022-08-10 10:28:26 +0200
commit: b9a31fed2b90ee69a5c23047fd2ff1c264ad9605 (patch)
tree: c7a6e319c5cc6ba9c7963b08f7a4cdf3c776c922
parent: 60e57f9c86a7aae67c2931200066aba059ec2721 (diff)
parent: 4f83706aa1263c04cb5e8763e1e8eb6c580bed3c (diff)
129 files changed, 1716 insertions, 2673 deletions
diff --git a/.circleci/config.yml b/.circleci/config.yml
index f6a875dd..e2df5c87 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -58,10 +58,10 @@ jobs:
             git submodule update
             mkdir build
             cd build
-            cmake -DUSER_VERSION_DIR=version ..
+            cmake -DWITH_GUDHI_THIRD_PARTY=OFF -DUSER_VERSION_DIR=version ..
             make user_version
             cd version
-            cmake -DCMAKE_BUILD_TYPE=Release -DWITH_GUDHI_EXAMPLE=OFF -DWITH_GUDHI_UTILITIES=OFF -DWITH_GUDHI_PYTHON=ON -DPython_ADDITIONAL_VERSIONS=3 .
+            cmake -DCMAKE_BUILD_TYPE=Release -DWITH_GUDHI_EXAMPLE=OFF -DWITH_GUDHI_UTILITIES=OFF -DWITH_GUDHI_PYTHON=ON -DPython_ADDITIONAL_VERSIONS=3 -DWITH_GUDHI_REMOTE_TEST=ON .
             cd python
             python3 setup.py build_ext --inplace
             make sphinx
@@ -79,7 +79,7 @@ jobs:
 
   doxygen:
     docker:
-      - image: gudhi/ci_for_gudhi:latest
+      - image: gudhi/doxygen_for_gudhi:latest
     steps:
       - checkout
       - run:
@@ -89,15 +89,15 @@ jobs:
             git submodule update
             mkdir build
             cd build
-            cmake -DCMAKE_BUILD_TYPE=Release -DWITH_GUDHI_EXAMPLE=OFF -DWITH_GUDHI_TEST=OFF -DWITH_GUDHI_UTILITIES=OFF -DWITH_GUDHI_PYTHON=OFF -DUSER_VERSION_DIR=version ..
+            cmake -DWITH_GUDHI_THIRD_PARTY=OFF -DUSER_VERSION_DIR=version ..
             make user_version
             cd version
             mkdir build
             cd build
-            cmake -DCMAKE_BUILD_TYPE=Release -DWITH_GUDHI_EXAMPLE=OFF -DWITH_GUDHI_TEST=OFF -DWITH_GUDHI_UTILITIES=OFF -DWITH_GUDHI_PYTHON=OFF ..
-            make doxygen 2>&1 | tee dox.log
-            grep warning dox.log
-            cp dox.log html/
+            cmake -DWITH_GUDHI_THIRD_PARTY=OFF ..
+            make doxygen
+            grep warning doxygen.log
+            cp doxygen.log html/
             cp -R html /tmp/doxygen
 
       - store_artifacts:
diff --git a/.github/for_maintainers/tests_strategy.md b/.github/for_maintainers/tests_strategy.md
index c25acf9b..d0ae76ef 100644
--- a/.github/for_maintainers/tests_strategy.md
+++ b/.github/for_maintainers/tests_strategy.md
@@ -4,17 +4,22 @@ This document tries to sum up the tests strategy that has been put in place for
 
 The aim is to help maintainers to anticipate third parties modifications, updates.
 
+## CMake options
+
+[CMake GUDHI options](../../src/cmake/modules/GUDHI_options.cmake) allows to activate/deactivate what should be built and tested.
+Note the special option `WITH_GUDHI_THIRD_PARTY` that, when set to `OFF`, accelerates doxygen documentation generation or `user_version` for instance.
+
 ## Builds
 
 ### Linux
 
-As all the third parties are already installed (thanks to docker), the compilations has been seperated by categories to be parallelized:
+As all the third parties are already installed (thanks to docker), the compilations have been separated in categories to be parallelized:
 
 * examples (C++)
 * tests (C++)
 * utils (C++)
 * doxygen (C++ documentation that is available in the artefacts)
-* python (including documentation and code coverage that are available in the artefacts)
+* python (including documentation and code coverage that are available in the artefacts; here the WITH_GUDHI_REMOTE_TEST option is enabled which adds datasets fetching test)
 
 (cf. `.circleci/config.yml`)
 
@@ -25,9 +30,9 @@ Without CGAL, and, with or without Eigen builds are performed inside the docker
 
 #### Update docker images
 
-C++ third parties installation are done thanks to apt on Ubuntu latest LTS.
+C++ third parties installation is done thanks to apt on Ubuntu latest LTS.
 
-Docker images need to be rebuild and push each time `.github/build-requirements`, `.github/test-requirements`, when a new third party is added, when a new CGAL version improves gudhi performances, ...
+Docker images need to be rebuilt and pushed each time `.github/build-requirements`, `.github/test-requirements`, when a new third party is added, when a new CGAL version improves gudhi performances, ...
 
 ```bash
 docker build -f Dockerfile_for_circleci_image -t gudhi/ci_for_gudhi:latest .
@@ -39,35 +44,35 @@ docker push gudhi/ci_for_gudhi_wo_cgal:latest
 
 ### Windows
 
-The compilations are not parallelized, as installation time (about 30 minutes) is too much compare to
+The compilations are not parallelized, as installation time (about 30 minutes) is too much compared to
 build and tests timings (about 30 minutes). Builds and tests include:
 
 * examples (C++)
 * tests (C++)
 * utils (C++)
-* python
+* python (here the WITH_GUDHI_REMOTE_TEST option is enabled which adds datasets fetching test)
 
 Doxygen (C++) is not generated.
 (cf. `azure-pipelines.yml`)
 
-C++ third parties installation are done thanks to [vcpkg](https://github.com/microsoft/vcpkg/).
-In case of installation issue, check in [vcpkg issues](https://github.com/microsoft/vcpkg/issues).
+C++ third parties installation is done thanks to [vcpkg](https://github.com/microsoft/vcpkg/).
+In case of an installation issue, check in [vcpkg issues](https://github.com/microsoft/vcpkg/issues).
 
 ### OSx
 
 The compilations are not parallelized, but they should, as installation time (about 4 minutes) is
-negligeable compare to build and tests timings (about 30 minutes). Builds and tests include:
+negligible compared to build and tests timings (about 30 minutes). Builds and tests include:
 
 * examples (C++)
 * tests (C++)
 * utils (C++)
-* python
+* python (here the WITH_GUDHI_REMOTE_TEST option is enabled which adds datasets fetching test)
 * Doxygen (C++)
 
 (cf. `azure-pipelines.yml`)
 
-C++ third parties installation are done thanks to [brew](https://formulae.brew.sh/formula/).
-In case of installation issue, check in formula issues.
+C++ third parties installation is done thanks to [brew](https://formulae.brew.sh/formula/).
+In case of an installation issue, check in formula issues.
 
 ## Pip packaging
 
@@ -80,9 +85,9 @@ Only the Linux pip package is based on a docker image (`gudhi/pip_for_gudhi` bas
 
 ### Update docker image
 
-C++ third parties installation are done thanks to yum on an image based on `quay.io/pypa/manylinux2014_x86_64`.
+C++ third parties installation is done thanks to yum on an image based on `quay.io/pypa/manylinux2014_x86_64`.
 
-Docker image need to be rebuild and push each time `.github/build-requirements`, when a new third party is added, when a new CGAL version improves gudhi performances, ...
+Docker image needs to be rebuilt and pushed each time `.github/build-requirements`, when a new third party is added, when a new CGAL version improves gudhi performances, ...
 As `.github/test-requirements` is not installed, no need to rebuild image when this file is modified.
 
 ```bash
diff --git a/.github/how_to_compile_gudhi_in_a_conda_env.md b/.github/how_to_compile_gudhi_in_a_conda_env.md
new file mode 100644
index 00000000..4acfca2e
--- /dev/null
+++ b/.github/how_to_compile_gudhi_in_a_conda_env.md
@@ -0,0 +1,93 @@
+# Install a conda development environment to compile GUDHI
+
+## Install miniconda
+
+Download the [installer](https://docs.conda.io/en/latest/miniconda.html) required by your system and follow the [instructions](https://conda.io/projects/conda/en/latest/user-guide/install/index.html).
+
+## Create a dedicated environment
+
+```bash
+conda install -c conda-forge mamba  # installation with mamba is faster
+conda create --name gudhi
+conda activate gudhi
+mamba install -c conda-forge python cmake doxygen eigen cgal-cpp
+```
+
+Some of the requirements are in the gudhi-devel repository (please refer to
+[how to use github to contribute to gudhi](how_to_use_github_to_contribute_to_gudhi.md)).
+Once the gudhi-devel repository is cloned on your machine (`git clone...`) - let's call it `/workdir/gudhi-devel` i.e. -
+and once the submodules are initialised (`git submodule update --init`):
+
+```bash
+pip install -r ext/gudhi-deploy/build-requirements.txt 
+pip install -r ext/gudhi-deploy/test-requirements.txt  # pytorch can be painful to install - not mandatory
+```
+
+## Compilation
+
+In order to compile all c++ utilities, examples, benchmarks, unitary tests, and python module:
+```bash
+cd /workdir/gudhi-devel
+rm -rf build; mkdir build  # /!\ any existing build folder will be removed
+cd build
+# To build all even examples and benchmarks
+cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_PREFIX_PATH=$CONDA_PREFIX -DWITH_GUDHI_EXAMPLE=ON -DWITH_GUDHI_BENCHMARK=ON ..
+```
+
+### Specific python compilation
+
+In order to compile only python module
+```bash
+cd /workdir/gudhi-devel
+rm -rf build; mkdir build  # /!\ any existing build folder will be removed
+cd build
+cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_PREFIX_PATH=$CONDA_PREFIX ..
+cd src/python
+# To build python module in parallel
+python setup.py build_ext -j 16 --inplace  # 16 is the number of CPU that are used to compile the python module. Can be any other value.
+# to clean the build
+# python setup.py clean --all
+```
+
+In order to use freshly compiled gudhi python module:
+```bash
+PYTHONPATH=/workdir/gudhi-devel/build/src/python python # or ipython, jupyter, ...
+```
+
+### Specific C++ documentation generation
+
+```bash
+cd /workdir/gudhi-devel
+rm -rf build; mkdir build  # /!\ any existing build folder will be removed
+cd build
+# python OFF to prevent python modules search makes cmake faster
+cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_PREFIX_PATH=$CONDA_PREFIX -DWITH_GUDHI_PYTHON=OFF -DUSER_VERSION_DIR=version ..
+make user_version;
+cd version
+mkdir build
+cd build
+# python OFF to prevent python modules search makes cmake faster
+cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_PREFIX_PATH=$CONDA_PREFIX -DWITH_GUDHI_PYTHON=OFF  ..
+make doxygen 2>&1 | tee dox.log
+grep warning dox.log # Warnings can be lost with parallel doxygen
+firefox html/index.html # [optional] To display the c++ documentation. Anything else than firefox can be used.
+```
+
+### Specific python documentation generation
+
+```bash
+cd /workdir/gudhi-devel
+rm -rf build; mkdir build  # /!\ any existing build folder will be removed
+cd build
+# python OFF to prevent python modules search makes cmake faster - it is the next cmake call in user version that matters
+cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_PREFIX_PATH=$CONDA_PREFIX -DWITH_GUDHI_PYTHON=OFF -DUSER_VERSION_DIR=version ..
+make user_version;
+cd version
+mkdir build
+cd build
+cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_PREFIX_PATH=$CONDA_PREFIX ..
+cd python
+# To build python module in parallel
+python setup.py build_ext -j 16 --inplace  # 16 is the number of CPU that are used to compile the python module. Can be any other value.
+firefox sphinx/index.html # [optional] To display the python documentation. Anything else than firefox can be used.
+```
+\ No newline at end of file
diff --git a/.gitignore b/.gitignore
index 6aab7337..9f427fb2 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,5 +1,5 @@
 # Classical CMake build directory
-build/
+/*build*
 
 # Generated by Cython
 src/python/gudhi/*.cpp
@@ -16,5 +16,3 @@ data/points/human.off_sc.txt
 # IDE specific
 # CLion
 .idea/
-cmake-build-debug/
-
diff --git a/CMakeLists.txt b/CMakeLists.txt
index ac877eea..6c233459 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -13,8 +13,12 @@ set(GUDHI_MISSING_MODULES "" CACHE INTERNAL "GUDHI_MISSING_MODULES")
 # This variable is used by Cython CMakeLists.txt and by GUDHI_third_party_libraries to know its path
 set(GUDHI_PYTHON_PATH "src/python")
 
-# For third parties libraries management - To be done last as CGAL updates CMAKE_MODULE_PATH
-include(GUDHI_third_party_libraries NO_POLICY_SCOPE)
+include(GUDHI_submodules)
+
+if (WITH_GUDHI_THIRD_PARTY)
+  # For third parties libraries management - To be done last as CGAL updates CMAKE_MODULE_PATH
+  include(GUDHI_third_party_libraries NO_POLICY_SCOPE)
+endif()
 
 include(GUDHI_compilation_flags)
 
@@ -52,7 +56,9 @@ foreach(GUDHI_MODULE ${GUDHI_MODULES})
   endforeach()
 endforeach()
 
-add_subdirectory(src/GudhUI)
+if (WITH_GUDHI_THIRD_PARTY)
+  add_subdirectory(src/GudhUI)
+endif()
 
 if (WITH_GUDHI_PYTHON)
   # specific for cython module
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 31264c37..e005b3be 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -30,7 +30,7 @@ jobs:
     - bash: |
         mkdir build
         cd build
-        cmake -DCMAKE_BUILD_TYPE:STRING=$(cmakeBuildType) -DWITH_GUDHI_EXAMPLE=ON -DWITH_GUDHI_TEST=ON -DWITH_GUDHI_UTILITIES=ON -DWITH_GUDHI_PYTHON=ON ..
+        cmake -DCMAKE_BUILD_TYPE:STRING=$(cmakeBuildType) -DWITH_GUDHI_EXAMPLE=ON -DWITH_GUDHI_TEST=ON -DWITH_GUDHI_UTILITIES=ON -DWITH_GUDHI_PYTHON=ON -DWITH_GUDHI_REMOTE_TEST=ON ..
         make
         make doxygen
         ctest --output-on-failure
@@ -74,7 +74,7 @@ jobs:
         IF %errorlevel% NEQ 0 exit /b %errorlevel%
         ctest --output-on-failure -C Release -E diff_files
         IF %errorlevel% NEQ 0 exit /b %errorlevel%
-        cmake  -DWITH_GUDHI_PYTHON=ON .
+        cmake  -DWITH_GUDHI_PYTHON=ON -DWITH_GUDHI_REMOTE_TEST=ON .
         IF %errorlevel% NEQ 0 exit /b %errorlevel%
         cd src\python
         copy "C:\vcpkg\installed\x64-windows\bin\mpfr*.dll" ".\gudhi\"
diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib
index 8462e731..0a3ef43d 100644
--- a/biblio/bibliography.bib
+++ b/biblio/bibliography.bib
@@ -1151,7 +1151,7 @@ language={English}
   editor =	{Lars Arge and J{\'a}nos Pach},
   publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
   address =	{Dagstuhl, Germany},
-  URL =		{https://drops.dagstuhl.de/opus/volltexte/2015/5098},
+  URL =		{https://drops.dagstuhl.de/opus/volltexte/2015/5098/},
   URN =		{urn:nbn:de:0030-drops-50981},
   doi =		{10.4230/LIPIcs.SOCG.2015.642},
   annote =	{Keywords: Simplicial complex, Compact data structures, Automaton, NP-hard}
@@ -1341,7 +1341,7 @@ doi="10.1007/978-3-030-43408-3_2",
   editor =	{Sergio Cabello and Danny Z. Chen},
   publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
   address =	{Dagstuhl, Germany},
-  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12177},
+  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12177/},
   URN =		{urn:nbn:de:0030-drops-121777},
   doi =		{10.4230/LIPIcs.SoCG.2020.19},
   annote =	{Keywords: Computational Topology, Topological Data Analysis, Edge Collapse, Simple Collapse, Persistent homology}
diff --git a/ext/gudhi-deploy b/ext/gudhi-deploy
-Subproject 290ade1086bedbc96a35df886cadecabbf4072e
+Subproject e9e9a4878731853d2d3149a5eac30df338a8197
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h
index 028ec9bb..aec8c1b1 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h
@@ -69,7 +69,7 @@ template<typename D> struct Is_Epeck_D<CGAL::Epeck_d<D>> { static const bool val
  * \ingroup alpha_complex
  * 
  * \details
- * The data structure is constructing a CGAL Delaunay triangulation (for more informations on CGAL Delaunay 
+ * The data structure is constructing a CGAL Delaunay triangulation (for more information on CGAL Delaunay 
  * triangulation, please refer to the corresponding chapter in page http://doc.cgal.org/latest/Triangulation/) from a
  * range of points or from an OFF file (cf. Points_off_reader).
  * 
@@ -461,10 +461,10 @@ class Alpha_complex {
   void propagate_alpha_filtration(SimplicialComplexForAlpha& complex, Simplex_handle f_simplex) {
     // From SimplicialComplexForAlpha type required to assign filtration values.
     using Filtration_value = typename SimplicialComplexForAlpha::Filtration_value;
-    using Vertex_handle = typename SimplicialComplexForAlpha::Vertex_handle;
 
     // ### Foreach Tau face of Sigma
-    for (auto f_boundary : complex.boundary_simplex_range(f_simplex)) {
+    for (auto face_opposite_vertex : complex.boundary_opposite_vertex_simplex_range(f_simplex)) {
+      auto f_boundary = face_opposite_vertex.first;
 #ifdef DEBUG_TRACES
       std::clog << " | --------------------------------------------------\n";
       std::clog << " | Tau ";
@@ -485,18 +485,10 @@ class Alpha_complex {
 #endif  // DEBUG_TRACES
         // ### Else
       } else {
-        // Find which vertex of f_simplex is missing in f_boundary. We could actually write a variant of boundary_simplex_range that gives pairs (f_boundary, vertex). We rely on the fact that simplex_vertex_range is sorted.
-        auto longlist = complex.simplex_vertex_range(f_simplex);
-        auto shortlist = complex.simplex_vertex_range(f_boundary);
-        auto longiter = std::begin(longlist);
-        auto shortiter = std::begin(shortlist);
-        auto enditer = std::end(shortlist);
-        while(shortiter != enditer && *longiter == *shortiter) { ++longiter; ++shortiter; }
-        Vertex_handle extra = *longiter;
         auto const& cache=get_cache(complex, f_boundary);
-        bool is_gab = kernel_.is_gabriel(cache, get_point_(extra));
+        bool is_gab = kernel_.is_gabriel(cache, get_point_(face_opposite_vertex.second));
 #ifdef DEBUG_TRACES
-        std::clog << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << extra << std::endl;
+        std::clog << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << face_opposite_vertex.second << std::endl;
 #endif  // DEBUG_TRACES
         // ### If Tau is not Gabriel of Sigma
         if (false == is_gab) {
diff --git a/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h b/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h
index aa255ec2..4a6af3a4 100644
--- a/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h
+++ b/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h
@@ -237,7 +237,7 @@ class Bitmap_cubical_complex : public T {
    * Filtration_simplex_iterator class provides an iterator though the whole structure in the order of filtration.
    * Secondary criteria for filtration are:
    * (1) Dimension of a cube (lower dimensional comes first).
-   * (2) Position in the data structure (the ones that are earlies in the data structure comes first).
+   * (2) Position in the data structure (the ones that are earliest in the data structure come first).
    **/
   class Filtration_simplex_range;
 
diff --git a/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex_base.h b/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex_base.h
index f8f80ded..bafe7981 100644
--- a/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex_base.h
+++ b/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex_base.h
@@ -43,7 +43,7 @@ namespace cubical_complex {
  * Each cell is represented by a single
  * bit (in case of black and white bitmaps, or by a single element of a type T
  * (here T is a filtration type of a bitmap, typically a double).
- * All the informations needed for homology and
+ * All the information needed for homology and
  * persistent homology computations (like dimension of a cell, boundary and
  * coboundary elements of a cell, are then obtained from the
  * position of the element in C.
diff --git a/src/Bottleneck_distance/include/gudhi/Neighbors_finder.h b/src/Bottleneck_distance/include/gudhi/Neighbors_finder.h
index c65e6082..1d56f0b4 100644
--- a/src/Bottleneck_distance/include/gudhi/Neighbors_finder.h
+++ b/src/Bottleneck_distance/include/gudhi/Neighbors_finder.h
@@ -86,7 +86,7 @@ class Neighbors_finder {
 };
 
 /** \internal \brief data structure used to find any point (including projections) in V near to a query point from U
- * (which can be a projection) in a layered graph layer given as parmeter.
+ * (which can be a projection) in a layered graph layer given as parameter.
  *
  * V points have to be added manually using their index and before the first pull. A neighbor pulled is automatically
  * removed.
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 8023e04c..f9f77ef7 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -12,8 +12,12 @@ set(GUDHI_MISSING_MODULES "" CACHE INTERNAL "GUDHI_MISSING_MODULES")
 # This variable is used by Cython CMakeLists.txt and by GUDHI_third_party_libraries to know its path
 set(GUDHI_PYTHON_PATH "python")
 
-# For third parties libraries management - To be done last as CGAL updates CMAKE_MODULE_PATH
-include(GUDHI_third_party_libraries NO_POLICY_SCOPE)
+include(GUDHI_submodules)
+
+if (WITH_GUDHI_THIRD_PARTY)
+  # For third parties libraries management - To be done last as CGAL updates CMAKE_MODULE_PATH
+  include(GUDHI_third_party_libraries NO_POLICY_SCOPE)
+endif()
 
 include(GUDHI_compilation_flags)
 
@@ -67,7 +71,9 @@ foreach(GUDHI_MODULE ${GUDHI_MODULES})
   endforeach()
 endforeach()
 
-add_subdirectory(GudhUI)
+if (WITH_GUDHI_THIRD_PARTY)
+  add_subdirectory(GudhUI)
+endif()
 
 message("++ GUDHI_MODULES list is:\"${GUDHI_MODULES}\"")
 message("++ GUDHI_MISSING_MODULES list is:\"${GUDHI_MISSING_MODULES}\"")
diff --git a/src/Cech_complex/benchmark/CMakeLists.txt b/src/Cech_complex/benchmark/CMakeLists.txt
index bc54c0f3..a6b3d70b 100644
--- a/src/Cech_complex/benchmark/CMakeLists.txt
+++ b/src/Cech_complex/benchmark/CMakeLists.txt
@@ -1,13 +1,15 @@
 project(Cech_complex_benchmark)
 
-# Do not forget to copy test files in current binary dir
-file(COPY "${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off" DESTINATION ${CMAKE_CURRENT_BINARY_DIR}/)
+if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 5.0.1)
+  # Do not forget to copy test files in current binary dir
+  file(COPY "${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off" DESTINATION ${CMAKE_CURRENT_BINARY_DIR}/)
 
-if(TARGET Boost::filesystem)
-  add_executable(cech_complex_benchmark cech_complex_benchmark.cpp)
-  target_link_libraries(cech_complex_benchmark Boost::filesystem)
+  if(TARGET Boost::filesystem)
+    add_executable(cech_complex_benchmark cech_complex_benchmark.cpp)
+    target_link_libraries(cech_complex_benchmark Boost::filesystem)
   
-  if (TBB_FOUND)
-    target_link_libraries(cech_complex_benchmark ${TBB_LIBRARIES})
+    if (TBB_FOUND)
+      target_link_libraries(cech_complex_benchmark ${TBB_LIBRARIES})
+    endif()
   endif()
-endif()
-\ No newline at end of file
+endif()
diff --git a/src/Cech_complex/benchmark/cech_complex_benchmark.cpp b/src/Cech_complex/benchmark/cech_complex_benchmark.cpp
index 2e4adce4..a9dc5d0d 100644
--- a/src/Cech_complex/benchmark/cech_complex_benchmark.cpp
+++ b/src/Cech_complex/benchmark/cech_complex_benchmark.cpp
@@ -10,12 +10,13 @@
 
 #include <gudhi/Points_off_io.h>
 #include <gudhi/distance_functions.h>
-#include <gudhi/graph_simplicial_complex.h>
 #include <gudhi/Clock.h>
 #include <gudhi/Rips_complex.h>
 #include <gudhi/Cech_complex.h>
 #include <gudhi/Simplex_tree.h>
-#include <gudhi/Miniball.hpp>
+
+#include <CGAL/Epick_d.h>
+#include <CGAL/Epeck_d.h>
 
 #include "boost/filesystem.hpp"  // includes all needed Boost.Filesystem declarations
 
@@ -26,107 +27,81 @@
 using Simplex_tree = Gudhi::Simplex_tree<>;
 using Filtration_value = Simplex_tree::Filtration_value;
 using Point = std::vector<Filtration_value>;
-using Point_cloud = std::vector<Point>;
 using Points_off_reader = Gudhi::Points_off_reader<Point>;
-using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>;
 using Rips_complex = Gudhi::rips_complex::Rips_complex<Filtration_value>;
-using Cech_complex = Gudhi::cech_complex::Cech_complex<Simplex_tree, Point_cloud>;
-
-class Minimal_enclosing_ball_radius {
- public:
-  // boost::range_value is not SFINAE-friendly so we cannot use it in the return type
-  template <typename Point>
-  typename std::iterator_traits<typename boost::range_iterator<Point>::type>::value_type operator()(
-      const Point& p1, const Point& p2) const {
-    // Type def
-    using Point_cloud = std::vector<Point>;
-    using Point_iterator = typename Point_cloud::const_iterator;
-    using Coordinate_iterator = typename Point::const_iterator;
-    using Min_sphere =
-        typename Gudhi::Miniball::Miniball<Gudhi::Miniball::CoordAccessor<Point_iterator, Coordinate_iterator>>;
-
-    Point_cloud point_cloud;
-    point_cloud.push_back(p1);
-    point_cloud.push_back(p2);
-
-    GUDHI_CHECK((p1.end() - p1.begin()) == (p2.end() - p2.begin()), "inconsistent point dimensions");
-    Min_sphere min_sphere(p1.end() - p1.begin(), point_cloud.begin(), point_cloud.end());
 
-    return std::sqrt(min_sphere.squared_radius());
-  }
-};
+template<typename Kernel>
+Simplex_tree benchmark_cech(const std::string& off_file_points, const Filtration_value& radius, const int& dim_max, const bool exact) {
+    using Point_cgal = typename Kernel::Point_d;
+    using Points_off_reader_cgal = Gudhi::Points_off_reader<Point_cgal>;
+    using Cech_complex = Gudhi::cech_complex::Cech_complex<Kernel, Simplex_tree>;
+
+    // Extract the points from the file filepoints
+    Points_off_reader_cgal off_reader_cgal(off_file_points);
+
+    Gudhi::Clock cech_clock("Cech computation");
+    Cech_complex cech_complex_from_points(off_reader_cgal.get_point_cloud(), radius);
+    Simplex_tree cech_stree;
+    cech_complex_from_points.create_complex(cech_stree, dim_max, exact);
+
+    // ------------------------------------------
+    // Display information about the Cech complex
+    // ------------------------------------------
+    double cech_sec = cech_clock.num_seconds();
+    std::clog << cech_sec << "  ;  ";
+    return cech_stree;
+}
 
 int main(int argc, char* argv[]) {
-  std::string off_file_points = "tore3D_1307.off";
-  Filtration_value threshold = 1e20;
-
-  // Extract the points from the file filepoints
-  Points_off_reader off_reader(off_file_points);
-
-  Gudhi::Clock euclidean_clock("Gudhi::Euclidean_distance");
-  // Compute the proximity graph of the points
-  Proximity_graph euclidean_prox_graph = Gudhi::compute_proximity_graph<Simplex_tree>(
-      off_reader.get_point_cloud(), threshold, Gudhi::Euclidean_distance());
-
-  std::clog << euclidean_clock << std::endl;
-
-  Gudhi::Clock miniball_clock("Minimal_enclosing_ball_radius");
-  // Compute the proximity graph of the points
-  Proximity_graph miniball_prox_graph = Gudhi::compute_proximity_graph<Simplex_tree>(
-      off_reader.get_point_cloud(), threshold, Minimal_enclosing_ball_radius());
-  std::clog << miniball_clock << std::endl;
-
-  Gudhi::Clock common_miniball_clock("Gudhi::Minimal_enclosing_ball_radius()");
-  // Compute the proximity graph of the points
-  Proximity_graph common_miniball_prox_graph = Gudhi::compute_proximity_graph<Simplex_tree>(
-      off_reader.get_point_cloud(), threshold, Gudhi::Minimal_enclosing_ball_radius());
-  std::clog << common_miniball_clock << std::endl;
-
-  boost::filesystem::path full_path(boost::filesystem::current_path());
-  std::clog << "Current path is : " << full_path << std::endl;
-
-  std::clog << "File name;Radius;Rips time;Cech time; Ratio Rips/Cech time;Rips nb simplices;Cech nb simplices;"
-            << std::endl;
-  boost::filesystem::directory_iterator end_itr;  // default construction yields past-the-end
-  for (boost::filesystem::directory_iterator itr(boost::filesystem::current_path()); itr != end_itr; ++itr) {
-    if (!boost::filesystem::is_directory(itr->status())) {
-      if (itr->path().extension() == ".off")  // see below
-      {
-        Points_off_reader off_reader(itr->path().string());
-        Point p0 = off_reader.get_point_cloud()[0];
-
-        for (Filtration_value radius = 0.1; radius < 0.4; radius += 0.1) {
-          std::clog << itr->path().stem() << ";";
-          std::clog << radius << ";";
-          Gudhi::Clock rips_clock("Rips computation");
-          Rips_complex rips_complex_from_points(off_reader.get_point_cloud(), radius,
-                                                Gudhi::Minimal_enclosing_ball_radius());
-          Simplex_tree rips_stree;
-          rips_complex_from_points.create_complex(rips_stree, p0.size() - 1);
-          // ------------------------------------------
-          // Display information about the Rips complex
-          // ------------------------------------------
-          double rips_sec = rips_clock.num_seconds();
-          std::clog << rips_sec << ";";
-
-          Gudhi::Clock cech_clock("Cech computation");
-          Cech_complex cech_complex_from_points(off_reader.get_point_cloud(), radius);
-          Simplex_tree cech_stree;
-          cech_complex_from_points.create_complex(cech_stree, p0.size() - 1);
-          // ------------------------------------------
-          // Display information about the Cech complex
-          // ------------------------------------------
-          double cech_sec = cech_clock.num_seconds();
-          std::clog << cech_sec << ";";
-          std::clog << cech_sec / rips_sec << ";";
-
-          assert(rips_stree.num_simplices() >= cech_stree.num_simplices());
-          std::clog << rips_stree.num_simplices() << ";";
-          std::clog << cech_stree.num_simplices() << ";" << std::endl;
+    boost::filesystem::path full_path(boost::filesystem::current_path());
+    std::clog << "Current path is : " << full_path << std::endl;
+
+    std::clog << "File name ; Radius ; Rips time ; Dim-3 Fast Cech time ; Dynamic_dim Fast Cech time ; "
+                 "Dim-3 Safe Cech time ; Dynamic_dim Safe Cech time ; Dim-3 Exact Cech time ; Dynamic_dim Exact Cech time ; "
+                 "Cech nb simplices ; Rips nb simplices;"
+              << std::endl;
+    boost::filesystem::directory_iterator end_itr;  // default construction yields past-the-end
+    // For every ".off" file in the current directory, and for 3 predefined thresholds, compare Rips and various Cech constructions
+    for (boost::filesystem::directory_iterator itr(boost::filesystem::current_path()); itr != end_itr; ++itr) {
+        if (!boost::filesystem::is_directory(itr->status())) {
+            if (itr->path().extension() == ".off") {
+                Points_off_reader off_reader(itr->path().string());
+                Point p0 = off_reader.get_point_cloud()[0];
+                // Loop over the different thresholds
+                for (Filtration_value radius = 0.1; radius < 0.35; radius += 0.1) {
+                    std::clog << itr->path().stem() << "  ;  ";
+                    std::clog << radius << "  ;  ";
+
+                    Gudhi::Clock rips_clock("Rips computation");
+                    Rips_complex rips_complex_from_points(off_reader.get_point_cloud(), radius, Gudhi::Euclidean_distance());
+                    Simplex_tree rips_stree;
+                    int dim_max = p0.size() - 1;
+                    rips_complex_from_points.create_complex(rips_stree, dim_max);
+                    // ------------------------------------------
+                    // Display information about the Rips complex
+                    // ------------------------------------------
+                    double rips_sec = rips_clock.num_seconds();
+                    std::clog << rips_sec << "  ;  ";
+
+                    // --------------
+                    // Cech complex
+                    // --------------
+                    // Fast
+                    benchmark_cech<CGAL::Epick_d<CGAL::Dimension_tag<3>>>(itr->path().string(), radius, dim_max, false);
+                    benchmark_cech<CGAL::Epick_d<CGAL::Dynamic_dimension_tag>>(itr->path().string(), radius, dim_max, false);
+                    // Safe
+                    benchmark_cech<CGAL::Epeck_d<CGAL::Dimension_tag<3>>>(itr->path().string(), radius, dim_max, false);
+                    benchmark_cech<CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>>(itr->path().string(), radius, dim_max, false);
+                    // Exact
+                    benchmark_cech<CGAL::Epeck_d<CGAL::Dimension_tag<3>>>(itr->path().string(), radius, dim_max, true);
+                    auto cech_stree = benchmark_cech<CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>>(itr->path().string(), radius, dim_max, true);
+
+                    std::clog << cech_stree.num_simplices() << "  ;  ";
+                    std::clog << rips_stree.num_simplices() << ";" << std::endl;
+                }
+            }
         }
-      }
     }
-  }
 
-  return 0;
+    return 0;
 }
diff --git a/src/Cech_complex/concept/SimplicialComplexForCech.h b/src/Cech_complex/concept/SimplicialComplexForCech.h
index 00c7df3a..6202fe92 100644
--- a/src/Cech_complex/concept/SimplicialComplexForCech.h
+++ b/src/Cech_complex/concept/SimplicialComplexForCech.h
@@ -47,8 +47,8 @@ struct SimplicialComplexForCech {
 
 };
 
-}  // namespace alpha_complex
+}  // namespace cech_complex
 
 }  // namespace Gudhi
 
-#endif  // CONCEPT_ALPHA_COMPLEX_SIMPLICIAL_COMPLEX_FOR_ALPHA_H_
+#endif  // CONCEPT_CECH_COMPLEX_SIMPLICIAL_COMPLEX_FOR_CECH_H_
diff --git a/src/Cech_complex/doc/Intro_cech_complex.h b/src/Cech_complex/doc/Intro_cech_complex.h
index 095fd320..595fb64b 100644
--- a/src/Cech_complex/doc/Intro_cech_complex.h
+++ b/src/Cech_complex/doc/Intro_cech_complex.h
@@ -28,7 +28,7 @@ namespace cech_complex {
  * <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a> constructed
  *  from a proximity graph. The set of all simplices is filtered by the radius of their minimal enclosing ball.
  *
- * The input shall be a point cloud in an Euclidean space.
+ * The input shall be a range of points where a point is defined as <a target="_blank" href="https://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Point__d.html">CGAL kernel Point_d.</a>
  * 
  * \remark For people only interested in the topology of the \ref cech_complex (for instance persistence),
  * \ref alpha_complex is equivalent to the \ref cech_complex and much smaller if you do not bound the radii.
@@ -37,8 +37,7 @@ namespace cech_complex {
  * \subsection cechalgorithm Algorithm
  *
  * Cech_complex first builds a proximity graph from a point cloud.
- * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from
- * `Gudhi::Minimal_enclosing_ball_radius` function.
+ * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed using CGAL kernel functions.
  * 
  * All edges that have a filtration value strictly greater than a user given maximal radius value, \f$max\_radius\f$,
  * are not inserted into the complex.
@@ -60,19 +59,9 @@ namespace cech_complex {
  *
  * \image html "cech_complex_representation.png" "Čech complex expansion"
  *
- * The minimal ball radius computation is insured by
- * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html">
- * the miniball software (V3.0)</a> - Smallest Enclosing Balls of Points - and distributed with GUDHI.
- * Please refer to
- * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/esa99_final.pdf">
- * the miniball software design description</a> for more information about this computation.
- *
  * This radius computation is the reason why the Cech_complex is taking much more time to be computed than the
  * \ref rips_complex but it offers more topological guarantees.
  *
- * If the Cech_complex interfaces are not detailed enough for your need, please refer to the example
- * \gudhi_example_link{Cech_complex,cech_complex_step_by_step.cpp}, where the graph construction over the Simplex_tree is more detailed.
- *
  * \subsection cechpointscloudexample Example from a point cloud
  * 
  * This example builds the proximity graph from the given points, and maximal radius values.
diff --git a/src/Cech_complex/example/CMakeLists.txt b/src/Cech_complex/example/CMakeLists.txt
index 1b08c7cb..7d52ed5e 100644
--- a/src/Cech_complex/example/CMakeLists.txt
+++ b/src/Cech_complex/example/CMakeLists.txt
@@ -1,17 +1,9 @@
 project(Cech_complex_examples)
 
-if (TARGET Boost::program_options)
-  add_executable ( Cech_complex_example_step_by_step cech_complex_step_by_step.cpp )
-  target_link_libraries(Cech_complex_example_step_by_step Boost::program_options)
+if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 5.0.1)
+  add_executable ( Cech_complex_example_from_points cech_complex_example_from_points.cpp)
   if (TBB_FOUND)
-    target_link_libraries(Cech_complex_example_step_by_step ${TBB_LIBRARIES})
+    target_link_libraries(Cech_complex_example_from_points ${TBB_LIBRARIES})
   endif()
-  add_test(NAME Cech_complex_utility_from_rips_on_tore_3D COMMAND $<TARGET_FILE:Cech_complex_example_step_by_step>
-      "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "-r" "0.25" "-d" "3")
+  add_test(NAME Cech_complex_example_from_points COMMAND $<TARGET_FILE:Cech_complex_example_from_points>)
 endif()
-
-add_executable ( Cech_complex_example_from_points cech_complex_example_from_points.cpp)
-if (TBB_FOUND)
-  target_link_libraries(Cech_complex_example_from_points ${TBB_LIBRARIES})
-endif()
-add_test(NAME Cech_complex_example_from_points COMMAND $<TARGET_FILE:Cech_complex_example_from_points>)
diff --git a/src/Cech_complex/example/cech_complex_example_from_points.cpp b/src/Cech_complex/example/cech_complex_example_from_points.cpp
index 1a1f708c..ef9071ec 100644
--- a/src/Cech_complex/example/cech_complex_example_from_points.cpp
+++ b/src/Cech_complex/example/cech_complex_example_from_points.cpp
@@ -1,30 +1,33 @@
 #include <gudhi/Cech_complex.h>
 #include <gudhi/Simplex_tree.h>
 
+#include <CGAL/Epeck_d.h>  // For EXACT or SAFE version
+
 #include <iostream>
 #include <string>
 #include <vector>
-#include <array>
 
 int main() {
   // Type definitions
-  using Point_cloud = std::vector<std::array<double, 2>>;
   using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
   using Filtration_value = Simplex_tree::Filtration_value;
-  using Cech_complex = Gudhi::cech_complex::Cech_complex<Simplex_tree, Point_cloud>;
+  using Kernel = CGAL::Epeck_d<CGAL::Dimension_tag<2>>;
+  using Point = typename Kernel::Point_d;
+  using Point_cloud = std::vector<Point>;
+  using Cech_complex = Gudhi::cech_complex::Cech_complex<Kernel, Simplex_tree>;
 
   Point_cloud points;
-  points.push_back({1., 0.});                  // 0
-  points.push_back({0., 1.});                  // 1
-  points.push_back({2., 1.});                  // 2
-  points.push_back({3., 2.});                  // 3
-  points.push_back({0., 3.});                  // 4
-  points.push_back({3. + std::sqrt(3.), 3.});  // 5
-  points.push_back({1., 4.});                  // 6
-  points.push_back({3., 4.});                  // 7
-  points.push_back({2., 4. + std::sqrt(3.)});  // 8
-  points.push_back({0., 4.});                  // 9
-  points.push_back({-0.5, 2.});                // 10
+  points.emplace_back(1., 0.);                    // 0
+  points.emplace_back(0., 1.);                    // 1
+  points.emplace_back(2., 1.);                    // 2
+  points.emplace_back(3., 2.);                    // 3
+  points.emplace_back(0., 3.);                    // 4
+  points.emplace_back(3. + std::sqrt(3.), 3.);    // 5
+  points.emplace_back(1., 4.);                    // 6
+  points.emplace_back(3., 4.);                    // 7
+  points.emplace_back(2., 4. + std::sqrt(3.));    // 8
+  points.emplace_back(0., 4.);                    // 9
+  points.emplace_back(-0.5, 2.);                  // 10
 
   // ----------------------------------------------------------------------------
   // Init of a Cech complex from points
diff --git a/src/Cech_complex/example/cech_complex_step_by_step.cpp b/src/Cech_complex/example/cech_complex_step_by_step.cpp
deleted file mode 100644
index f59f0293..00000000
--- a/src/Cech_complex/example/cech_complex_step_by_step.cpp
+++ /dev/null
@@ -1,154 +0,0 @@
-/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
- *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
- *    Author(s):       Vincent Rouvreau
- *
- *    Copyright (C) 2018 Inria
- *
- *    Modification(s):
- *      - YYYY/MM Author: Description of the modification
- */
-
-#include <gudhi/graph_simplicial_complex.h>
-#include <gudhi/distance_functions.h>
-#include <gudhi/Simplex_tree.h>
-#include <gudhi/Points_off_io.h>
-
-#include <gudhi/Miniball.hpp>
-
-#include <boost/program_options.hpp>
-
-#include <string>
-#include <vector>
-#include <limits>   // infinity
-#include <utility>  // for pair
-#include <map>
-
-// ----------------------------------------------------------------------------
-// rips_persistence_step_by_step is an example of each step that is required to
-// build a Rips over a Simplex_tree. Please refer to rips_persistence to see
-// how to do the same thing with the Rips_complex wrapper for less detailed
-// steps.
-// ----------------------------------------------------------------------------
-
-// Types definition
-using Simplex_tree = Gudhi::Simplex_tree<>;
-using Simplex_handle = Simplex_tree::Simplex_handle;
-using Filtration_value = Simplex_tree::Filtration_value;
-using Point = std::vector<double>;
-using Points_off_reader = Gudhi::Points_off_reader<Point>;
-using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>;
-
-class Cech_blocker {
- private:
-  using Point_cloud = std::vector<Point>;
-  using Point_iterator = Point_cloud::const_iterator;
-  using Coordinate_iterator = Point::const_iterator;
-  using Min_sphere = Gudhi::Miniball::Miniball<Gudhi::Miniball::CoordAccessor<Point_iterator, Coordinate_iterator>>;
-
- public:
-  bool operator()(Simplex_handle sh) {
-    std::vector<Point> points;
-    for (auto vertex : simplex_tree_.simplex_vertex_range(sh)) {
-      points.push_back(point_cloud_[vertex]);
-#ifdef DEBUG_TRACES
-      std::clog << "#(" << vertex << ")#";
-#endif  // DEBUG_TRACES
-    }
-    Filtration_value radius = Gudhi::Minimal_enclosing_ball_radius()(points);
-#ifdef DEBUG_TRACES
-    std::clog << "radius = " << radius << " - " << (radius > max_radius_) << std::endl;
-#endif  // DEBUG_TRACES
-    simplex_tree_.assign_filtration(sh, radius);
-    return (radius > max_radius_);
-  }
-  Cech_blocker(Simplex_tree& simplex_tree, Filtration_value max_radius, const std::vector<Point>& point_cloud)
-      : simplex_tree_(simplex_tree), max_radius_(max_radius), point_cloud_(point_cloud) {
-    dimension_ = point_cloud_[0].size();
-  }
-
- private:
-  Simplex_tree simplex_tree_;
-  Filtration_value max_radius_;
-  std::vector<Point> point_cloud_;
-  int dimension_;
-};
-
-void program_options(int argc, char* argv[], std::string& off_file_points, Filtration_value& max_radius, int& dim_max);
-
-int main(int argc, char* argv[]) {
-  std::string off_file_points;
-  Filtration_value max_radius;
-  int dim_max;
-
-  program_options(argc, argv, off_file_points, max_radius, dim_max);
-
-  // Extract the points from the file filepoints
-  Points_off_reader off_reader(off_file_points);
-
-  // Compute the proximity graph of the points
-  Proximity_graph prox_graph = Gudhi::compute_proximity_graph<Simplex_tree>(off_reader.get_point_cloud(), max_radius,
-                                                                            Gudhi::Minimal_enclosing_ball_radius());
-
-  // Construct the Rips complex in a Simplex Tree
-  Simplex_tree st;
-  // insert the proximity graph in the simplex tree
-  st.insert_graph(prox_graph);
-  // expand the graph until dimension dim_max
-  st.expansion_with_blockers(dim_max, Cech_blocker(st, max_radius, off_reader.get_point_cloud()));
-
-  std::clog << "The complex contains " << st.num_simplices() << " simplices \n";
-  std::clog << "   and has dimension " << st.dimension() << " \n";
-
-  // Sort the simplices in the order of the filtration
-  st.initialize_filtration();
-
-#if DEBUG_TRACES
-  std::clog << "********************************************************************\n";
-  std::clog << "* The complex contains " << st.num_simplices() << " simplices - dimension=" << st.dimension() << "\n";
-  std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
-  for (auto f_simplex : st.filtration_simplex_range()) {
-    std::clog << "   "
-              << "[" << st.filtration(f_simplex) << "] ";
-    for (auto vertex : st.simplex_vertex_range(f_simplex)) {
-      std::clog << static_cast<int>(vertex) << " ";
-    }
-    std::clog << std::endl;
-  }
-#endif  // DEBUG_TRACES
-
-  return 0;
-}
-
-void program_options(int argc, char* argv[], std::string& off_file_points, Filtration_value& max_radius, int& dim_max) {
-  namespace po = boost::program_options;
-  po::options_description hidden("Hidden options");
-  hidden.add_options()("input-file", po::value<std::string>(&off_file_points),
-                       "Name of an OFF file containing a point set.\n");
-
-  po::options_description visible("Allowed options", 100);
-  visible.add_options()("help,h", "produce help message")(
-      "max-radius,r",
-      po::value<Filtration_value>(&max_radius)->default_value(std::numeric_limits<Filtration_value>::infinity()),
-      "Maximal length of an edge for the Rips complex construction.")(
-      "cpx-dimension,d", po::value<int>(&dim_max)->default_value(1),
-      "Maximal dimension of the Rips complex we want to compute.");
-
-  po::positional_options_description pos;
-  pos.add("input-file", 1);
-
-  po::options_description all;
-  all.add(visible).add(hidden);
-
-  po::variables_map vm;
-  po::store(po::command_line_parser(argc, argv).options(all).positional(pos).run(), vm);
-  po::notify(vm);
-
-  if (vm.count("help") || !vm.count("input-file")) {
-    std::clog << std::endl;
-    std::clog << "Construct a Cech complex defined on a set of input points.\n \n";
-
-    std::clog << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
-    std::clog << visible << std::endl;
-    exit(-1);
-  }
-}
diff --git a/src/Cech_complex/include/gudhi/Cech_complex.h b/src/Cech_complex/include/gudhi/Cech_complex.h
index b0871e10..08b7a72f 100644
--- a/src/Cech_complex/include/gudhi/Cech_complex.h
+++ b/src/Cech_complex/include/gudhi/Cech_complex.h
@@ -11,14 +11,13 @@
 #ifndef CECH_COMPLEX_H_
 #define CECH_COMPLEX_H_
 
-#include <gudhi/distance_functions.h>        // for Gudhi::Minimal_enclosing_ball_radius
+#include <gudhi/Sphere_circumradius.h>       // for Gudhi::cech_complex::Sphere_circumradius
 #include <gudhi/graph_simplicial_complex.h>  // for Gudhi::Proximity_graph
 #include <gudhi/Debug_utils.h>               // for GUDHI_CHECK
 #include <gudhi/Cech_complex_blocker.h>      // for Gudhi::cech_complex::Cech_blocker
 
 #include <iostream>
 #include <stdexcept>  // for exception management
-#include <vector>
 
 namespace Gudhi {
 
@@ -26,55 +25,52 @@ namespace cech_complex {
 
 /**
  * \class Cech_complex
- * \brief Cech complex data structure.
+ * \brief Cech complex class.
  *
  * \ingroup cech_complex
  *
  * \details
- * The data structure is a proximity graph, containing edges when the edge length is less or equal
- * to a given max_radius. Edge length is computed from `Gudhi::Minimal_enclosing_ball_radius` distance function.
+ * Cech complex is a simplicial complex where the set of all simplices is filtered
+ * by the radius of their minimal enclosing ball and bounded by the given max_radius.
  *
- * \tparam SimplicialComplexForProximityGraph furnishes `Vertex_handle` and `Filtration_value` type definition required
- * by `Gudhi::Proximity_graph`.
+ * \tparam Kernel CGAL kernel: either Epick_d or Epeck_d.
+ *
+ * \tparam SimplicialComplexForCechComplex furnishes `Vertex_handle` and `Filtration_value` type definition required
+ * by `Gudhi::Proximity_graph` and Cech blocker.
  *
- * \tparam ForwardPointRange must be a range for which `std::begin()` and `std::end()` methods return input
- * iterators on a point. `std::begin()` and `std::end()` methods are also required for a point.
  */
-template <typename SimplicialComplexForProximityGraph, typename ForwardPointRange>
+template <typename Kernel, typename SimplicialComplexForCechComplex>
 class Cech_complex {
  private:
   // Required by compute_proximity_graph
-  using Vertex_handle = typename SimplicialComplexForProximityGraph::Vertex_handle;
-  using Filtration_value = typename SimplicialComplexForProximityGraph::Filtration_value;
-  using Proximity_graph = Gudhi::Proximity_graph<SimplicialComplexForProximityGraph>;
-
-  // Retrieve Coordinate type from ForwardPointRange
-  using Point_from_range_iterator = typename boost::range_const_iterator<ForwardPointRange>::type;
-  using Point_from_range = typename std::iterator_traits<Point_from_range_iterator>::value_type;
-  using Coordinate_iterator = typename boost::range_const_iterator<Point_from_range>::type;
-  using Coordinate = typename std::iterator_traits<Coordinate_iterator>::value_type;
-
- public:
-  // Point and Point_cloud type definition
-  using Point = std::vector<Coordinate>;
-  using Point_cloud = std::vector<Point>;
-
- public:
-  /** \brief Cech_complex constructor from a list of points.
+  using Vertex_handle = typename SimplicialComplexForCechComplex::Vertex_handle;
+  using Filtration_value = typename SimplicialComplexForCechComplex::Filtration_value;
+  using Proximity_graph = Gudhi::Proximity_graph<SimplicialComplexForCechComplex>;
+
+  using cech_blocker = Cech_blocker<SimplicialComplexForCechComplex, Cech_complex, Kernel>;
+
+  using Point_d = typename cech_blocker::Point_d;
+  using Point_cloud = std::vector<Point_d>;
+
+  // Numeric type of coordinates in the kernel
+  using FT = typename cech_blocker::FT;
+  // Sphere is a pair of point and squared radius.
+  using Sphere = typename cech_blocker::Sphere;
+
+  public:
+  /** \brief Cech_complex constructor from a range of points.
    *
-   * @param[in] points Range of points.
+   * @param[in] points Range of points where each point is defined as `kernel::Point_d`.
    * @param[in] max_radius Maximal radius value.
    *
-   * \tparam ForwardPointRange must be a range of Point. Point must be a range of <b>copyable</b> Cartesian coordinates.
-   *
    */
-  Cech_complex(const ForwardPointRange& points, Filtration_value max_radius) : max_radius_(max_radius) {
-    // Point cloud deep copy
-    point_cloud_.reserve(boost::size(points));
-    for (auto&& point : points) point_cloud_.emplace_back(std::begin(point), std::end(point));
+  template<typename InputPointRange >
+  Cech_complex(const InputPointRange & points, Filtration_value max_radius) : max_radius_(max_radius) {
+
+    point_cloud_.assign(std::begin(points), std::end(points));
 
-    cech_skeleton_graph_ = Gudhi::compute_proximity_graph<SimplicialComplexForProximityGraph>(
-        point_cloud_, max_radius_, Gudhi::Minimal_enclosing_ball_radius());
+    cech_skeleton_graph_ = Gudhi::compute_proximity_graph<SimplicialComplexForCechComplex>(
+        point_cloud_, max_radius_, Sphere_circumradius<Kernel, Filtration_value>());
   }
 
   /** \brief Initializes the simplicial complex from the proximity graph and expands it until a given maximal
@@ -82,19 +78,19 @@ class Cech_complex {
    *
    * @param[in] complex SimplicialComplexForCech to be created.
    * @param[in] dim_max graph expansion until this given maximal dimension.
+   * @param[in] exact Exact filtration values computation. Not exact if `Kernel` is not <a target="_blank"
+   * href="https://doc.cgal.org/latest/Kernel_d/structCGAL_1_1Epeck__d.html">CGAL::Epeck_d</a>.
    * @exception std::invalid_argument In debug mode, if `complex.num_vertices()` does not return 0.
    *
    */
-  template <typename SimplicialComplexForCechComplex>
-  void create_complex(SimplicialComplexForCechComplex& complex, int dim_max) {
+  void create_complex(SimplicialComplexForCechComplex& complex, int dim_max, const bool exact = false) {
     GUDHI_CHECK(complex.num_vertices() == 0,
                 std::invalid_argument("Cech_complex::create_complex - simplicial complex is not empty"));
 
     // insert the proximity graph in the simplicial complex
     complex.insert_graph(cech_skeleton_graph_);
     // expand the graph until dimension dim_max
-    complex.expansion_with_blockers(dim_max,
-                                    Cech_blocker<SimplicialComplexForCechComplex, Cech_complex>(&complex, this));
+    complex.expansion_with_blockers(dim_max, cech_blocker(&complex, this, exact));
   }
 
   /** @return max_radius value given at construction. */
@@ -103,12 +99,18 @@ class Cech_complex {
   /** @param[in] vertex Point position in the range.
    * @return The point.
    */
-  const Point& get_point(Vertex_handle vertex) const { return point_cloud_[vertex]; }
+  const Point_d& get_point(Vertex_handle vertex) const { return point_cloud_[vertex]; }
+
+  /**
+   * @return Vector of cached spheres.
+   */
+  std::vector<Sphere> & get_cache() { return cache_; }
 
  private:
   Proximity_graph cech_skeleton_graph_;
   Filtration_value max_radius_;
   Point_cloud point_cloud_;
+  std::vector<Sphere> cache_;
 };
 
 }  // namespace cech_complex
diff --git a/src/Cech_complex/include/gudhi/Cech_complex_blocker.h b/src/Cech_complex/include/gudhi/Cech_complex_blocker.h
index 31b9aab5..3ea82826 100644
--- a/src/Cech_complex/include/gudhi/Cech_complex_blocker.h
+++ b/src/Cech_complex/include/gudhi/Cech_complex_blocker.h
@@ -11,10 +11,12 @@
 #ifndef CECH_COMPLEX_BLOCKER_H_
 #define CECH_COMPLEX_BLOCKER_H_
 
-#include <gudhi/distance_functions.h>  // for Gudhi::Minimal_enclosing_ball_radius
+#include <CGAL/NT_converter.h> // for casting from FT to Filtration_value
+#include <CGAL/Lazy_exact_nt.h> // for CGAL::exact
 
 #include <iostream>
 #include <vector>
+#include <set>
 #include <cmath>  // for std::sqrt
 
 namespace Gudhi {
@@ -30,46 +32,115 @@ namespace cech_complex {
  * \details
  * Čech blocker is an oracle constructed from a Cech_complex and a simplicial complex.
  *
- * \tparam SimplicialComplexForProximityGraph furnishes `Simplex_handle` and `Filtration_value` type definition,
+ * \tparam SimplicialComplexForCech furnishes `Simplex_handle` and `Filtration_value` type definition,
  * `simplex_vertex_range(Simplex_handle sh)`and `assign_filtration(Simplex_handle sh, Filtration_value filt)` methods.
  *
- * \tparam Chech_complex is required by the blocker.
+ * \tparam Cech_complex is required by the blocker.
+ *
+ * \tparam Kernel CGAL kernel: either Epick_d or Epeck_d.
  */
-template <typename SimplicialComplexForCech, typename Cech_complex>
+template <typename SimplicialComplexForCech, typename Cech_complex, typename Kernel>
 class Cech_blocker {
+
+ public:
+
+  using Point_d = typename Kernel::Point_d;
+  // Numeric type of coordinates in the kernel
+  using FT = typename Kernel::FT;
+  // Sphere is a pair of point and squared radius.
+  using Sphere = typename std::pair<Point_d, FT>;
+
  private:
-  using Point_cloud = typename Cech_complex::Point_cloud;
 
   using Simplex_handle = typename SimplicialComplexForCech::Simplex_handle;
   using Filtration_value = typename SimplicialComplexForCech::Filtration_value;
+  using Simplex_key = typename SimplicialComplexForCech::Simplex_key;
+
+  template<class PointIterator>
+  Sphere get_sphere(PointIterator begin, PointIterator end) const {
+    Point_d c = kernel_.construct_circumcenter_d_object()(begin, end);
+    FT r = kernel_.squared_distance_d_object()(c, *begin);
+    return std::make_pair(std::move(c), std::move(r));
+  }
 
  public:
+
   /** \internal \brief Čech complex blocker operator() - the oracle - assigns the filtration value from the simplex
    * radius and returns if the simplex expansion must be blocked.
    *  \param[in] sh The Simplex_handle.
    *  \return true if the simplex radius is greater than the Cech_complex max_radius*/
   bool operator()(Simplex_handle sh) {
+    using Point_cloud =  std::vector<Point_d>;
+    Filtration_value radius = 0;
+    bool is_min_enclos_ball = false;
     Point_cloud points;
-    for (auto vertex : sc_ptr_->simplex_vertex_range(sh)) {
-      points.push_back(cc_ptr_->get_point(vertex));
+    points.reserve(sc_ptr_->dimension(sh)+1);
+
+    // for each face of simplex sh, test outsider point is indeed inside enclosing ball, if yes, take it and exit loop, otherwise, new sphere is circumsphere of all vertices
+    for (auto face_opposite_vertex : sc_ptr_->boundary_opposite_vertex_simplex_range(sh)) {
+        auto k = sc_ptr_->key(face_opposite_vertex.first);
+        Simplex_key sph_key;
+        if(k != sc_ptr_->null_key()) {
+            sph_key = k;
+        }
+        else {
+            for (auto vertex : sc_ptr_->simplex_vertex_range(face_opposite_vertex.first)) {
+                points.push_back(cc_ptr_->get_point(vertex));
+#ifdef DEBUG_TRACES
+                std::clog << "#(" << vertex << ")#";
+#endif  // DEBUG_TRACES
+            }
+            // Put edge sphere in cache
+            sph_key = cc_ptr_->get_cache().size();
+            sc_ptr_->assign_key(face_opposite_vertex.first, sph_key);
+            cc_ptr_->get_cache().push_back(get_sphere(points.cbegin(), points.cend()));
+            // Clear face points
+            points.clear();
+        }
+        // Check if the minimal enclosing ball of current face contains the extra point/opposite vertex
+        Sphere const& sph = cc_ptr_->get_cache()[sph_key];
+        if (kernel_.squared_distance_d_object()(sph.first, cc_ptr_->get_point(face_opposite_vertex.second)) <= sph.second) {
+            is_min_enclos_ball = true;
+            sc_ptr_->assign_key(sh, sph_key);
+            radius = sc_ptr_->filtration(face_opposite_vertex.first);
 #ifdef DEBUG_TRACES
-      std::clog << "#(" << vertex << ")#";
+            std::clog << "center: " << sph.first << ", radius: " <<  radius << std::endl;
 #endif  // DEBUG_TRACES
+            break;
+        }
     }
-    Filtration_value radius = Gudhi::Minimal_enclosing_ball_radius()(points);
+    // Spheres of each face don't contain the whole simplex
+    if(!is_min_enclos_ball) {
+        for (auto vertex : sc_ptr_->simplex_vertex_range(sh)) {
+            points.push_back(cc_ptr_->get_point(vertex));
+        }
+        Sphere sph = get_sphere(points.cbegin(), points.cend());
+#if CGAL_VERSION_NR >= 1050000000
+        if(exact_) CGAL::exact(sph.second);
+#endif
+        CGAL::NT_converter<FT, Filtration_value> cast_to_fv;
+        radius = std::sqrt(cast_to_fv(sph.second));
+
+        sc_ptr_->assign_key(sh, cc_ptr_->get_cache().size());
+        cc_ptr_->get_cache().push_back(std::move(sph));
+    }
+
 #ifdef DEBUG_TRACES
     if (radius > cc_ptr_->max_radius()) std::clog << "radius > max_radius => expansion is blocked\n";
 #endif  // DEBUG_TRACES
-    sc_ptr_->assign_filtration(sh, radius);
+    // Check that the filtration to be assigned (radius) would be valid
+    if (radius > sc_ptr_->filtration(sh)) sc_ptr_->assign_filtration(sh, radius);
     return (radius > cc_ptr_->max_radius());
   }
 
   /** \internal \brief Čech complex blocker constructor. */
-  Cech_blocker(SimplicialComplexForCech* sc_ptr, Cech_complex* cc_ptr) : sc_ptr_(sc_ptr), cc_ptr_(cc_ptr) {}
+  Cech_blocker(SimplicialComplexForCech* sc_ptr, Cech_complex* cc_ptr, const bool exact) : sc_ptr_(sc_ptr), cc_ptr_(cc_ptr), exact_(exact) {}
 
  private:
   SimplicialComplexForCech* sc_ptr_;
   Cech_complex* cc_ptr_;
+  Kernel kernel_;
+  const bool exact_;
 };
 
 }  // namespace cech_complex
diff --git a/src/Cech_complex/include/gudhi/Miniball.COPYRIGHT b/src/Cech_complex/include/gudhi/Miniball.COPYRIGHT
deleted file mode 100644
index dbe4c553..00000000
--- a/src/Cech_complex/include/gudhi/Miniball.COPYRIGHT
+++ /dev/null
@@ -1,4 +0,0 @@
-The miniball software is available under the GNU General Public License (GPLv3 - https://www.gnu.org/copyleft/gpl.html).
-If your intended use is not compliant with this license, please buy a commercial license (EUR 500 - https://people.inf.ethz.ch/gaertner/subdir/software/miniball/license.html).
-You need a license if the software that you develop using Miniball V3.0 is not open source.
-
diff --git a/src/Cech_complex/include/gudhi/Miniball.README b/src/Cech_complex/include/gudhi/Miniball.README
deleted file mode 100644
index 033d8953..00000000
--- a/src/Cech_complex/include/gudhi/Miniball.README
+++ /dev/null
@@ -1,26 +0,0 @@
-https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html
-
-Smallest Enclosing Balls of Points - Fast and Robust in C++.
-(high-quality software for smallest enclosing balls of balls is available in the computational geometry algorithms library CGAL)
-
-
-This is the miniball software (V3.0) for computing smallest enclosing balls of points in arbitrary dimensions. It consists of a C++ header file Miniball.hpp (around 500 lines of code) and two example programs miniball_example.cpp and miniball_example_containers.cpp that demonstrate the usage. The first example stores the coordinates of the input points in a two-dimensional array, the second example uses a list of vectors to show how generic containers can be used.
-
-Credits: Aditya Gupta and Alexandros Konstantinakis-Karmis have significantly contributed to this version of the software.
-
-Changes - https://people.inf.ethz.ch/gaertner/subdir/software/miniball/changes.txt - from previous versions.
-
-The theory - https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/esa99_final.pdf -  behind the miniball software (Proc. 7th Annual European Symposium on Algorithms (ESA), Lecture Notes in Computer Science 1643, Springer-Verlag, pp.325-338, 1999).
-
-Main Features:
-
-    Very fast in low dimensions. 1 million points in 5-space are processed within 0.05 seconds on any recent machine.
-
-    High numerical stability. Almost all input degeneracies (cospherical points, multiple points, points very close together) are routinely handled.
-
-    Easily integrates into your code. You can freely choose the coordinate type of your points and the container to store the points. If you still need to adapt the code, the header is small and readable and contains documentation for all major methods. 
-
-
-Changes done for the GUDHI version of MiniBall:
-  - Add include guard
-  - Move Miniball namespace inside a new Gudhi namespace
diff --git a/src/Cech_complex/include/gudhi/Miniball.hpp b/src/Cech_complex/include/gudhi/Miniball.hpp
deleted file mode 100644
index ce6cbb5b..00000000
--- a/src/Cech_complex/include/gudhi/Miniball.hpp
+++ /dev/null
@@ -1,523 +0,0 @@
-//    Copright (C) 1999-2013, Bernd Gaertner
-//    $Rev: 3581 $
-//
-//    This program is free software: you can redistribute it and/or modify
-//    it under the terms of the GNU General Public License as published by
-//    the Free Software Foundation, either version 3 of the License, or
-//    (at your option) any later version.
-
-//    This program is distributed in the hope that it will be useful,
-//    but WITHOUT ANY WARRANTY; without even the implied warranty of
-//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-//    GNU General Public License for more details.
-
-//    You should have received a copy of the GNU General Public License
-//    along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-//    Contact:
-//    --------
-//    Bernd Gaertner
-//    Institute of Theoretical Computer Science 
-//    ETH Zuerich
-//    CAB G31.1
-//    CH-8092 Zuerich, Switzerland
-//    http://www.inf.ethz.ch/personal/gaertner
-
-#ifndef MINIBALL_HPP_
-#define MINIBALL_HPP_
-
-#include <cassert>
-#include <algorithm>
-#include <list>
-#include <ctime>
-#include <limits>
-
-namespace Gudhi {
-
-namespace Miniball {
-
-  // Global Functions
-  // ================
-  template <typename NT>
-  inline NT mb_sqr (NT r) {return r*r;}
-
-  // Functors
-  // ========
-
-  // functor to map a point iterator to the corresponding coordinate iterator;
-  // generic version for points whose coordinate containers have begin()
-  template < typename Pit_, typename Cit_ >
-  struct CoordAccessor {
-    typedef Pit_                                  Pit;
-    typedef Cit_                                  Cit;
-    inline  Cit operator() (Pit it) const { return (*it).begin(); }
-  };
-
-  // partial specialization for points whose coordinate containers are arrays
-  template < typename Pit_, typename Cit_ >
-  struct CoordAccessor<Pit_, Cit_*> {
-    typedef Pit_                                  Pit;      
-    typedef Cit_*                                 Cit;
-    inline  Cit operator() (Pit it) const { return *it; }
-  };
-
-  // Class Declaration
-  // =================
-
-  template <typename CoordAccessor>
-  class Miniball {
-  private:
-    // types
-    // The iterator type to go through the input points
-    typedef typename CoordAccessor::Pit                         Pit; 
-    // The iterator type to go through the coordinates of a single point. 
-    typedef typename CoordAccessor::Cit                         Cit; 
-    // The coordinate type
-    typedef typename std::iterator_traits<Cit>::value_type      NT;  
-    // The iterator to go through the support points
-    typedef typename std::list<Pit>::iterator                   Sit;
-
-    // data members...
-    const int d; // dimension
-    Pit points_begin;        
-    Pit points_end;          
-    CoordAccessor coord_accessor;  
-    double time;  
-    const NT nt0; // NT(0)                         
-
-    //...for the algorithms
-    std::list<Pit> L;                       
-    Sit support_end;                        
-    int fsize;   // number of forced points                                   
-    int ssize;   // number of support points                               
-
-    // ...for the ball updates
-    NT* current_c;                         
-    NT  current_sqr_r;                      
-    NT** c;                                    
-    NT* sqr_r;                    
- 
-    // helper arrays
-    NT* q0;
-    NT* z;
-    NT* f;
-    NT** v;
-    NT** a;
-
-  public:
-    // The iterator type to go through the support points
-    typedef typename std::list<Pit>::const_iterator SupportPointIterator;
-  
-    // PRE:  [begin, end) is a nonempty range
-    // POST: computes the smallest enclosing ball of the points in the range
-    //       [begin, end); the functor a maps a point iterator to an iterator 
-    //       through the d coordinates of the point  
-    Miniball (int d_, Pit begin, Pit end, CoordAccessor ca = CoordAccessor());
-
-    // POST: returns a pointer to the first element of an array that holds
-    //       the d coordinates of the center of the computed ball  
-    const NT* center () const;
-
-    // POST: returns the squared radius of the computed ball  
-    NT squared_radius () const;
- 
-    // POST: returns the number of support points of the computed ball;
-    //       the support points form a minimal set with the same smallest
-    //       enclosing ball as the input set; in particular, the support
-    //       points are on the boundary of the computed ball, and their
-    //       number is at most d+1 
-    int nr_support_points () const;
- 
-    // POST: returns an iterator to the first support point 
-    SupportPointIterator support_points_begin () const;
-
-    // POST: returns a past-the-end iterator for the range of support points  
-    SupportPointIterator support_points_end () const;
-
-    // POST: returns the maximum excess of any input point w.r.t. the computed 
-    //       ball, divided by the squared radius of the computed ball. The 
-    //       excess of a point is the difference between its squared distance
-    //       from the center and the squared radius; Ideally, the return value 
-    //       is 0. subopt is set to the absolute value of the most negative 
-    //       coefficient in the affine combination of the support points that 
-    //       yields the center. Ideally, this is a convex combination, and there 
-    //       is no negative coefficient in which case subopt is set to 0.  
-    NT relative_error (NT& subopt) const;
-  
-    // POST: return true if the relative error is at most tol, and the
-    //       suboptimality is 0; the default tolerance is 10 times the
-    //       coordinate type's machine epsilon  
-    bool is_valid (NT tol = NT(10) * std::numeric_limits<NT>::epsilon()) const;
-
-    // POST: returns the time in seconds taken by the constructor call for 
-    //       computing the smallest enclosing ball  
-    double get_time() const;
-
-    // POST: deletes dynamically allocated arrays
-    ~Miniball();
-
-  private:  
-    void mtf_mb (Sit n);
-    void mtf_move_to_front (Sit j);
-    void pivot_mb (Pit n);
-    void pivot_move_to_front (Pit j);
-    NT excess (Pit pit) const;
-    void pop ();
-    bool push (Pit pit);
-    NT suboptimality () const;
-    void create_arrays();
-    void delete_arrays();
-  };
-
-  // Class Definition
-  // ================
-  template <typename CoordAccessor>
-  Miniball<CoordAccessor>::Miniball (int d_, Pit begin, Pit end, 
-				     CoordAccessor ca) 
-    : d (d_), 
-      points_begin (begin), 
-      points_end (end), 
-      coord_accessor (ca), 
-      time (clock()), 
-      nt0 (NT(0)), 
-      L(), 
-      support_end (L.begin()), 
-      fsize(0), 
-      ssize(0), 
-      current_c (NULL), 
-      current_sqr_r (NT(-1)),
-      c (NULL),
-      sqr_r (NULL),
-      q0 (NULL),
-      z (NULL),
-      f (NULL),
-      v (NULL),
-      a (NULL)
-  {	
-    assert (points_begin != points_end);
-    create_arrays();
-
-    // set initial center
-    for (int j=0; j<d; ++j) c[0][j] = nt0;
-    current_c = c[0];
-
-    // compute miniball
-    pivot_mb (points_end);
-
-    // update time
-    time = (clock() - time) / CLOCKS_PER_SEC;
-  }
-  
-  template <typename CoordAccessor>
-  Miniball<CoordAccessor>::~Miniball()
-  {
-    delete_arrays();
-  }
-
-  template <typename CoordAccessor>
-  void Miniball<CoordAccessor>::create_arrays() 
-  {
-    c = new NT*[d+1]; 
-    v = new NT*[d+1]; 
-    a = new NT*[d+1];
-    for (int i=0; i<d+1; ++i) {
-      c[i] = new NT[d];
-      v[i] = new NT[d];
-      a[i] = new NT[d];
-    }
-    sqr_r = new NT[d+1];
-    q0 = new NT[d];
-    z = new NT[d+1];
-    f = new NT[d+1];
-  } 
-
-  template <typename CoordAccessor>
-  void Miniball<CoordAccessor>::delete_arrays() 
-  {
-    delete[] f;
-    delete[] z;
-    delete[] q0;
-    delete[] sqr_r;
-    for (int i=0; i<d+1; ++i) {
-      delete[] a[i];
-      delete[] v[i];
-      delete[] c[i];
-    }
-    delete[] a;
-    delete[] v;
-    delete[] c;
-  }
-
-  template <typename CoordAccessor>
-  const typename Miniball<CoordAccessor>::NT* 
-  Miniball<CoordAccessor>::center () const 
-  {
-    return current_c;
-  }
- 
-  template <typename CoordAccessor>
-  typename Miniball<CoordAccessor>::NT 
-  Miniball<CoordAccessor>::squared_radius () const 
-  {
-    return current_sqr_r;
-  }
-
-  template <typename CoordAccessor>
-  int Miniball<CoordAccessor>::nr_support_points () const 
-  {
-    assert (ssize < d+2);
-    return ssize;
-  } 
-
-  template <typename CoordAccessor>  
-  typename Miniball<CoordAccessor>::SupportPointIterator 
-  Miniball<CoordAccessor>::support_points_begin () const 
-  {
-    return L.begin();
-  }
-
-  template <typename CoordAccessor>  
-  typename Miniball<CoordAccessor>::SupportPointIterator 
-  Miniball<CoordAccessor>::support_points_end () const  
-  {
-    return support_end;
-  }
-
-  template <typename CoordAccessor>  
-  typename Miniball<CoordAccessor>::NT 
-  Miniball<CoordAccessor>::relative_error (NT& subopt) const 
-  {
-    NT e, max_e = nt0;
-    // compute maximum absolute excess of support points
-    for (SupportPointIterator it = support_points_begin(); 
-	 it != support_points_end(); ++it) {
-      e = excess (*it);
-      if (e < nt0) e = -e;
-      if (e > max_e) {
-	max_e = e; 
-      }
-    }
-    // compute maximum excess of any point
-    for (Pit i = points_begin; i != points_end; ++i)
-      if ((e = excess (i)) > max_e)
-	max_e = e;
-   
-    subopt = suboptimality();
-    assert (current_sqr_r > nt0 || max_e == nt0);
-    return (current_sqr_r == nt0 ? nt0 : max_e / current_sqr_r);
-  }
-
-  template <typename CoordAccessor>  
-  bool Miniball<CoordAccessor>::is_valid (NT tol) const
-  {
-    NT suboptimality;
-    return ( (relative_error (suboptimality) <= tol) && (suboptimality == 0) );
-  }
-
-  template <typename CoordAccessor>  
-  double Miniball<CoordAccessor>::get_time() const 
-  {
-    return time;
-  }
-
-  template <typename CoordAccessor>  
-  void Miniball<CoordAccessor>::mtf_mb (Sit n)
-  {
-    // Algorithm 1: mtf_mb (L_{n-1}, B), where L_{n-1} = [L.begin, n)  
-    // B: the set of forced points, defining the current ball
-    // S: the superset of support points computed by the algorithm
-    // --------------------------------------------------------------
-    // from B. Gaertner, Fast and Robust Smallest Enclosing Balls, ESA 1999,
-    // http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf  
-  
-    //   PRE: B = S  
-    assert (fsize == ssize);
-   
-    support_end = L.begin();
-    if ((fsize) == d+1) return;  
-  
-    // incremental construction
-    for (Sit i = L.begin(); i != n;) 
-      {
-	// INV: (support_end - L.begin() == |S|-|B|)
-	assert (std::distance (L.begin(), support_end) == ssize - fsize);
-       
-	Sit j = i++; 
-	if (excess(*j) > nt0) 
-	  if (push(*j)) {          // B := B + p_i
-	    mtf_mb (j);            // mtf_mb (L_{i-1}, B + p_i)
-	    pop();                 // B := B - p_i
-	    mtf_move_to_front(j);  
-	  }
-      }
-    // POST: the range [L.begin(), support_end) stores the set S\B
-  }
-
-  template <typename CoordAccessor>  
-  void Miniball<CoordAccessor>::mtf_move_to_front (Sit j) 
-  {
-    if (support_end == j)
-      support_end++;
-    L.splice (L.begin(), L, j);
-  }
-
-  template <typename CoordAccessor>  
-  void Miniball<CoordAccessor>::pivot_mb (Pit n) 
-  {
-    // Algorithm 2: pivot_mb (L_{n-1}), where L_{n-1} = [L.begin, n)  
-    // --------------------------------------------------------------
-    // from B. Gaertner, Fast and Robust Smallest Enclosing Balls, ESA 1999,
-    // http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf  
-    NT          old_sqr_r;
-    const NT*   c;
-    Pit         pivot, k;
-    NT          e, max_e, sqr_r;
-    Cit p;
-    do {
-      old_sqr_r = current_sqr_r;
-      sqr_r = current_sqr_r;
-
-      pivot = points_begin;
-      max_e = nt0;
-      for (k = points_begin; k != n; ++k) {
-	p = coord_accessor(k);
-	e = -sqr_r;
-	c = current_c;
-	for (int j=0; j<d; ++j)
-	  e += mb_sqr<NT>(*p++-*c++);
-	if (e > max_e) {
-	  max_e = e;
-	  pivot = k;
-	}
-      }
-
-      if (max_e > nt0) {
-	// check if the pivot is already contained in the support set
-	if (std::find(L.begin(), support_end, pivot) == support_end) {
-	  assert (fsize == 0);
-	  if (push (pivot)) {
-	    mtf_mb(support_end);
-	    pop();
-	    pivot_move_to_front(pivot);
-	  }
-	}
-      }
-    } while (old_sqr_r < current_sqr_r);
-  }
-
-  template <typename CoordAccessor>  
-  void Miniball<CoordAccessor>::pivot_move_to_front (Pit j) 
-  {
-    L.push_front(j);
-    if (std::distance(L.begin(), support_end) == d+2)
-      support_end--;
-  }
-
-  template <typename CoordAccessor>  
-  inline typename Miniball<CoordAccessor>::NT 
-  Miniball<CoordAccessor>::excess (Pit pit) const 
-  {
-    Cit p = coord_accessor(pit);
-    NT e = -current_sqr_r;
-    NT* c = current_c;
-    for (int k=0; k<d; ++k){
-      e += mb_sqr<NT>(*p++-*c++);
-    }
-    return e;
-  }
-
-  template <typename CoordAccessor>  
-  void Miniball<CoordAccessor>::pop ()  
-  {
-    --fsize;
-  }
-
-  template <typename CoordAccessor>  
-  bool Miniball<CoordAccessor>::push (Pit pit) 
-  {
-    int i, j;
-    NT eps = mb_sqr<NT>(std::numeric_limits<NT>::epsilon());
-   
-    Cit cit = coord_accessor(pit);
-    Cit p = cit;
- 
-    if (fsize==0) {
-      for (i=0; i<d; ++i)
-	q0[i] = *p++;
-      for (i=0; i<d; ++i)
-	c[0][i] = q0[i];
-      sqr_r[0] = nt0;
-    } 
-    else {
-      // set v_fsize to Q_fsize
-      for (i=0; i<d; ++i)
-	//v[fsize][i] = p[i]-q0[i];
-	v[fsize][i] = *p++-q0[i];
-      
-      // compute the a_{fsize,i}, i< fsize
-      for (i=1; i<fsize; ++i) {
-	a[fsize][i] = nt0;
-	for (j=0; j<d; ++j)
-	  a[fsize][i] += v[i][j] * v[fsize][j];
-	a[fsize][i]*=(2/z[i]);
-      }
-      
-      // update v_fsize to Q_fsize-\bar{Q}_fsize
-      for (i=1; i<fsize; ++i) {
-	for (j=0; j<d; ++j)
-	  v[fsize][j] -= a[fsize][i]*v[i][j];
-      }
-      
-      // compute z_fsize
-      z[fsize]=nt0;
-      for (j=0; j<d; ++j)
-	z[fsize] += mb_sqr<NT>(v[fsize][j]);
-      z[fsize]*=2;
-      
-      // reject push if z_fsize too small
-      if (z[fsize]<eps*current_sqr_r) {
-	return false;
-      }
-      
-      // update c, sqr_r
-      p=cit;
-      NT e = -sqr_r[fsize-1];
-      for (i=0; i<d; ++i)
-	e += mb_sqr<NT>(*p++-c[fsize-1][i]);
-      f[fsize]=e/z[fsize];
-      
-      for (i=0; i<d; ++i)
-	c[fsize][i] = c[fsize-1][i]+f[fsize]*v[fsize][i];
-      sqr_r[fsize] = sqr_r[fsize-1] + e*f[fsize]/2;
-    }
-    current_c = c[fsize];
-    current_sqr_r = sqr_r[fsize];
-    ssize = ++fsize;
-    return true;
-  }
- 
-  template <typename CoordAccessor>  
-  typename Miniball<CoordAccessor>::NT 
-  Miniball<CoordAccessor>::suboptimality () const
-  {
-    NT* l = new NT[d+1];
-    NT min_l = nt0;
-    l[0] = NT(1);
-    for (int i=ssize-1; i>0; --i) {
-      l[i] = f[i];
-      for (int k=ssize-1; k>i; --k)
-	l[i]-=a[k][i]*l[k];
-      if (l[i] < min_l) min_l = l[i];
-      l[0] -= l[i];
-    }
-    if (l[0] < min_l) min_l = l[0];
-    delete[] l;
-    if (min_l < nt0)
-      return -min_l;
-    return nt0;
-  }
-}  // namespace Miniball
-
-}  // namespace Gudhi
-
-#endif  // MINIBALL_HPP_
diff --git a/src/Cech_complex/include/gudhi/Sphere_circumradius.h b/src/Cech_complex/include/gudhi/Sphere_circumradius.h
new file mode 100644
index 00000000..790f6950
--- /dev/null
+++ b/src/Cech_complex/include/gudhi/Sphere_circumradius.h
@@ -0,0 +1,65 @@
+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Hind Montassif
+ *
+ *    Copyright (C) 2021 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef SPHERE_CIRCUMRADIUS_H_
+#define SPHERE_CIRCUMRADIUS_H_
+
+#include <CGAL/Epick_d.h> // for #include <CGAL/NT_converter.h> which is not working/compiling alone
+
+#include <cmath>  // for std::sqrt
+#include <vector>
+
+namespace Gudhi {
+
+namespace cech_complex {
+
+/** \private @brief Compute the circumradius of the sphere passing through points given by a range of coordinates.
+ * The points are assumed to have the same dimension. */
+template<typename Kernel, typename Filtration_value>
+class Sphere_circumradius {
+ private:
+    Kernel kernel_;
+ public:
+    using FT = typename Kernel::FT;
+    using Point = typename Kernel::Point_d;
+    using Point_cloud = typename std::vector<Point>;
+
+    CGAL::NT_converter<FT, Filtration_value> cast_to_fv;
+
+   /** \brief Circumradius of sphere passing through two points using CGAL.
+   *
+   * @param[in] point_1
+   * @param[in] point_2
+   * @return Sphere circumradius passing through two points.
+   * \tparam Point must be a Kernel::Point_d from CGAL.
+   *
+   */
+  Filtration_value operator()(const Point& point_1, const Point& point_2) const {
+    return std::sqrt(cast_to_fv(kernel_.squared_distance_d_object()(point_1, point_2))) / 2.;
+  }
+
+  /** \brief Circumradius of sphere passing through point cloud using CGAL.
+   *
+   * @param[in] point_cloud The points.
+   * @return Sphere circumradius passing through the points.
+   * \tparam Point_cloud must be a range of Kernel::Point_d points from CGAL.
+   *
+   */
+  Filtration_value operator()(const Point_cloud& point_cloud) const {
+    return std::sqrt(cast_to_fv(kernel_.compute_squared_radius_d_object()(point_cloud.begin(), point_cloud.end())));
+  }
+
+};
+
+}  // namespace cech_complex
+
+}  // namespace Gudhi
+
+#endif  // SPHERE_CIRCUMRADIUS_H_
diff --git a/src/Cech_complex/test/CMakeLists.txt b/src/Cech_complex/test/CMakeLists.txt
index e6a2a18f..2d736f27 100644
--- a/src/Cech_complex/test/CMakeLists.txt
+++ b/src/Cech_complex/test/CMakeLists.txt
@@ -1,11 +1,14 @@
-include(GUDHI_boost_test)
+if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 5.0.1)
+  include(GUDHI_boost_test)
 
-add_executable ( Cech_complex_test_unit test_cech_complex.cpp )
-if (TBB_FOUND)
-  target_link_libraries(Cech_complex_test_unit ${TBB_LIBRARIES})
-endif()
+  add_executable ( Cech_complex_test_unit test_cech_complex.cpp )
+  if (TBB_FOUND)
+    target_link_libraries(Cech_complex_test_unit ${TBB_LIBRARIES})
+  endif()
+
+  # Do not forget to copy test files in current binary dir
+  file(COPY "${CMAKE_SOURCE_DIR}/data/points/alphacomplexdoc.off" DESTINATION ${CMAKE_CURRENT_BINARY_DIR}/)
 
-# Do not forget to copy test files in current binary dir
-file(COPY "${CMAKE_SOURCE_DIR}/data/points/alphacomplexdoc.off" DESTINATION ${CMAKE_CURRENT_BINARY_DIR}/)
+  gudhi_add_boost_test(Cech_complex_test_unit)
 
-gudhi_add_boost_test(Cech_complex_test_unit)
+endif()
diff --git a/src/Cech_complex/test/test_cech_complex.cpp b/src/Cech_complex/test/test_cech_complex.cpp
index 6e00d7b5..f5980e6d 100644
--- a/src/Cech_complex/test/test_cech_complex.cpp
+++ b/src/Cech_complex/test/test_cech_complex.cpp
@@ -22,21 +22,20 @@
 // to construct Cech_complex from a OFF file of points
 #include <gudhi/Points_off_io.h>
 #include <gudhi/Simplex_tree.h>
-#include <gudhi/distance_functions.h>
 #include <gudhi/Unitary_tests_utils.h>
-#include <gudhi/Miniball.hpp>
+
+#include <CGAL/Epeck_d.h>  // For EXACT or SAFE version
 
 // Type definitions
 using Simplex_tree = Gudhi::Simplex_tree<>;
 using Filtration_value = Simplex_tree::Filtration_value;
-using Point = std::vector<Filtration_value>;
+using Kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>;
+using FT = typename Kernel::FT;
+using Point = typename Kernel::Point_d;
+
 using Point_cloud = std::vector<Point>;
 using Points_off_reader = Gudhi::Points_off_reader<Point>;
-using Cech_complex = Gudhi::cech_complex::Cech_complex<Simplex_tree, Point_cloud>;
-
-using Point_iterator = Point_cloud::const_iterator;
-using Coordinate_iterator = Point::const_iterator;
-using Min_sphere = Gudhi::Miniball::Miniball<Gudhi::Miniball::CoordAccessor<Point_iterator, Coordinate_iterator>>;
+using Cech_complex = Gudhi::cech_complex::Cech_complex<Kernel, Simplex_tree>;
 
 BOOST_AUTO_TEST_CASE(Cech_complex_for_documentation) {
   // ----------------------------------------------------------------------------
@@ -45,17 +44,29 @@ BOOST_AUTO_TEST_CASE(Cech_complex_for_documentation) {
   //
   // ----------------------------------------------------------------------------
   Point_cloud points;
-  points.push_back({1., 0.});                  // 0
-  points.push_back({0., 1.});                  // 1
-  points.push_back({2., 1.});                  // 2
-  points.push_back({3., 2.});                  // 3
-  points.push_back({0., 3.});                  // 4
-  points.push_back({3. + std::sqrt(3.), 3.});  // 5
-  points.push_back({1., 4.});                  // 6
-  points.push_back({3., 4.});                  // 7
-  points.push_back({2., 4. + std::sqrt(3.)});  // 8
-  points.push_back({0., 4.});                  // 9
-  points.push_back({-0.5, 2.});                // 10
+
+  std::vector<FT> point0({1., 0.});
+  points.emplace_back(point0.begin(), point0.end());
+  std::vector<FT> point1({0., 1.});
+  points.emplace_back(point1.begin(), point1.end());
+  std::vector<FT> point2({2., 1.});
+  points.emplace_back(point2.begin(), point2.end());
+  std::vector<FT> point3({3., 2.});
+  points.emplace_back(point3.begin(), point3.end());
+  std::vector<FT> point4({0., 3.});
+  points.emplace_back(point4.begin(), point4.end());
+  std::vector<FT> point5({3. + std::sqrt(3.), 3.});
+  points.emplace_back(point5.begin(), point5.end());
+  std::vector<FT> point6({1., 4.});
+  points.emplace_back(point6.begin(), point6.end());
+  std::vector<FT> point7({3., 4.});
+  points.emplace_back(point7.begin(), point7.end());
+  std::vector<FT> point8({2., 4. + std::sqrt(3.)});
+  points.emplace_back(point8.begin(), point8.end());
+  std::vector<FT> point9({0., 4.});
+  points.emplace_back(point9.begin(), point9.end());
+  std::vector<FT> point10({-0.5, 2.});
+  points.emplace_back(point10.begin(), point10.end());
 
   Filtration_value max_radius = 1.0;
   std::clog << "========== NUMBER OF POINTS = " << points.size() << " - Cech max_radius = " << max_radius
@@ -96,11 +107,11 @@ BOOST_AUTO_TEST_CASE(Cech_complex_for_documentation) {
         std::clog << vertex << ",";
         vp.push_back(points.at(vertex));
       }
-      std::clog << ") - distance =" << Gudhi::Minimal_enclosing_ball_radius()(vp.at(0), vp.at(1))
+      std::clog << ") - distance =" << Gudhi::cech_complex::Sphere_circumradius<Kernel, Filtration_value>()(vp.at(0), vp.at(1))
                 << " - filtration =" << st.filtration(f_simplex) << std::endl;
       BOOST_CHECK(vp.size() == 2);
       GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex),
-                                      Gudhi::Minimal_enclosing_ball_radius()(vp.at(0), vp.at(1)));
+                                      Gudhi::cech_complex::Sphere_circumradius<Kernel, Filtration_value>()(vp.at(0), vp.at(1)));
     }
   }
 
@@ -125,35 +136,34 @@ BOOST_AUTO_TEST_CASE(Cech_complex_for_documentation) {
   for (std::size_t vertex = 0; vertex <= 2; vertex++) {
     points012.push_back(cech_complex_for_doc.get_point(vertex));
   }
-  std::size_t dimension = points[0].end() - points[0].begin();
-  Min_sphere ms012(dimension, points012.begin(), points012.end());
 
-  Simplex_tree::Filtration_value f012 = st2.filtration(st2.find({0, 1, 2}));
-  std::clog << "f012= " << f012 << " | ms012_radius= " << std::sqrt(ms012.squared_radius()) << std::endl;
+  Kernel kern;
+  Filtration_value f012 = st2.filtration(st2.find({0, 1, 2}));
+  std::clog << "f012= " << f012 << std::endl;
 
-  GUDHI_TEST_FLOAT_EQUALITY_CHECK(f012, std::sqrt(ms012.squared_radius()));
+  CGAL::NT_converter<FT, Filtration_value> cast_to_fv;
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(f012, std::sqrt(cast_to_fv(kern.compute_squared_radius_d_object()(points012.begin(), points012.end()))));
 
   Point_cloud points1410;
   points1410.push_back(cech_complex_for_doc.get_point(1));
   points1410.push_back(cech_complex_for_doc.get_point(4));
   points1410.push_back(cech_complex_for_doc.get_point(10));
-  Min_sphere ms1410(dimension, points1410.begin(), points1410.end());
 
-  Simplex_tree::Filtration_value f1410 = st2.filtration(st2.find({1, 4, 10}));
-  std::clog << "f1410= " << f1410 << " | ms1410_radius= " << std::sqrt(ms1410.squared_radius()) << std::endl;
+  Filtration_value f1410 = st2.filtration(st2.find({1, 4, 10}));
+  std::clog << "f1410= " << f1410 << std::endl;
 
-  GUDHI_TEST_FLOAT_EQUALITY_CHECK(f1410, std::sqrt(ms1410.squared_radius()));
+  // In this case, the computed circumsphere using CGAL kernel does not match the minimal enclosing ball; the filtration value check is therefore done against a hardcoded value
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(f1410, 1.);
 
   Point_cloud points469;
   points469.push_back(cech_complex_for_doc.get_point(4));
   points469.push_back(cech_complex_for_doc.get_point(6));
   points469.push_back(cech_complex_for_doc.get_point(9));
-  Min_sphere ms469(dimension, points469.begin(), points469.end());
 
-  Simplex_tree::Filtration_value f469 = st2.filtration(st2.find({4, 6, 9}));
-  std::clog << "f469= " << f469 << " | ms469_radius= " << std::sqrt(ms469.squared_radius()) << std::endl;
+  Filtration_value f469 = st2.filtration(st2.find({4, 6, 9}));
+  std::clog << "f469= " << f469 << std::endl;
 
-  GUDHI_TEST_FLOAT_EQUALITY_CHECK(f469, std::sqrt(ms469.squared_radius()));
+  GUDHI_TEST_FLOAT_EQUALITY_CHECK(f469, std::sqrt(cast_to_fv(kern.compute_squared_radius_d_object()(points469.begin(), points469.end()))));
 
   BOOST_CHECK((st2.find({6, 7, 8}) == st2.null_simplex()));
   BOOST_CHECK((st2.find({3, 5, 7}) == st2.null_simplex()));
@@ -235,7 +245,7 @@ BOOST_AUTO_TEST_CASE(Cech_create_complex_throw) {
   //
   // ----------------------------------------------------------------------------
   std::string off_file_name("alphacomplexdoc.off");
-  double max_radius = 12.0;
+  Filtration_value max_radius = 12.0;
   std::clog << "========== OFF FILE NAME = " << off_file_name << " - Cech max_radius=" << max_radius
             << "==========" << std::endl;
 
diff --git a/src/Cech_complex/utilities/CMakeLists.txt b/src/Cech_complex/utilities/CMakeLists.txt
index b183c8d8..e80a698e 100644
--- a/src/Cech_complex/utilities/CMakeLists.txt
+++ b/src/Cech_complex/utilities/CMakeLists.txt
@@ -1,15 +1,17 @@
-project(Cech_complex_utilities)
+if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 5.0.1)
+  project(Cech_complex_utilities)
 
-if (TARGET Boost::program_options)
-  add_executable(cech_persistence cech_persistence.cpp)
-  target_link_libraries(cech_persistence Boost::program_options)
+  if (TARGET Boost::program_options)
+    add_executable(cech_persistence cech_persistence.cpp)
+    target_link_libraries(cech_persistence Boost::program_options)
 
-  if (TBB_FOUND)
-    target_link_libraries(cech_persistence ${TBB_LIBRARIES})
-  endif()
+    if (TBB_FOUND)
+      target_link_libraries(cech_persistence ${TBB_LIBRARIES})
+    endif()
 
-  add_test(NAME Cech_complex_utility_from_rips_on_tore_3D COMMAND $<TARGET_FILE:cech_persistence>
-      "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "-r" "0.25" "-m" "0.5" "-d" "3" "-p" "3")
+    add_test(NAME Cech_complex_utility_from_rips_on_tore_3D COMMAND $<TARGET_FILE:cech_persistence>
+        "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "-r" "0.25" "-m" "0.5" "-d" "3" "-p" "3")
 
-  install(TARGETS cech_persistence DESTINATION bin)
-endif()
-\ No newline at end of file
+    install(TARGETS cech_persistence DESTINATION bin)
+  endif()
+endif()
diff --git a/src/Cech_complex/utilities/cech_persistence.cpp b/src/Cech_complex/utilities/cech_persistence.cpp
index daea08e2..75d10c0f 100644
--- a/src/Cech_complex/utilities/cech_persistence.cpp
+++ b/src/Cech_complex/utilities/cech_persistence.cpp
@@ -9,13 +9,14 @@
  */
 
 #include <gudhi/Cech_complex.h>
-#include <gudhi/distance_functions.h>
 #include <gudhi/Simplex_tree.h>
 #include <gudhi/Persistent_cohomology.h>
 #include <gudhi/Points_off_io.h>
 
 #include <boost/program_options.hpp>
 
+#include <CGAL/Epeck_d.h>  // For EXACT or SAFE version
+
 #include <string>
 #include <vector>
 #include <limits>  // infinity
@@ -23,10 +24,11 @@
 // Types definition
 using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
 using Filtration_value = Simplex_tree::Filtration_value;
-using Point = std::vector<double>;
-using Point_cloud = std::vector<Point>;
+
+using Kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>;
+using Point = typename Kernel::Point_d;
 using Points_off_reader = Gudhi::Points_off_reader<Point>;
-using Cech_complex = Gudhi::cech_complex::Cech_complex<Simplex_tree, Point_cloud>;
+using Cech_complex = Gudhi::cech_complex::Cech_complex<Kernel, Simplex_tree>;
 using Field_Zp = Gudhi::persistent_cohomology::Field_Zp;
 using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp>;
 
diff --git a/src/Collapse/example/edge_collapse_conserve_persistence.cpp b/src/Collapse/example/edge_collapse_conserve_persistence.cpp
index b2c55e7a..19960597 100644
--- a/src/Collapse/example/edge_collapse_conserve_persistence.cpp
+++ b/src/Collapse/example/edge_collapse_conserve_persistence.cpp
@@ -103,7 +103,7 @@ int main(int argc, char* argv[]) {
                                                                                  Gudhi::Euclidean_distance());
 
   if (num_edges(proximity_graph) <= 0) {
-    std::cerr << "Total number of egdes are zero." << std::endl;
+    std::cerr << "Total number of edges is zero." << std::endl;
     exit(-1);
   }
 
diff --git a/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h b/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h
index c823901f..d0b3fe4a 100644
--- a/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h
+++ b/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h
@@ -53,7 +53,7 @@ struct Flag_complex_edge_collapser {
 #ifdef GUDHI_COLLAPSE_USE_DENSE_ARRAY
   // Minimal matrix interface
   // Using this matrix generally helps performance, but the memory use may be excessive for a very sparse graph
-  // (and in extreme cases the constant initialization of the matrix may start to dominate the runnning time).
+  // (and in extreme cases the constant initialization of the matrix may start to dominate the running time).
   // Are there cases where the matrix is too big but a hash table would help?
   std::vector<Filtration_value> neighbors_data;
   void init_neighbors_dense(){
diff --git a/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp b/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp
index 11ee5871..38efb9e6 100644
--- a/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp
+++ b/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp
@@ -45,7 +45,7 @@ int main(int argc, char* argv[]) {
                   min_persistence);
 
   Distance_matrix distances = Gudhi::read_lower_triangular_matrix_from_csv_file<Filtration_value>(csv_matrix_file);
-  std::cout << "Read the distance matrix succesfully, of size: " << distances.size() << std::endl;
+  std::cout << "Read the distance matrix successfully, of size: " << distances.size() << std::endl;
 
   Proximity_graph proximity_graph = Gudhi::compute_proximity_graph<Simplex_tree>(boost::irange((size_t)0,
                                                                                                distances.size()),
diff --git a/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp b/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp
index 0eea742c..d8f42ab6 100644
--- a/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp
+++ b/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp
@@ -77,7 +77,7 @@ int main(int argc, char* argv[]) {
                                                                                  Gudhi::Euclidean_distance());
 
   if (num_edges(proximity_graph) <= 0) {
-    std::cerr << "Total number of egdes are zero." << std::endl;
+    std::cerr << "Total number of edges is zero." << std::endl;
     exit(-1);
   }
 
diff --git a/src/Contraction/doc/so3.svg b/src/Contraction/doc/so3.svg
index adea3f38..f10cab98 100644
--- a/src/Contraction/doc/so3.svg
+++ b/src/Contraction/doc/so3.svg
@@ -177,7 +177,7 @@
          x="309.4176"
          y="300.58682"
          id="tspan4515-4"
-         style="text-align:center;text-anchor:middle">Rips complex built uppon these points</tspan><tspan
+         style="text-align:center;text-anchor:middle">Rips complex built upon these points</tspan><tspan
          sodipodi:role="line"
          x="309.4176"
          y="308.96704"
diff --git a/src/Contraction/example/Garland_heckbert/Error_quadric.h b/src/Contraction/example/Garland_heckbert/Error_quadric.h
index 49250d7a..ae46232c 100644
--- a/src/Contraction/example/Garland_heckbert/Error_quadric.h
+++ b/src/Contraction/example/Garland_heckbert/Error_quadric.h
@@ -29,7 +29,7 @@ template <typename Point> class Error_quadric {
    * Quadric corresponding to the L2 distance to the plane.
    *
    * According to the notation of Garland Heckbert, they
-   * denote a quadric symetric matrix as :
+   * denote a quadric symmetric matrix as :
    * Q = [ q11 q12 q13 q14]
    *     [ q12 q22 q23 q24]
    *     [ q13 q23 q33 q34]
diff --git a/src/Contraction/include/gudhi/Edge_contraction.h b/src/Contraction/include/gudhi/Edge_contraction.h
index 58d627c2..0b43c3b3 100644
--- a/src/Contraction/include/gudhi/Edge_contraction.h
+++ b/src/Contraction/include/gudhi/Edge_contraction.h
@@ -46,7 +46,7 @@ the operations needed for edge contraction algorithms have polynomial complexity
 Therefore, the simplification can be done without enumerating the set of simplices that is often non tracktable in high-dimension and is then very efficient
 (sub-linear with regards to the number of simplices in practice).
 
-A typical application of this package is homology group computation. It is illustrated in the next figure where a Rips complex is built uppon a set of high-dimensional points and
+A typical application of this package is homology group computation. It is illustrated in the next figure where a Rips complex is built upon a set of high-dimensional points and
 simplified with edge contractions.
 It has initially a big number of simplices (around 20 millions) but simplifying it to a much reduced form with only 15 vertices (and 714 simplices) takes only few seconds on a desktop machine (see the example bellow).
 One can then compute homology group with a simplicial complex having very few simplices instead of running the homology algorithm on the much bigger initial set of 
@@ -65,7 +65,7 @@ This class design is policy based and heavily inspired from the similar edge col
 Four policies can be customized in this package:
 
 \li Cost_policy: specify how much cost an edge contraction of a given edge. The edge with lowest cost is iteratively picked and contracted if valid.
-\li Valid_contraction_policy: specify if a given edge contraction is valid. For instance, this policy can check the link condition which ensures that the homotopy type is preserved afer the edge contraction.
+\li Valid_contraction_policy: specify if a given edge contraction is valid. For instance, this policy can check the link condition which ensures that the homotopy type is preserved after the edge contraction.
 \li Placement_policy: every time an edge is contracted, its points are merge to one point specified by this policy. This may be the middle of the edge of some more sophisticated point such as the minimum of a cost as in 
 \cite Garland.
 
@@ -92,7 +92,7 @@ Despite this package is able to deal with \a arbitrary simplicial complexes (any
 it is still \a 65% times faster than the CGAL package which is focused on 2-manifold. 
 The main reason is that few blockers appears during the simplification and hence,
 the algorithm only have to deal with the graph and not higher-dimensional simplices
-(in this case triangles). However, we recall that higher-dimensional simplices are \a implicitely 
+(in this case triangles). However, we recall that higher-dimensional simplices are \a implicitly 
 stored in the \ref skbl data-structure. Hence, one has to store
 simplices in an external map if some information needs to be associated with them (information that could be a filtration value or 
 an orientation for instance).
@@ -153,7 +153,7 @@ void build_rips(ComplexType& complex, double offset){
 int main (int argc, char *argv[])
 {
 	if (argc!=3){
-		std::cerr << "Usage "<<argv[0]<<" ../../data/SO3_10000.off 0.3 to load the file ../../data/SO3_10000.off and contract the Rips complex built with paremeter 0.3.\n";
+		std::cerr << "Usage "<<argv[0]<<" ../../data/SO3_10000.off 0.3 to load the file ../../data/SO3_10000.off and contract the Rips complex built with parameter 0.3.\n";
 		return -1;
 	}
 
diff --git a/src/Contraction/include/gudhi/Skeleton_blocker_contractor.h b/src/Contraction/include/gudhi/Skeleton_blocker_contractor.h
index a0d9f2b2..6911ca2e 100644
--- a/src/Contraction/include/gudhi/Skeleton_blocker_contractor.h
+++ b/src/Contraction/include/gudhi/Skeleton_blocker_contractor.h
@@ -171,8 +171,13 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
     Self const* algorithm_;
   };
 
+#if CGAL_VERSION_NR < 1050500000
   typedef CGAL::Modifiable_priority_queue<Edge_handle, Compare_cost, Undirected_edge_id> PQ;
-  typedef typename PQ::handle pq_handle;
+#else
+  typedef CGAL::Modifiable_priority_queue<Edge_handle, Compare_cost, Undirected_edge_id, CGAL::CGAL_BOOST_PENDING_RELAXED_HEAP> PQ;
+#endif
+  
+  typedef bool pq_handle;
 
 
   // An Edge_data is associated with EVERY edge in the complex (collapsible or not).
@@ -196,7 +201,7 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
     }
 
     bool is_in_PQ() const {
-      return PQHandle_ != PQ::null_handle();
+      return PQHandle_ != false;
     }
 
     void set_PQ_handle(pq_handle h) {
@@ -204,7 +209,7 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
     }
 
     void reset_PQ_handle() {
-      PQHandle_ = PQ::null_handle();
+      PQHandle_ = false;
     }
 
    private:
@@ -238,16 +243,22 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
   }
 
   void insert_in_PQ(Edge_handle edge, Edge_data& data) {
-    data.set_PQ_handle(heap_PQ_->push(edge));
+    heap_PQ_->push(edge);
+    data.set_PQ_handle(true);
     ++current_num_edges_heap_;
   }
 
   void update_in_PQ(Edge_handle edge, Edge_data& data) {
+#if CGAL_VERSION_NR < 1050500000
     data.set_PQ_handle(heap_PQ_->update(edge, data.PQ_handle()));
+#else
+    heap_PQ_->update(edge);
+#endif
   }
 
   void remove_from_PQ(Edge_handle edge, Edge_data& data) {
-    data.set_PQ_handle(heap_PQ_->erase(edge, data.PQ_handle()));
+    heap_PQ_->erase(edge);
+    data.set_PQ_handle(false);
     --current_num_edges_heap_;
   }
 
@@ -280,7 +291,7 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
 
     std::size_t id = 0;
 
-    // xxx do a parralel for
+    // xxx do a parallel for
     for (auto edge : complex_.edge_range()) {
       complex_[edge].index() = id++;
       Profile const& profile = create_profile(edge);
@@ -474,7 +485,7 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
   }
 
   void update_changed_edges() {
-    // xxx do a parralel for
+    // xxx do a parallel for
     DBG("update edges");
 
     // sequential loop
@@ -530,7 +541,7 @@ typename GeometricSimplifiableComplex::Vertex_handle> {
     // by definition of a blocker
 
     // todo uniqument utile pour la link condition
-    // laisser a l'utilisateur ? booleen update_heap_on_removed_blocker?
+    // laisser a l'utilisateur ? boolean update_heap_on_removed_blocker?
     Simplex blocker_copy(*blocker);
     for (auto x = blocker_copy.begin(); x != blocker_copy.end(); ++x) {
       for (auto y = x; ++y != blocker_copy.end();) {
diff --git a/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Hasse_diagram_cell.h b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Hasse_diagram_cell.h
index 59e9a350..9b57da3c 100644
--- a/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Hasse_diagram_cell.h
+++ b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Hasse_diagram_cell.h
@@ -95,7 +95,7 @@ class Hasse_diagram_cell {
         deleted_(false) {}
 
   /**
-   * Construcor of a cell of dimension dim having given additional information.
+   * Constructor of a cell of dimension dim having given additional information.
    **/
   Hasse_diagram_cell(Additional_information ai, int dim)
       : dimension(dim), additional_info(ai), position(0), deleted_(false) {}
@@ -125,7 +125,7 @@ class Hasse_diagram_cell {
   inline Additional_information& get_additional_information() { return this->additional_info; }
 
   /**
-   * Procedure to retrive position of the cell in the structure. It is used in
+   * Procedure to retrieve the position of the cell in the structure. It is used in
    * the implementation of Hasse diagram and set by it. Note that removal of
    * cell and subsequent call of clean_up_the_structure will change those
    * positions.
@@ -186,7 +186,7 @@ class Hasse_diagram_cell {
   friend std::ostream& operator<<(
       std::ostream& out, const Hasse_diagram_cell<Incidence_type, Filtration_type, Additional_information>& c) {
     // cout << "position : " << c.position << ", dimension : " << c.dimension << ", filtration: " << c.filtration << ",
-    // size of boudary : " <<  c.boundary.size() << "\n";
+    // size of boundary : " <<  c.boundary.size() << "\n";
     out << c.position << " " << c.dimension << " " << c.filtration << std::endl;
     for (std::size_t bd = 0; bd != c.boundary.size(); ++bd) {
       // do not write out the cells that has been deleted
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h
index b29f0906..dc6f5f90 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h
@@ -51,7 +51,7 @@ struct Function_affine_plane_in_Rd {
    * plane in the d-dimensional Euclidean space.
    *
    * @param[in] normal_matrix A normal matrix of the affine plane. The number of rows should
-   * correspond to the ambient dimension, the number of columns should corespond to
+   * correspond to the ambient dimension, the number of columns should correspond to
    * the size of the normal basis (codimension).
    * @param[in] offset The offset vector of the affine plane.
    * The dimension of the vector should be the ambient dimension of the manifold.
@@ -66,7 +66,7 @@ struct Function_affine_plane_in_Rd {
    * plane in the d-dimensional Euclidean space that passes through origin.
    *
    * @param[in] normal_matrix A normal matrix of the affine plane. The number of rows should
-   * correspond to the ambient dimension, the number of columns should corespond to
+   * correspond to the ambient dimension, the number of columns should correspond to
    * the size of the normal basis (codimension).
    */
   Function_affine_plane_in_Rd(const Eigen::MatrixXd& normal_matrix)
diff --git a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Permutahedral_representation_iterators.h b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Permutahedral_representation_iterators.h
index db145741..1a63d2f7 100644
--- a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Permutahedral_representation_iterators.h
+++ b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Permutahedral_representation_iterators.h
@@ -26,12 +26,12 @@ namespace Gudhi {
 
 namespace coxeter_triangulation {
 
-/* \addtogroup coxeter_triangulation
+/** \addtogroup coxeter_triangulation
  * Iterator types for Permutahedral_representation
  * @{
  */
 
-/* \brief Iterator over the vertices of a simplex
+/** \brief Iterator over the vertices of a simplex
  * represented by its permutahedral representation.
  *
  * Forward iterator, 'value_type' is Permutahedral_representation::Vertex.*/
@@ -83,7 +83,7 @@ class Vertex_iterator
 };  // Vertex_iterator
 
 /*---------------------------------------------------------------------------*/
-/* \brief Iterator over the k-faces of a simplex
+/** \brief Iterator over the k-faces of a simplex
  *  given by its permutahedral representation.
  *
  * Forward iterator, value_type is Permutahedral_representation. */
@@ -141,7 +141,7 @@ class Face_iterator : public boost::iterator_facade<Face_iterator<Permutahedral_
 };  // Face_iterator
 
 /*---------------------------------------------------------------------------*/
-/* \brief Iterator over the k-cofaces of a simplex
+/** \brief Iterator over the k-cofaces of a simplex
  *  given by its permutahedral representation.
  *
  * Forward iterator, value_type is Permutahedral_representation. */
@@ -247,6 +247,8 @@ class Coface_iterator
 
 };  // Coface_iterator
 
+/** @} */
+
 }  // namespace coxeter_triangulation
 
 }  // namespace Gudhi
diff --git a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Size_range.h b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Size_range.h
index c43effc8..6b137744 100644
--- a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Size_range.h
+++ b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Size_range.h
@@ -19,7 +19,7 @@ namespace Gudhi {
 
 namespace coxeter_triangulation {
 
-/** \brief Auxillary iterator class for sizes of parts in an ordered set partition.
+/** \brief Auxiliary iterator class for sizes of parts in an ordered set partition.
  */
 template <class T_it>
 class Size_iterator
diff --git a/src/Doxyfile.in b/src/Doxyfile.in
index 54ec9078..6e0e0333 100644
--- a/src/Doxyfile.in
+++ b/src/Doxyfile.in
@@ -152,7 +152,7 @@ FULL_PATH_NAMES        = YES
 # will be relative from the directory where doxygen is started.
 # This tag requires that the tag FULL_PATH_NAMES is set to YES.
 
-STRIP_FROM_PATH        =
+STRIP_FROM_PATH        = @CMAKE_SOURCE_DIR@
 
 # The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of the
 # path mentioned in the documentation of a class, which tells the reader which
@@ -162,7 +162,8 @@ STRIP_FROM_PATH        =
 # using the -I flag.
 
 STRIP_FROM_INC_PATH    = include \
-                         concept
+                         concept \
+                         @CMAKE_SOURCE_DIR@
 
 # If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter (but
 # less readable) file names. This can be useful is your file systems doesn't
@@ -711,7 +712,7 @@ CITE_BIB_FILES         = @CMAKE_SOURCE_DIR@/biblio/bibliography.bib \
 # messages are off.
 # The default value is: NO.
 
-QUIET                  = NO
+QUIET                  = YES
 
 # The WARNINGS tag can be used to turn on/off the warning messages that are
 # generated to standard error (stderr) by doxygen. If WARNINGS is set to YES
@@ -765,7 +766,7 @@ WARN_FORMAT            = "$file:$line: $text"
 # messages should be written. If left blank the output is written to standard
 # error (stderr).
 
-WARN_LOGFILE           =
+WARN_LOGFILE           = doxygen.log
 
 #---------------------------------------------------------------------------
 # Configuration options related to the input files
@@ -832,7 +833,7 @@ EXCLUDE                = @CMAKE_SOURCE_DIR@/data/ \
                          @CMAKE_SOURCE_DIR@/ext/ \
                          @CMAKE_SOURCE_DIR@/README.md \
                          @CMAKE_SOURCE_DIR@/.github \
-                         @CMAKE_CURRENT_BINARY_DIR@/new_gudhi_version_creation.md \
+                         @CMAKE_CURRENT_BINARY_DIR@ \
                          @GUDHI_DOXYGEN_SOURCE_PREFIX@/GudhUI/ \
                          @GUDHI_DOXYGEN_SOURCE_PREFIX@/cmake/ \
                          @GUDHI_DOXYGEN_SOURCE_PREFIX@/python/
@@ -1117,7 +1118,7 @@ HTML_FOOTER            = @GUDHI_DOXYGEN_COMMON_DOC_PATH@/footer.html
 # obsolete.
 # This tag requires that the tag GENERATE_HTML is set to YES.
 
-HTML_STYLESHEET        = @GUDHI_DOXYGEN_COMMON_DOC_PATH@/stylesheet.css
+HTML_STYLESHEET        =
 
 # The HTML_EXTRA_STYLESHEET tag can be used to specify additional user-defined
 # cascading style sheets that are included after the standard style sheets
@@ -1130,7 +1131,7 @@ HTML_STYLESHEET        = @GUDHI_DOXYGEN_COMMON_DOC_PATH@/stylesheet.css
 # list). For an example see the documentation.
 # This tag requires that the tag GENERATE_HTML is set to YES.
 
-HTML_EXTRA_STYLESHEET  =
+HTML_EXTRA_STYLESHEET  = @GUDHI_DOXYGEN_COMMON_DOC_PATH@/stylesheet.css
 
 # The HTML_EXTRA_FILES tag can be used to specify one or more extra images or
 # other source files which should be copied to the HTML output directory. Note
@@ -2092,14 +2093,7 @@ EXTERNAL_PAGES         = YES
 # Configuration options related to the dot tool
 #---------------------------------------------------------------------------
 
-# If the CLASS_DIAGRAMS tag is set to YES, doxygen will generate a class diagram
-# (in HTML and LaTeX) for classes with base or super classes. Setting the tag to
-# NO turns the diagrams off. Note that this option also works with HAVE_DOT
-# disabled, but it is recommended to install and use dot, since it yields more
-# powerful graphs.
-# The default value is: YES.
-
-CLASS_DIAGRAMS         = NO
+@GUDHI_DOXYGEN_CLASS_DIAGRAMS@
 
 # You can include diagrams made with dia in doxygen documentation. Doxygen will
 # then run dia to produce the diagram and insert it in the documentation. The
diff --git a/src/GudhUI/todo.txt b/src/GudhUI/todo.txt
index 19d99a77..e59d06d4 100644
--- a/src/GudhUI/todo.txt
+++ b/src/GudhUI/todo.txt
@@ -18,5 +18,5 @@ x faire le lien MainWindow - Model
 
 
 -- bug
-x bug ordre contraction -> just that first vertex placement dont work great
+x bug ordre contraction -> just that first vertex placement doesn't work great
 x pb construction rips
diff --git a/src/GudhUI/utils/Critical_points.h b/src/GudhUI/utils/Critical_points.h
index 97e58737..65695434 100644
--- a/src/GudhUI/utils/Critical_points.h
+++ b/src/GudhUI/utils/Critical_points.h
@@ -103,7 +103,7 @@ template<typename SkBlComplex> class Critical_points {
       // reduced to one point -> contractible
       return 1;
     else
-      // we dont know
+      // we don't know
       return 2;
   }
 
diff --git a/src/GudhUI/utils/Edge_contractor.h b/src/GudhUI/utils/Edge_contractor.h
index 0707b186..a71d0742 100644
--- a/src/GudhUI/utils/Edge_contractor.h
+++ b/src/GudhUI/utils/Edge_contractor.h
@@ -65,7 +65,7 @@ template<typename SkBlComplex> class Edge_contractor {
 
   /**
    * @brief Modify complex to be the expansion of the k-nearest neighbor
-   * symetric graph.
+   * symmetric graph.
    */
   Edge_contractor(SkBlComplex& complex, unsigned num_contractions) :
       complex_(complex), num_contractions_(num_contractions) {
diff --git a/src/GudhUI/utils/Furthest_point_epsilon_net.h b/src/GudhUI/utils/Furthest_point_epsilon_net.h
index 6eb71071..195d0014 100644
--- a/src/GudhUI/utils/Furthest_point_epsilon_net.h
+++ b/src/GudhUI/utils/Furthest_point_epsilon_net.h
@@ -27,7 +27,7 @@ template<typename SkBlComplex> class Furthest_point_epsilon_net {
 
   /**
    * Let V be the set of vertices.
-   * Initially v0 is one arbitrarly vertex and the set V0 is {v0}.
+   * Initially v0 is one, arbitrary, vertex and the set V0 is {v0}.
    * Then Vk is computed as follows.
    * First we compute the vertex pk that is the furthest from Vk
    * then Vk = Vk \cup pk.
@@ -54,7 +54,7 @@ template<typename SkBlComplex> class Furthest_point_epsilon_net {
 
   /**
    * @brief Modify complex to be the expansion of the k-nearest neighbor
-   * symetric graph.
+   * symmetric graph.
    */
   Furthest_point_epsilon_net(SkBlComplex& complex) :
       complex_(complex) {
diff --git a/src/GudhUI/utils/K_nearest_builder.h b/src/GudhUI/utils/K_nearest_builder.h
index 34483e58..454b2587 100644
--- a/src/GudhUI/utils/K_nearest_builder.h
+++ b/src/GudhUI/utils/K_nearest_builder.h
@@ -41,7 +41,7 @@ template<typename SkBlComplex> class K_nearest_builder {
  public:
   /**
    * @brief Modify complex to be the expansion of the k-nearest neighbor
-   * symetric graph.
+   * symmetric graph.
    */
   K_nearest_builder(SkBlComplex& complex, unsigned k) : complex_(complex) {
     complex.keep_only_vertices();
diff --git a/src/GudhUI/utils/Lloyd_builder.h b/src/GudhUI/utils/Lloyd_builder.h
index c042564f..57e3dc0f 100644
--- a/src/GudhUI/utils/Lloyd_builder.h
+++ b/src/GudhUI/utils/Lloyd_builder.h
@@ -27,7 +27,7 @@ template<typename SkBlComplex> class Lloyd_builder {
 
   /**
    * @brief Modify complex to be the expansion of the k-nearest neighbor
-   * symetric graph.
+   * symmetric graph.
    */
   Lloyd_builder(SkBlComplex& complex, unsigned num_iterations) : complex_(complex), dim(-1) {
     if (!complex_.empty()) {
diff --git a/src/GudhUI/utils/Vertex_collapsor.h b/src/GudhUI/utils/Vertex_collapsor.h
index 030e4bb0..b1c48efd 100644
--- a/src/GudhUI/utils/Vertex_collapsor.h
+++ b/src/GudhUI/utils/Vertex_collapsor.h
@@ -31,7 +31,7 @@ template<typename SkBlComplex> class Vertex_collapsor {
 
   /**
    * @brief Modify complex to be the expansion of the k-nearest neighbor
-   * symetric graph.
+   * symmetric graph.
    */
   Vertex_collapsor(SkBlComplex& complex, size_t num_collapses) :
       complex_(complex), num_collapses_(num_collapses) {
diff --git a/src/Nerve_GIC/utilities/km.py.COPYRIGHT b/src/Nerve_GIC/utilities/km.py.COPYRIGHT
index bef7b121..5358d287 100644
--- a/src/Nerve_GIC/utilities/km.py.COPYRIGHT
+++ b/src/Nerve_GIC/utilities/km.py.COPYRIGHT
@@ -1,7 +1,7 @@
 km.py is a fork of https://github.com/MLWave/kepler-mapper.
 Only the visualization part has been kept (Mapper part has been removed).
 
-This file has te following Copyright :
+This file has the following Copyright :
 
 The MIT License (MIT)
 
diff --git a/src/Persistence_representations/include/gudhi/Persistence_intervals.h b/src/Persistence_representations/include/gudhi/Persistence_intervals.h
index a6c1d6f0..f4324cb2 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_intervals.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_intervals.h
@@ -109,7 +109,7 @@ class Persistence_intervals {
   std::vector<size_t> cumulative_histogram_of_lengths(size_t number_of_bins = 10) const;
 
   /**
-   * In this procedure we assume that each barcode is a characteristic function of a hight equal to its length. The
+   * In this procedure we assume that each barcode is a characteristic function of a height equal to its length. The
    *persistence diagram is a sum of such a functions. The procedure below construct a function being a
    * sum of the characteristic functions of persistence intervals. The first two parameters are the range in which the
    *function is to be computed and the last parameter is the number of bins in
@@ -207,7 +207,7 @@ class Persistence_intervals {
   /**
    * This is a simple function projecting the persistence intervals to a real number. The function we use here is a sum
    *of squared lengths of intervals. It can be naturally interpreted as
-   * sum of step function, where the step hight it equal to the length of the interval.
+   * sum of step function, where the step height it equal to the length of the interval.
    * At the moment this function is not tested, since it is quite likely to be changed in the future. Given this, when
    *using it, keep in mind that it
    * will be most likely changed in the next versions.
diff --git a/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp b/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp
index 030b072a..3bec8830 100644
--- a/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp
+++ b/src/Persistent_cohomology/benchmark/performance_rips_persistence.cpp
@@ -49,7 +49,7 @@ void timing_persistence(FilteredComplex & cpx
  * with a Hasse diagram. The Hasse diagram represents explicitly all 
  * codimension 1 incidence relations in the complex, and hence leads to 
  * a faster computation of persistence because boundaries are precomputed. 
- * Hovewer, the simplex tree may be constructed directly from a point cloud and
+ * However, the simplex tree may be constructed directly from a point cloud and
  * is more compact.
  * We compute persistent homology with coefficient fields Z/2Z and Z/1223Z.
  * We present also timings for the computation of multi-field persistent 
diff --git a/src/Persistent_cohomology/concept/FilteredComplex.h b/src/Persistent_cohomology/concept/FilteredComplex.h
index 26ac7ac8..59ce25e3 100644
--- a/src/Persistent_cohomology/concept/FilteredComplex.h
+++ b/src/Persistent_cohomology/concept/FilteredComplex.h
@@ -103,7 +103,7 @@ Filtration_simplex_range filtration_simplex_range();
 /** @} */
  
 
-/* \brief Iterator over the simplices of the complex,
+/** \brief Iterator over the simplices of the complex,
   * in an arbitrary order.
   *
   * 'value_type' must be 'Simplex_handle'.*/
diff --git a/src/Persistent_cohomology/example/custom_persistence_sort.cpp b/src/Persistent_cohomology/example/custom_persistence_sort.cpp
index 410cd987..bba0b2f7 100644
--- a/src/Persistent_cohomology/example/custom_persistence_sort.cpp
+++ b/src/Persistent_cohomology/example/custom_persistence_sort.cpp
@@ -33,7 +33,7 @@ using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomolog
       Gudhi::persistent_cohomology::Field_Zp >;
 
 std::vector<Point> random_points() {
-  // Instanciate a random point generator
+  // Instantiate a random point generator
   CGAL::Random rng(0);
 
   // Generate "points_number" random points in a vector
diff --git a/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp b/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp
index bffaabdd..3da6771e 100644
--- a/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp
+++ b/src/Persistent_cohomology/example/persistence_from_simple_simplex_tree.cpp
@@ -95,7 +95,7 @@ int main(int argc, char * const argv[]) {
   SimplexVector = {9, 10, 11};
   st.insert_simplex_and_subfaces(SimplexVector, 0.3);
 
-  // ++ NINETH
+  // ++ NINTH
   std::clog << "   - INSERT (2,10,12)" << std::endl;
   SimplexVector = {2, 10, 12};
   st.insert_simplex_and_subfaces(SimplexVector, 0.3);
diff --git a/src/Persistent_cohomology/example/rips_multifield_persistence.cpp b/src/Persistent_cohomology/example/rips_multifield_persistence.cpp
index 2edf5bc4..ca26a5b9 100644
--- a/src/Persistent_cohomology/example/rips_multifield_persistence.cpp
+++ b/src/Persistent_cohomology/example/rips_multifield_persistence.cpp
@@ -104,7 +104,7 @@ void program_options(int argc, char * argv[]
       ("min-field-charac,p", po::value<int>(&min_p)->default_value(2),
        "Minimal characteristic p of the coefficient field Z/pZ.")
       ("max-field-charac,q", po::value<int>(&max_p)->default_value(1223),
-       "Minimial characteristic q of the coefficient field Z/pZ.")
+       "Maximal characteristic q of the coefficient field Z/pZ.")
       ("min-persistence,m", po::value<Filtration_value>(&min_persistence),
        "Minimal lifetime of homology feature to be recorded. Default is 0");
 
diff --git a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
index d428e497..2301a66b 100644
--- a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
+++ b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
@@ -211,7 +211,7 @@ class Persistent_cohomology {
   /** \brief Update the cohomology groups under the insertion of an edge.
    *
    * The 0-homology is maintained with a simple Union-Find data structure, which
-   * explains the existance of a specific function of edge insertions. */
+   * explains the existence of a specific function of edge insertions. */
   void update_cohomology_groups_edge(Simplex_handle sigma) {
     Simplex_handle u, v;
     boost::tie(u, v) = cpx_->endpoints(sigma);
diff --git a/src/Rips_complex/example/example_one_skeleton_rips_from_correlation_matrix.cpp b/src/Rips_complex/example/example_one_skeleton_rips_from_correlation_matrix.cpp
index 3d2ba54f..3811d1f1 100644
--- a/src/Rips_complex/example/example_one_skeleton_rips_from_correlation_matrix.cpp
+++ b/src/Rips_complex/example/example_one_skeleton_rips_from_correlation_matrix.cpp
@@ -40,7 +40,7 @@ int main() {
         throw "The input matrix is not a correlation matrix. The program will now terminate.\n";
       }
       correlations[i][j] = 1 - correlations[i][j];
-      // Here we make sure that we will get the treshold value equal to maximal
+      // Here we make sure that we will get the threshold value equal to maximal
       // distance in the matrix.
       if (correlations[i][j] > threshold) threshold = correlations[i][j];
     }
diff --git a/src/Simplex_tree/example/graph_expansion_with_blocker.cpp b/src/Simplex_tree/example/graph_expansion_with_blocker.cpp
index df52bf43..eef8b665 100644
--- a/src/Simplex_tree/example/graph_expansion_with_blocker.cpp
+++ b/src/Simplex_tree/example/graph_expansion_with_blocker.cpp
@@ -42,7 +42,7 @@ int main(int argc, char* const argv[]) {
       std::clog << vertex << ", ";
     }
     std::clog << "] ( " << stree.filtration(sh);
-    // User can re-assign a new filtration value directly in the blocker (default is the maximal value of boudaries)
+    // User can re-assign a new filtration value directly in the blocker (default is the maximal value of boundaries)
     stree.assign_filtration(sh, stree.filtration(sh) + 1.);
 
     std::clog << " + 1. ) = " << result << std::endl;
diff --git a/src/Simplex_tree/example/simple_simplex_tree.cpp b/src/Simplex_tree/example/simple_simplex_tree.cpp
index e8bec596..965711da 100644
--- a/src/Simplex_tree/example/simple_simplex_tree.cpp
+++ b/src/Simplex_tree/example/simple_simplex_tree.cpp
@@ -129,7 +129,7 @@ int main(int argc, char* const argv[]) {
     std::clog << "   - 3 NOT INSERTED" << std::endl;
   }
 
-  // ++ NINETH
+  // ++ NINTH
   std::clog << "   * INSERT (3,0)" << std::endl;
   typeVectorVertex ninethSimplexVector = {3, 0};
   returnValue = simplexTree.insert_simplex(ninethSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree.h b/src/Simplex_tree/include/gudhi/Simplex_tree.h
index 6dce947c..9059219c 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree.h
@@ -42,6 +42,10 @@
 
 namespace Gudhi {
 
+/** \addtogroup simplex_tree 
+ *  @{
+ */
+
 /**
  * \class Extended_simplex_type Simplex_tree.h gudhi/Simplex_tree.h
  * \brief Extended simplex type data structure for representing the type of simplices in an extended filtration.
@@ -97,8 +101,7 @@ class Simplex_tree {
   // Simplex_key next to each other).
   typedef typename boost::container::flat_map<Vertex_handle, Node> Dictionary;
 
-  /* \brief Set of nodes sharing a same parent in the simplex tree. */
-  /* \brief Set of nodes sharing a same parent in the simplex tree. */
+  /** \brief Set of nodes sharing a same parent in the simplex tree. */
   typedef Simplex_tree_siblings<Simplex_tree, Dictionary> Siblings;
 
 
@@ -965,7 +968,7 @@ class Simplex_tree {
         // If we reached the end of the vertices, and the simplex has more vertices than the given simplex
         // => we found a coface
 
-        // Add a coface if we wan't the star or if the number of vertices of the current simplex matches with nbVertices
+        // Add a coface if we want the star or if the number of vertices of the current simplex matches with nbVertices
         bool addCoface = (star || curr_nbVertices == nbVertices);
         if (addCoface)
           cofaces.push_back(simplex);
@@ -1338,7 +1341,7 @@ class Simplex_tree {
     }
   }
 
-  /* \private Returns the Simplex_handle composed of the vertex list (from the Simplex_handle), plus the given
+  /** \private Returns the Simplex_handle composed of the vertex list (from the Simplex_handle), plus the given
    * Vertex_handle if the Vertex_handle is found in the Simplex_handle children list.
    * Returns null_simplex() if it does not exist
   */
@@ -1491,7 +1494,7 @@ class Simplex_tree {
 
       int sh_dimension = dimension(sh);
       if (sh_dimension >= dimension_)
-        // Stop browsing as soon as the dimension is reached, no need to go furter
+        // Stop browsing as soon as the dimension is reached, no need to go further
         return false;
       new_dimension = (std::max)(new_dimension, sh_dimension);
     }
@@ -1801,7 +1804,7 @@ struct Simplex_tree_options_fast_persistence {
   static const bool contiguous_vertices = true;
 };
 
-/** @} */  // end defgroup simplex_tree
+/** @}*/  // end addtogroup simplex_tree
 
 }  // namespace Gudhi
 
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_iterators.h b/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_iterators.h
index 394c6ee1..b63a5595 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_iterators.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_iterators.h
@@ -22,12 +22,12 @@
 
 namespace Gudhi {
 
-/* \addtogroup simplex_tree
+/** \addtogroup simplex_tree 
  * Iterators and range types for the Simplex_tree.
- * @{
+ *  @{
  */
 
-/* \brief Iterator over the vertices of a simplex
+/** \brief Iterator over the vertices of a simplex
  * in a SimplexTree.
  *
  * Forward iterator, 'value_type' is SimplexTree::Vertex_handle.*/
@@ -73,7 +73,7 @@ class Simplex_tree_simplex_vertex_iterator : public boost::iterator_facade<
 };
 
 /*---------------------------------------------------------------------------*/
-/* \brief Iterator over the simplices of the boundary of a
+/** \brief Iterator over the simplices of the boundary of a
  *  simplex.
  *
  * Forward iterator, value_type is SimplexTree::Simplex_handle.*/
@@ -181,7 +181,7 @@ class Simplex_tree_boundary_simplex_iterator : public boost::iterator_facade<
   SimplexTree * st_;  // simplex containing the simplicial complex
 };
 
-/* \brief Iterator over the simplices of the boundary of a simplex and their opposite vertices.
+/** \brief Iterator over the simplices of the boundary of a simplex and their opposite vertices.
  *
  * Forward iterator, value_type is std::pair<SimplexTree::Simplex_handle, SimplexTree::Vertex_handle>.*/
 template<class SimplexTree>
@@ -291,7 +291,7 @@ class Simplex_tree_boundary_opposite_vertex_simplex_iterator : public boost::ite
 };
 
 /*---------------------------------------------------------------------------*/
-/* \brief Iterator over the simplices of a simplicial complex.
+/** \brief Iterator over the simplices of a simplicial complex.
  *
  * Forward iterator, value_type is SimplexTree::Simplex_handle.*/
 template<class SimplexTree>
@@ -364,7 +364,7 @@ class Simplex_tree_complex_simplex_iterator : public boost::iterator_facade<
   SimplexTree * st_;
 };
 
-/* \brief Iterator over the simplices of the skeleton of a given
+/** \brief Iterator over the simplices of the skeleton of a given
  * dimension of the simplicial complex.
  *
  * Forward iterator, value_type is SimplexTree::Simplex_handle.*/
@@ -447,7 +447,8 @@ class Simplex_tree_skeleton_simplex_iterator : public boost::iterator_facade<
   int curr_dim_;
 };
 
-/* @} */  // end addtogroup simplex_tree
+/** @}*/  // end addtogroup simplex_tree
+
 }  // namespace Gudhi
 
 #endif  // SIMPLEX_TREE_SIMPLEX_TREE_ITERATORS_H_
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_node_explicit_storage.h b/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_node_explicit_storage.h
index ae140859..63023daa 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_node_explicit_storage.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_node_explicit_storage.h
@@ -15,16 +15,15 @@
 
 namespace Gudhi {
 
-/* \addtogroup simplex_tree
+/** \addtogroup simplex_tree
  * Represents a node of a Simplex_tree.
  * @{
  */
 
-/*
- * \brief Node of a simplex tree with filtration value
+/** \brief Node of a simplex tree with filtration value
  * and simplex key.
  *
- * It stores explicitely its own filtration value and its own Simplex_key.
+ * It stores explicitly its own filtration value and its own Simplex_key.
  */
 template<class SimplexTree>
 struct Simplex_tree_node_explicit_storage : SimplexTree::Filtration_simplex_base, SimplexTree::Key_simplex_base {
@@ -54,7 +53,8 @@ struct Simplex_tree_node_explicit_storage : SimplexTree::Filtration_simplex_base
   Siblings * children_;
 };
 
-/* @} */  // end addtogroup simplex_tree
+/** @}*/  // end addtogroup simplex_tree
+
 }  // namespace Gudhi
 
 #endif  // SIMPLEX_TREE_SIMPLEX_TREE_NODE_EXPLICIT_STORAGE_H_
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_siblings.h b/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_siblings.h
index ae25d290..d849eeba 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_siblings.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree/Simplex_tree_siblings.h
@@ -20,12 +20,12 @@
 
 namespace Gudhi {
 
-/* \addtogroup simplex_tree
+/** \addtogroup simplex_tree
  * Represents a set of node of a Simplex_tree that share the same parent.
  * @{
  */
 
-/* \brief Data structure to store a set of nodes in a SimplexTree sharing
+/** \brief Data structure to store a set of nodes in a SimplexTree sharing
  * the same parent node.*/
 template<class SimplexTree, class MapContainer>
 class Simplex_tree_siblings {
@@ -58,7 +58,7 @@ class Simplex_tree_siblings {
         members_() {
   }
 
-  /* \brief Constructor with initialized set of members.
+  /** \brief Constructor with initialized set of members.
    *
    * 'members' must be sorted and unique.*/
   template<typename RandomAccessVertexRange>
@@ -72,8 +72,7 @@ class Simplex_tree_siblings {
     }
   }
 
-  /*
-   * \brief Inserts a Node in the set of siblings nodes.
+  /** \brief Inserts a Node in the set of siblings nodes.
    *
    * If already present, assigns the minimal filtration value 
    * between input filtration_value and the value already 
@@ -114,7 +113,8 @@ class Simplex_tree_siblings {
   Dictionary members_;
 };
 
-/* @} */  // end addtogroup simplex_tree
+/** @}*/  // end addtogroup simplex_tree
+
 }  // namespace Gudhi
 
 #endif  // SIMPLEX_TREE_SIMPLEX_TREE_SIBLINGS_H_
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree/indexing_tag.h b/src/Simplex_tree/include/gudhi/Simplex_tree/indexing_tag.h
index 3e395ae2..29c76e50 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree/indexing_tag.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree/indexing_tag.h
@@ -20,7 +20,7 @@ namespace Gudhi {
 struct linear_indexing_tag {
 };
 
-/* \brief Tag for a zigzag ordering of simplices. */
+/** \brief Tag for a zigzag ordering of simplices. */
 //  struct zigzag_indexing_tag {};
 }  // namespace Gudhi
 
diff --git a/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp b/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp
index 6d63d8ae..54e23204 100644
--- a/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp
+++ b/src/Simplex_tree/test/simplex_tree_graph_expansion_unit_test.cpp
@@ -93,7 +93,7 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_3, typeST, li
         std::clog << vertex << ", ";
       }
       std::clog << "] ( " << simplex_tree.filtration(sh);
-      // User can re-assign a new filtration value directly in the blocker (default is the maximal value of boudaries)
+      // User can re-assign a new filtration value directly in the blocker (default is the maximal value of boundaries)
       simplex_tree.assign_filtration(sh, simplex_tree.filtration(sh) + 1.);
 
       std::clog << " + 1. ) = " << result << std::endl;
@@ -160,7 +160,7 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_expansion_with_blockers_2, typeST, li
         std::clog << vertex << ", ";
       }
       std::clog << "] ( " << simplex_tree.filtration(sh);
-      // User can re-assign a new filtration value directly in the blocker (default is the maximal value of boudaries)
+      // User can re-assign a new filtration value directly in the blocker (default is the maximal value of boundaries)
       simplex_tree.assign_filtration(sh, simplex_tree.filtration(sh) + 1.);
 
       std::clog << " + 1. ) = " << result << std::endl;
diff --git a/src/Simplex_tree/test/simplex_tree_unit_test.cpp b/src/Simplex_tree/test/simplex_tree_unit_test.cpp
index b18e2ec4..79bb5a93 100644
--- a/src/Simplex_tree/test/simplex_tree_unit_test.cpp
+++ b/src/Simplex_tree/test/simplex_tree_unit_test.cpp
@@ -287,7 +287,7 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_insertion, typeST, list_of_tested_var
   set_and_test_simplex_tree_dim_fil(st, eighthSimplexVector.size(), eighthSimplex.second);
   BOOST_CHECK(st.num_vertices() == (size_t) 4);
 
-  // ++ NINETH
+  // ++ NINTH
   std::clog << "   - INSERT (3,0)" << std::endl;
   typeVectorVertex ninethSimplexVector{3, 0};
   BOOST_CHECK(ninethSimplexVector.size() == 2);
@@ -361,7 +361,7 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_insertion, typeST, list_of_tested_var
   test_simplex_tree_contains(st, seventhSimplex, 8); // (2,1,0) -> 8
   std::clog << "simplex_tree_insertion - eighth - 3" << std::endl;
   test_simplex_tree_contains(st, eighthSimplex, 3); // (3) -> 3
-  std::clog << "simplex_tree_insertion - nineth - 7" << std::endl;
+  std::clog << "simplex_tree_insertion - ninth - 7" << std::endl;
   test_simplex_tree_contains(st, ninethSimplex, 7); // (3,0) -> 7
 
   // Display the Simplex_tree - Can not be done in the middle of 2 inserts
diff --git a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_simplex.h b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_simplex.h
index 12fe6469..d83c0ab3 100644
--- a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_simplex.h
+++ b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_simplex.h
@@ -134,7 +134,7 @@ class Skeleton_blocker_simplex {
   }
 
   /**
-   * Substracts a from the simplex.
+   * Subtracts a from the simplex.
    */
   void difference(const Skeleton_blocker_simplex & a) {
     std::vector<T> v;
diff --git a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_sub_complex.h b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_sub_complex.h
index 4c48ff31..5abd64d7 100644
--- a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_sub_complex.h
+++ b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/Skeleton_blocker_sub_complex.h
@@ -76,8 +76,8 @@ class Skeleton_blocker_sub_complex : public ComplexType {
  public:
   /**
    * Add a vertex 'global' of K to L. When added to L, this vertex will receive
-   * another number, addresses(global), its local adress.
-   * return the adress where the vertex lay on L.
+   * another number, addresses(global), its local address.
+   * return the address where the vertex lay on L.
    * The vertex corresponding to 'global' must not be already present
    * in the complex.
    */
@@ -174,7 +174,7 @@ class Skeleton_blocker_sub_complex : public ComplexType {
 
   // /**
   //  * Allocates a simplex in L corresponding to the simplex s in K
-  //  * with its local adresses and returns an AddressSimplex.
+  //  * with its local addresses and returns an AddressSimplex.
   //  */
   // boost::optional<Simplex> get_address(const Root_simplex_handle & s) const;
 
@@ -226,7 +226,7 @@ bool proper_face_in_union(
 }
 
 // Remark: this function should be friend in order to leave get_adresses private
-// however doing so seemes currently not possible due to a visual studio bug c2668
+// however doing so seems currently not possible due to a visual studio bug c2668
 // "the compiler does not support partial ordering of template functions as specified in the C++ Standard"
 // http://www.serkey.com/error-c2668-ambiguous-call-to-overloaded-function-bb45ft.html
 
diff --git a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/internal/Trie.h b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/internal/Trie.h
index a43fa034..18ae6a92 100644
--- a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/internal/Trie.h
+++ b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/internal/Trie.h
@@ -107,7 +107,7 @@ struct Trie {
   }
 
   /**
-   * Goes to the root in the trie to consitute simplex
+   * Goes to the root in the trie to constitute simplex
    */
   void add_vertices_up_to_the_root(Simplex& res) const {
     res.add_vertex(v);
diff --git a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/iterators/Skeleton_blockers_triangles_iterators.h b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/iterators/Skeleton_blockers_triangles_iterators.h
index 37c0b4d3..2c49a1b8 100644
--- a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/iterators/Skeleton_blockers_triangles_iterators.h
+++ b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker/iterators/Skeleton_blockers_triangles_iterators.h
@@ -21,7 +21,7 @@ namespace skeleton_blocker {
 /**
  * \brief Iterator over the triangles that are
  * adjacent to a vertex of the simplicial complex.
- * \remark Will be removed soon -> dont look
+ * \remark Will be removed soon -> don't look
  */
 template<typename Complex, typename LinkType>
 class Triangle_around_vertex_iterator : public boost::iterator_facade
@@ -95,7 +95,7 @@ class Triangle_around_vertex_iterator : public boost::iterator_facade
 /**
  * \brief Iterator over the triangles of the
  * simplicial complex.
- * \remark Will be removed soon -> dont look
+ * \remark Will be removed soon -> don't look
  *
  */
 template<typename SkeletonBlockerComplex>
diff --git a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker_complex.h b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker_complex.h
index 031bcb9c..8ceaa480 100644
--- a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker_complex.h
+++ b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker_complex.h
@@ -438,7 +438,7 @@ class Skeleton_blocker_complex {
   }
 
   /**
-   * return the id of a vertex of adress local present in the graph
+   * return the id of a vertex of address local present in the graph
    */
   Root_vertex_handle get_id(Vertex_handle local) const {
     assert(0 <= local.vertex && local.vertex < boost::num_vertices(skeleton));
@@ -740,7 +740,7 @@ class Skeleton_blocker_complex {
    * complex to the smallest flag complex that contains it.
    */
   void remove_blockers() {
-    // Desallocate the blockers
+    // Deallocate the blockers
     while (!blocker_map_.empty()) {
       delete_blocker(blocker_map_.begin()->second);
     }
@@ -764,8 +764,8 @@ class Skeleton_blocker_complex {
 
  public:
   /**
-   * Removes the simplex s from the set of blockers
-   * and desallocate s.
+   * Removes the simplex sigma from the set of blockers
+   * and deallocate sigma.
    */
   void delete_blocker(Blocker_handle sigma) {
     if (visitor)
@@ -960,7 +960,7 @@ class Skeleton_blocker_complex {
   }
 
   /*
-   * @brief returnrs true iff the complex is empty.
+   * @brief returns true iff the complex is empty.
    */
   bool empty() const {
     return num_vertices() == 0;
@@ -1043,7 +1043,7 @@ class Skeleton_blocker_complex {
     if (num_vertices() == 1)
       return true;
     for (auto vi : vertex_range()) {
-      // xxx todo faire une methode bool is_in_blocker(Vertex_handle)
+      // xxx todo create a method: bool is_in_blocker(Vertex_handle)
       if (blocker_map_.find(vi) == blocker_map_.end()) {
         // no blocker passes through the vertex, we just need to
         // check if the current vertex is linked to all others vertices of the complex
diff --git a/src/Tangential_complex/include/gudhi/Tangential_complex.h b/src/Tangential_complex/include/gudhi/Tangential_complex.h
index f3491f91..cc424810 100644
--- a/src/Tangential_complex/include/gudhi/Tangential_complex.h
+++ b/src/Tangential_complex/include/gudhi/Tangential_complex.h
@@ -1152,7 +1152,7 @@ class Tangential_complex {
 
 #ifdef GUDHI_TC_VERY_VERBOSE
     std::cerr << "Inserted " << num_inserted_points << " points / " << num_attempts_to_insert_points
-              << " attemps to compute the star\n";
+              << " attempts to compute the star\n";
 #endif
 
     update_star(i);
diff --git a/src/Witness_complex/include/gudhi/Active_witness/Active_witness.h b/src/Witness_complex/include/gudhi/Active_witness/Active_witness.h
index 2ae1d6e0..1aebb045 100644
--- a/src/Witness_complex/include/gudhi/Active_witness/Active_witness.h
+++ b/src/Witness_complex/include/gudhi/Active_witness/Active_witness.h
@@ -18,7 +18,7 @@ namespace Gudhi {
 
 namespace witness_complex {
 
-  /* \class Active_witness
+  /** \class Active_witness
    *  \brief Class representing a list of nearest neighbors to a given witness.
    *  \details Every element is a pair of a landmark identifier and the squared distance to it.
   */
diff --git a/src/Witness_complex/include/gudhi/Active_witness/Active_witness_iterator.h b/src/Witness_complex/include/gudhi/Active_witness/Active_witness_iterator.h
index 4f8fddba..18f19650 100644
--- a/src/Witness_complex/include/gudhi/Active_witness/Active_witness_iterator.h
+++ b/src/Witness_complex/include/gudhi/Active_witness/Active_witness_iterator.h
@@ -18,7 +18,7 @@ namespace Gudhi {
 
 namespace witness_complex {
 
-/* \brief Iterator in the nearest landmark list.
+/** \brief Iterator in the nearest landmark list.
  *  \details After the iterator reaches the end of the list,
  *          the list is augmented by a (nearest landmark, distance) pair if possible.
  *          If all the landmarks are present in the list, iterator returns the specific end value
diff --git a/src/Witness_complex/include/gudhi/Strong_witness_complex.h b/src/Witness_complex/include/gudhi/Strong_witness_complex.h
index b3699f77..ddc0da32 100644
--- a/src/Witness_complex/include/gudhi/Strong_witness_complex.h
+++ b/src/Witness_complex/include/gudhi/Strong_witness_complex.h
@@ -125,7 +125,7 @@ class Strong_witness_complex {
   //@}
 
  private:
-    /* \brief Adds recursively all the faces of a certain dimension dim-1 witnessed by the same witness.
+    /** \brief Adds recursively all the faces of a certain dimension dim-1 witnessed by the same witness.
      * Iterator is needed to know until how far we can take landmarks to form simplexes.
      * simplex is the prefix of the simplexes to insert.
      * The landmark pointed by aw_it is added to all formed simplices.
diff --git a/src/Witness_complex/include/gudhi/Witness_complex.h b/src/Witness_complex/include/gudhi/Witness_complex.h
index d655c7f6..66ae7af2 100644
--- a/src/Witness_complex/include/gudhi/Witness_complex.h
+++ b/src/Witness_complex/include/gudhi/Witness_complex.h
@@ -127,7 +127,7 @@ class Witness_complex {
   //@}
 
  private:
-  /* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness.
+  /** \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness.
    * Iterator is needed to know until how far we can take landmarks to form simplexes.
    * simplex is the prefix of the simplexes to insert.
    * The output value indicates if the witness rests active or not.
diff --git a/src/Witness_complex/include/gudhi/Witness_complex/all_faces_in.h b/src/Witness_complex/include/gudhi/Witness_complex/all_faces_in.h
index 5845728a..007ab084 100644
--- a/src/Witness_complex/include/gudhi/Witness_complex/all_faces_in.h
+++ b/src/Witness_complex/include/gudhi/Witness_complex/all_faces_in.h
@@ -11,7 +11,7 @@
 #ifndef WITNESS_COMPLEX_ALL_FACES_IN_H_
 #define WITNESS_COMPLEX_ALL_FACES_IN_H_
 
-/* \brief Check if the facets of the k-dimensional simplex witnessed 
+/** \brief Check if the facets of the k-dimensional simplex witnessed 
  *  by witness witness_id are already in the complex.
  *  inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
  */
diff --git a/src/cmake/modules/FindTBB.cmake b/src/cmake/modules/FindTBB.cmake
index 13f4d929..e6c42dc7 100644
--- a/src/cmake/modules/FindTBB.cmake
+++ b/src/cmake/modules/FindTBB.cmake
@@ -34,7 +34,7 @@
 #
 # GvdB: Mac OS X distribution places libraries directly in lib directory.
 #
-# For backwards compatibility, you may explicitely set the CMake variables TBB_ARCHITECTURE and TBB_COMPILER.
+# For backwards compatibility, you may explicitly set the CMake variables TBB_ARCHITECTURE and TBB_COMPILER.
 # TBB_ARCHITECTURE [ ia32 | em64t | itanium ]
 #   which architecture to use
 # TBB_COMPILER e.g. vc9 or cc3.2.3_libc2.3.2_kernel2.4.21 or cc4.0.1_os10.4.9
@@ -54,8 +54,8 @@
 #   TBB_MALLOC_DEBUG_LIBRARY, the TBB debug malloc library
 # TBB_FOUND, If false, don't try to use TBB.
 # TBB_INTERFACE_VERSION, as defined in tbb/tbb_stddef.h
-# TBB_MALLOCPROXY_DEBUG_LIBRARY, the TBB debug malloc_proxy library (not included in TBB_LIBRARIES since it's optionnal)
-# TBB_MALLOCPROXY_RELEASE_LIBRARY, the TBB release malloc_proxy library (not included in TBB_LIBRARIES since it's optionnal)
+# TBB_MALLOCPROXY_DEBUG_LIBRARY, the TBB debug malloc_proxy library (not included in TBB_LIBRARIES since it's optional)
+# TBB_MALLOCPROXY_RELEASE_LIBRARY, the TBB release malloc_proxy library (not included in TBB_LIBRARIES since it's optional)
 
 include(CheckCXXSourceCompiles)
 
diff --git a/src/cmake/modules/GUDHI_doxygen_target.cmake b/src/cmake/modules/GUDHI_doxygen_target.cmake
index 6b9514de..327513da 100644
--- a/src/cmake/modules/GUDHI_doxygen_target.cmake
+++ b/src/cmake/modules/GUDHI_doxygen_target.cmake
@@ -45,6 +45,11 @@ if(DOXYGEN_FOUND)
   endif()
 
   message("++ Doxygen version ${DOXYGEN_VERSION}")
+  if (DOXYGEN_VERSION VERSION_LESS 1.9.3)
+    set(GUDHI_DOXYGEN_CLASS_DIAGRAMS "CLASS_DIAGRAMS = NO")
+  else()
+    set(GUDHI_DOXYGEN_CLASS_DIAGRAMS "")
+  endif()
   if (DOXYGEN_VERSION VERSION_LESS 1.9.2)
     set(GUDHI_DOXYGEN_MATHJAX_VERSION "MATHJAX_VERSION = MathJax_2")
     set(GUDHI_DOXYGEN_MATHJAX_EXTENSIONS "TeX/AMSmath TeX/AMSsymbols")
@@ -52,6 +57,7 @@ if(DOXYGEN_FOUND)
     set(GUDHI_DOXYGEN_MATHJAX_VERSION "MATHJAX_VERSION = MathJax_3")
     set(GUDHI_DOXYGEN_MATHJAX_EXTENSIONS "ams")
   endif()
+
   configure_file(${GUDHI_DOXYGEN_SOURCE_PREFIX}/Doxyfile.in "${CMAKE_CURRENT_BINARY_DIR}/Doxyfile" @ONLY)
 
   add_custom_target(doxygen ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile
diff --git a/src/cmake/modules/GUDHI_modules.cmake b/src/cmake/modules/GUDHI_modules.cmake
index 13248f7e..ec1f756b 100644
--- a/src/cmake/modules/GUDHI_modules.cmake
+++ b/src/cmake/modules/GUDHI_modules.cmake
@@ -2,7 +2,7 @@
 
 set(GUDHI_MODULES_FULL_LIST "")
 function(add_gudhi_module file_path)
-  option("WITH_MODULE_GUDHI_${file_path}" "Activate/desactivate ${file_path} compilation and installation" ON)
+  option("WITH_MODULE_GUDHI_${file_path}" "Activate/deactivate ${file_path} compilation and installation" ON)
   if (WITH_MODULE_GUDHI_${file_path})
     set(GUDHI_MODULES ${GUDHI_MODULES} ${file_path} CACHE INTERNAL "GUDHI_MODULES")
   else()
@@ -10,7 +10,7 @@ function(add_gudhi_module file_path)
   endif()
   # Required by user_version
   set(GUDHI_MODULES_FULL_LIST ${GUDHI_MODULES_FULL_LIST} ${file_path} PARENT_SCOPE)
-  # Include module headers is independant - You may ask for no Alpha complex module but Python interface i.e.
+  # Include module headers is independent - You may ask for no Alpha complex module but Python interface i.e.
   if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/src/${file_path}/include/)
     include_directories(src/${file_path}/include/)
   endif()
diff --git a/src/cmake/modules/GUDHI_options.cmake b/src/cmake/modules/GUDHI_options.cmake
index 3cd0a489..5e28c87d 100644
--- a/src/cmake/modules/GUDHI_options.cmake
+++ b/src/cmake/modules/GUDHI_options.cmake
@@ -1,5 +1,15 @@
-option(WITH_GUDHI_BENCHMARK "Activate/desactivate benchmark compilation" OFF)
-option(WITH_GUDHI_EXAMPLE "Activate/desactivate examples compilation and installation" OFF)
-option(WITH_GUDHI_PYTHON "Activate/desactivate python module compilation and installation" ON)
-option(WITH_GUDHI_TEST "Activate/desactivate examples compilation and installation" ON)
-option(WITH_GUDHI_UTILITIES "Activate/desactivate utilities compilation and installation" ON)
+option(WITH_GUDHI_BENCHMARK "Activate/deactivate benchmark compilation" OFF)
+option(WITH_GUDHI_EXAMPLE "Activate/deactivate examples compilation and installation" OFF)
+option(WITH_GUDHI_REMOTE_TEST "Activate/deactivate datasets fetching test which uses the Internet" OFF)
+option(WITH_GUDHI_PYTHON "Activate/deactivate python module compilation and installation" ON)
+option(WITH_GUDHI_TEST "Activate/deactivate examples compilation and installation" ON)
+option(WITH_GUDHI_UTILITIES "Activate/deactivate utilities compilation and installation" ON)
+option(WITH_GUDHI_THIRD_PARTY "Activate/deactivate third party libraries cmake detection. When set to OFF, it is usefull for doxygen or user_version i.e." ON)
+
+if (NOT WITH_GUDHI_THIRD_PARTY)
+  set (WITH_GUDHI_BENCHMARK OFF)
+  set (WITH_GUDHI_EXAMPLE OFF)
+  set (WITH_GUDHI_PYTHON OFF)
+  set (WITH_GUDHI_TEST OFF)
+  set (WITH_GUDHI_UTILITIES OFF)
+endif()
+\ No newline at end of file
diff --git a/src/cmake/modules/GUDHI_submodules.cmake b/src/cmake/modules/GUDHI_submodules.cmake
new file mode 100644
index 00000000..78b045bd
--- /dev/null
+++ b/src/cmake/modules/GUDHI_submodules.cmake
@@ -0,0 +1,5 @@
+# For those who dislike bundled dependencies, this indicates where to find a preinstalled Hera.
+set(HERA_WASSERSTEIN_INTERNAL_INCLUDE_DIR ${CMAKE_SOURCE_DIR}/ext/hera/wasserstein/include)
+set(HERA_WASSERSTEIN_INCLUDE_DIR ${HERA_WASSERSTEIN_INTERNAL_INCLUDE_DIR} CACHE PATH "Directory where one can find Hera's wasserstein.h")
+set(HERA_BOTTLENECK_INTERNAL_INCLUDE_DIR ${CMAKE_SOURCE_DIR}/ext/hera/bottleneck/include)
+set(HERA_BOTTLENECK_INCLUDE_DIR ${HERA_BOTTLENECK_INTERNAL_INCLUDE_DIR} CACHE PATH "Directory where one can find Hera's bottleneck.h")
+\ No newline at end of file
diff --git a/src/cmake/modules/GUDHI_third_party_libraries.cmake b/src/cmake/modules/GUDHI_third_party_libraries.cmake
index 6a94d1f5..2cf6787e 100644
--- a/src/cmake/modules/GUDHI_third_party_libraries.cmake
+++ b/src/cmake/modules/GUDHI_third_party_libraries.cmake
@@ -48,12 +48,6 @@ if(CGAL_FOUND)
   include( ${CGAL_USE_FILE} )
 endif()
 
-# For those who dislike bundled dependencies, this indicates where to find a preinstalled Hera.
-set(HERA_WASSERSTEIN_INTERNAL_INCLUDE_DIR ${CMAKE_SOURCE_DIR}/ext/hera/wasserstein/include)
-set(HERA_WASSERSTEIN_INCLUDE_DIR ${HERA_WASSERSTEIN_INTERNAL_INCLUDE_DIR} CACHE PATH "Directory where one can find Hera's wasserstein.h")
-set(HERA_BOTTLENECK_INTERNAL_INCLUDE_DIR ${CMAKE_SOURCE_DIR}/ext/hera/bottleneck/include)
-set(HERA_BOTTLENECK_INCLUDE_DIR ${HERA_BOTTLENECK_INTERNAL_INCLUDE_DIR} CACHE PATH "Directory where one can find Hera's bottleneck.h")
-
 option(WITH_GUDHI_USE_TBB "Build with Intel TBB parallelization" ON)
 
 # Find TBB package for parallel sort - not mandatory, just optional.
@@ -174,7 +168,7 @@ if (WITH_GUDHI_PYTHON)
     message(FATAL_ERROR "ERROR: GUDHI_PYTHON_PATH is not valid.")
   endif(NOT GUDHI_PYTHON_PATH)
   
-  option(WITH_GUDHI_PYTHON_RUNTIME_LIBRARY_DIRS "Build with setting runtime_library_dirs. Usefull when setting rpath is not allowed" ON)
+  option(WITH_GUDHI_PYTHON_RUNTIME_LIBRARY_DIRS "Build with setting runtime_library_dirs. Useful when setting rpath is not allowed" ON)
   
   if(PYTHONINTERP_FOUND AND CYTHON_FOUND)
     if(SPHINX_FOUND)
diff --git a/src/cmake/modules/GUDHI_user_version_target.cmake b/src/cmake/modules/GUDHI_user_version_target.cmake
index 9e76c3d9..4487ad86 100644
--- a/src/cmake/modules/GUDHI_user_version_target.cmake
+++ b/src/cmake/modules/GUDHI_user_version_target.cmake
@@ -14,8 +14,6 @@ add_custom_command(TARGET user_version PRE_BUILD COMMAND ${CMAKE_COMMAND} -E
                    make_directory ${GUDHI_USER_VERSION_DIR}
                    COMMENT "user_version creation in ${GUDHI_USER_VERSION_DIR}")
 
-file(COPY "${CMAKE_SOURCE_DIR}/src/Doxyfile.in" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/")
-
 # Generate bib files for Doxygen - cf. root CMakeLists.txt for explanation
 string(TIMESTAMP GUDHI_VERSION_YEAR "%Y")
 configure_file(${CMAKE_SOURCE_DIR}/biblio/how_to_cite_gudhi.bib.in "${CMAKE_CURRENT_BINARY_DIR}/biblio/how_to_cite_gudhi.bib" @ONLY)
diff --git a/src/common/doc/examples.h b/src/common/doc/examples.h
index 556a24f1..1634b19e 100644
--- a/src/common/doc/examples.h
+++ b/src/common/doc/examples.h
@@ -40,7 +40,6 @@
  * @example edge_collapse_basic_example.cpp
  * \section Cech_complex_example_section Cech_complex
  * @example cech_persistence.cpp
- * @example cech_complex_step_by_step.cpp
  * @example cech_complex_example_from_points.cpp
  * \section Bitmap_cubical_complex_example_section Bitmap_cubical_complex
  * @example periodic_cubical_complex_persistence.cpp
diff --git a/src/common/doc/footer.html b/src/common/doc/footer.html
index 4168c6bc..08a2cbd0 100644
--- a/src/common/doc/footer.html
+++ b/src/common/doc/footer.html
@@ -1,5 +1,9 @@
-<!-- HTML footer for doxygen 1.8.6-->
+<!-- HTML footer for doxygen 1.9.4-->
 <!-- start footer part -->
+<!--BEGIN GENERATE_TREEVIEW-->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+<!--END GENERATE_TREEVIEW-->
+<ul>
 <table style="width:100%">
   <tr class="no-bullet shadow-black">
       <td class="network-entypo">
@@ -10,14 +14,15 @@
 <!--END PROJECT_NAME-->
       </td>
       <td class="network-entypo">
-<!--BEGIN GENERATE_TREEVIEW-->
         $generatedby
         <a href="http://www.doxygen.org/index.html">
         Doxygen</a> $doxygenversion
-<!--END GENERATE_TREEVIEW-->
       </td>
   </tr>
 </table>
-
+</ul>
+<!--BEGIN GENERATE_TREEVIEW-->
+</div>
+<!--END GENERATE_TREEVIEW-->
 </body>
 </html>
diff --git a/src/common/doc/header.html b/src/common/doc/header.html
index 7c20478b..a97e1b2f 100644
--- a/src/common/doc/header.html
+++ b/src/common/doc/header.html
@@ -8,9 +8,6 @@
 <meta name="generator" content="Doxygen $doxygenversion"/>
 <!--BEGIN PROJECT_NAME--><title>$projectname: $title</title><!--END PROJECT_NAME-->
 <!--BEGIN !PROJECT_NAME--><title>$title</title><!--END !PROJECT_NAME-->
-<!-- GUDHI website css for header BEGIN -->
-<link rel="stylesheet" type="text/css" href="https://gudhi.inria.fr/assets/css/styles_feeling_responsive.css" />
-<!-- GUDHI website css for header END -->
 <link href="$relpath^tabs.css" rel="stylesheet" type="text/css"/>
 <script type="text/javascript" src="$relpath^jquery.js"></script>
 <script type="text/javascript" src="$relpath^dynsections.js"></script>
@@ -18,13 +15,17 @@ $treeview
 $search
 $mathjax
 <link href="$relpath^$stylesheet" rel="stylesheet" type="text/css" />
+<!-- GUDHI website css for header BEGIN -->
+<link rel="stylesheet" type="text/css" href="https://gudhi.inria.fr/assets/css/styles_feeling_responsive.css" />
+<!-- GUDHI website css for header END -->
 $extrastylesheet
 </head>
 <body>
 
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
 <!-- GUDHI website header BEGIN -->
 <div id="navigation" class="sticky">
-  <nav class="top-bar" role="navigation" data-topbar>
+  <nav class="top-bar" role="navigation" data-topbar="true">
     <ul class="title-area">
       <li class="name">
       <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI library</a></h1>
@@ -38,7 +39,7 @@ $extrastylesheet
               <li><a  href="/contact/">Contact</a></li>
       </ul>
       <ul class="left">
-              <li><a  href="/"> <img src="/assets/img/home.png" alt="  GUDHI">  GUDHI </a></li>
+              <li><a  href="/"> <img src="/assets/img/home.png" alt="  GUDHI"/>  GUDHI </a></li>
               <li class="divider"></li>
               <li class="has-dropdown">
                 <a  href="#">Project</a>
@@ -85,7 +86,6 @@ $extrastylesheet
 </div><!-- /#navigation -->
 <!-- GUDHI website header END -->
 
-<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
 
 <!--BEGIN TITLEAREA-->
 <div id="titlearea">
diff --git a/src/common/doc/installation.h b/src/common/doc/installation.h
index 24a7fc7a..28526498 100644
--- a/src/common/doc/installation.h
+++ b/src/common/doc/installation.h
@@ -40,13 +40,20 @@ make \endverbatim
  * `make test` is using <a href="https://cmake.org/cmake/help/latest/manual/ctest.1.html">Ctest</a> (CMake test driver
  * program). If some of the tests are failing, please send us the result of the following command:
  * \verbatim ctest --output-on-failure \endverbatim
+ * Testing fetching datasets feature requires the use of the internet and is disabled by default. If you want to include this test, set WITH_GUDHI_REMOTE_TEST to ON when building in the previous step (note that this test is included in the python module):
+ * \verbatim cmake -DCMAKE_BUILD_TYPE=Release -DWITH_GUDHI_TEST=ON -DWITH_GUDHI_REMOTE_TEST=ON --DWITH_GUDHI_PYTHON=ON .. \endverbatim
  * 
- * \subsection documentationgeneration Documentation
- * To generate the documentation, <a target="_blank" href="http://www.doxygen.org/">Doxygen</a> is required.
- * Run the following command in a terminal:
+ * \subsection documentationgeneration C++ documentation
+ * To generate the C++ documentation, the <a target="_blank" href="http://www.doxygen.org/">doxygen</a> program
+ * is required (version &ge; 1.9.3 is advised). Run the following command in a terminal:
  * \verbatim make doxygen \endverbatim
  * Documentation will be generated in a folder named <code>html</code>.
  *
+ * In case there is not a full setup present and only the documentation should be build the following command sequence
+ * can be used:
+\verbatim  cmake -DWITH_GUDHI_THIRD_PARTY=OFF ..
+make doxygen\endverbatim
+ *
  * \subsection helloworld Hello world !
  * The <a target="_blank" href="https://github.com/GUDHI/hello-gudhi-world">Hello world for GUDHI</a>
  * project is an example to help developers to make their own C++ project on top of the GUDHI library.
diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md
index 4f2f1692..ce903405 100644
--- a/src/common/doc/main_page.md
+++ b/src/common/doc/main_page.md
@@ -180,8 +180,8 @@
     <td width="15%">
       <b>Author:</b> Vincent Rouvreau<br>
       <b>Introduced in:</b> GUDHI 2.2.0<br>
-      <b>Copyright:</b> MIT [(GPL v3)](../../licensing/)<br>
-      <b>Includes:</b> [Miniball](https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html)<br>
+      <b>Copyright:</b> MIT [(LGPL v3)](../../licensing/)<br>
+      <b>Requires:</b> \ref cgal
     </td>
  </tr>
  <tr>
diff --git a/src/common/doc/stylesheet.css b/src/common/doc/stylesheet.css
index 1df177a4..fb030e1f 100644..100755
--- a/src/common/doc/stylesheet.css
+++ b/src/common/doc/stylesheet.css
@@ -1,1367 +1,28 @@
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- 
 #projectname
 {
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+  border: 0px none;
 }
-    
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 {
-	font: 60% Tahoma, Arial,sans-serif;
-	margin: 0px;
-	padding: 0px;
+  font: 60% Tahoma, Arial,sans-serif;
 }
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 {
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-{
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-
-.dotgraph
-{
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+  font: 80% Tahoma, Arial,sans-serif;
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+.arrow
 {
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-/* tooltip related style info */
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-	max-width: 80%;
-	opacity: 0.9;
-	padding: 1ex 1em 1em;
-	position: absolute;
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+    width: auto;
+    height: auto;
+    padding-left: 16px;
 }
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-  {
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+// With the doxygen versions <= 1.9.2 the default setting 'overflow: hidden;' causes problems.
+// With the commit:
+//   Commit: 590198b416cd53313d150428d2f912586065ea0d [590198b]
+//   Date: Wednesday, December 1, 2021 1:37:26 PM
+//   issue #8924 Horizontal scroll bar missing in HTML for wide class="dotgraph" objects
+// for the doxygen 1.9.3 version this has already been corrected but to run properly with the <= 1.9.2 version
+// this setting is required
+ul {
+  overflow: visible;
 }
-
diff --git a/src/common/include/gudhi/distance_functions.h b/src/common/include/gudhi/distance_functions.h
index 9bbc62b7..5e5a1e31 100644
--- a/src/common/include/gudhi/distance_functions.h
+++ b/src/common/include/gudhi/distance_functions.h
@@ -13,8 +13,6 @@
 
 #include <gudhi/Debug_utils.h>
 
-#include <gudhi/Miniball.hpp>
-
 #include <boost/range/metafunctions.hpp>
 #include <boost/range/size.hpp>
 
@@ -59,53 +57,6 @@ class Euclidean_distance {
   }
 };
 
-/** @brief Compute the radius of the minimal enclosing ball between Points given by a range of coordinates.
- * The points are assumed to have the same dimension. */
-class Minimal_enclosing_ball_radius {
- public:
-  /** \brief Minimal_enclosing_ball_radius from two points.
-   *
-   * @param[in] point_1 First point.
-   * @param[in] point_2 second point.
-   * @return The minimal enclosing ball radius for the two points (aka. Euclidean distance / 2.).
-   *
-   * \tparam Point must be a range of Cartesian coordinates.
-   *
-   */
-  template< typename Point >
-  typename std::iterator_traits<typename boost::range_iterator<Point>::type>::value_type
-  operator()(const Point& point_1, const Point& point_2) const {
-    return Euclidean_distance()(point_1, point_2) / 2.;
-  }
-  /** \brief Minimal_enclosing_ball_radius from a point cloud.
-   *
-   * @param[in] point_cloud The points.
-   * @return The minimal enclosing ball radius for the points.
-   *
-   * \tparam Point_cloud must be a range of points with Cartesian coordinates.
-   * Point_cloud is a range over a range of Coordinate.
-   *
-   */
-  template< typename Point_cloud,
-            typename Point_iterator = typename boost::range_const_iterator<Point_cloud>::type,
-            typename Point = typename std::iterator_traits<Point_iterator>::value_type,
-            typename Coordinate_iterator = typename boost::range_const_iterator<Point>::type,
-            typename Coordinate = typename std::iterator_traits<Coordinate_iterator>::value_type>
-  Coordinate
-  operator()(const Point_cloud& point_cloud) const {
-    using Min_sphere = Miniball::Miniball<Miniball::CoordAccessor<Point_iterator, Coordinate_iterator>>;
-
-    Min_sphere ms(boost::size(*point_cloud.begin()), point_cloud.begin(), point_cloud.end());
-#ifdef DEBUG_TRACES
-    std::clog << "Minimal_enclosing_ball_radius = " << std::sqrt(ms.squared_radius()) << " | nb points = "
-              << boost::size(point_cloud) << " | dimension = "
-              << boost::size(*point_cloud.begin()) << std::endl;
-#endif  // DEBUG_TRACES
-
-    return std::sqrt(ms.squared_radius());
-  }
-};
-
 }  // namespace Gudhi
 
 #endif  // DISTANCE_FUNCTIONS_H_
diff --git a/src/common/include/gudhi/reader_utils.h b/src/common/include/gudhi/reader_utils.h
index 29d5423d..a7d82541 100644
--- a/src/common/include/gudhi/reader_utils.h
+++ b/src/common/include/gudhi/reader_utils.h
@@ -231,7 +231,7 @@ std::vector<std::vector<Filtration_value>> read_lower_triangular_matrix_from_csv
 
   std::string line;
 
-  // the first line is emtpy, so we ignore it:
+  // the first line is empty, so we ignore it:
   std::getline(in, line);
   std::vector<Filtration_value> values_in_this_line;
   result.push_back(values_in_this_line);
diff --git a/src/common/include/gudhi/writing_persistence_to_file.h b/src/common/include/gudhi/writing_persistence_to_file.h
index 2e36b831..3a0df1a8 100644
--- a/src/common/include/gudhi/writing_persistence_to_file.h
+++ b/src/common/include/gudhi/writing_persistence_to_file.h
@@ -48,7 +48,7 @@ class Persistence_interval_common {
       : birth_(birth), death_(death), dimension_(dim), arith_element_(field) {}
 
   /**
-   * Operator to compare two persistence pairs. During the comparision all the
+   * Operator to compare two persistence pairs. During the comparison all the
    * fields: birth, death, dimensiona and arith_element_ are taken into account
    * and they all have to be equal for two pairs to be equal.
   **/
@@ -65,7 +65,7 @@ class Persistence_interval_common {
   /**
    * Operator to compare objects of a type Persistence_interval_common.
    * One intervals is smaller than the other if it has lower persistence.
-   * Note that this operator do not take Arith_element into account when doing comparisions.
+   * Note that this operator do not take Arith_element into account when doing comparisons.
   **/
   bool operator<(const Persistence_interval_common& i2) const {
     return fabs(this->death_ - this->birth_) < fabs(i2.death_ - i2.birth_);
diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt
index 54221151..65adef75 100644
--- a/src/python/CMakeLists.txt
+++ b/src/python/CMakeLists.txt
@@ -70,6 +70,7 @@ if(PYTHONINTERP_FOUND)
     set(GUDHI_PYTHON_MODULES "${GUDHI_PYTHON_MODULES}'euclidean_strong_witness_complex', ")
     # Modules that should not be auto-imported in __init__.py
     set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'representations', ")
+    set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'tensorflow', ")
     set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'wasserstein', ")
     set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'point_cloud', ")
     set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'weighted_rips_complex', ")
@@ -289,7 +290,8 @@ if(PYTHONINTERP_FOUND)
     # Other .py files
     file(COPY "gudhi/persistence_graphical_tools.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
     file(COPY "gudhi/representations" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi/")
-    file(COPY "gudhi/wasserstein" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
+    file(COPY "gudhi/wasserstein" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")    
+    file(COPY "gudhi/tensorflow" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
     file(COPY "gudhi/point_cloud" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
     file(COPY "gudhi/clustering" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi" FILES_MATCHING PATTERN "*.py")
     file(COPY "gudhi/weighted_rips_complex.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
@@ -329,9 +331,9 @@ if(PYTHONINTERP_FOUND)
                   if(NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 5.1.0)
                     set (GUDHI_SPHINX_MESSAGE "Generating API documentation with Sphinx in ${CMAKE_CURRENT_BINARY_DIR}/sphinx/")
                     # User warning - Sphinx is a static pages generator, and configured to work fine with user_version
-                    # Images and biblio warnings because not found on developper version
+                    # Images and biblio warnings because not found on developer version
                     if (GUDHI_PYTHON_PATH STREQUAL "src/python")
-                      set (GUDHI_SPHINX_MESSAGE "${GUDHI_SPHINX_MESSAGE} \n WARNING : Sphinx is configured for user version, you run it on developper version. Images and biblio will miss")
+                      set (GUDHI_SPHINX_MESSAGE "${GUDHI_SPHINX_MESSAGE} \n WARNING : Sphinx is configured for user version, you run it on developer version. Images and biblio will miss")
                     endif()
                     # sphinx target requires gudhi.so, because conf.py reads gudhi version from it
                     add_custom_target(sphinx
@@ -484,7 +486,7 @@ if(PYTHONINTERP_FOUND)
       add_gudhi_py_test(test_euclidean_witness_complex)
 
       # Datasets generators
-      add_gudhi_py_test(test_datasets_generators) # TODO separate full python datasets generators in another test file independant from CGAL ?
+      add_gudhi_py_test(test_datasets_generators) # TODO separate full python datasets generators in another test file independent from CGAL ?
 
     endif (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
 
@@ -562,6 +564,11 @@ if(PYTHONINTERP_FOUND)
       add_gudhi_py_test(test_representations)
     endif()
 
+    # Differentiation
+    if(TENSORFLOW_FOUND)
+      add_gudhi_py_test(test_diff)
+    endif()
+
     # Betti curves
     if(SKLEARN_FOUND AND SCIPY_FOUND)
       add_gudhi_py_test(test_betti_curve_representations)
@@ -591,6 +598,11 @@ if(PYTHONINTERP_FOUND)
       add_gudhi_py_test(test_dtm_rips_complex)
     endif()
 
+    # Fetch remote datasets
+    if(WITH_GUDHI_REMOTE_TEST)
+      add_gudhi_py_test(test_remote_datasets)
+    endif()
+
     # persistence graphical tools
     if(MATPLOTLIB_FOUND)
       add_gudhi_py_test(test_persistence_graphical_tools)
diff --git a/src/python/doc/cubical_complex_sum.inc b/src/python/doc/cubical_complex_sum.inc
index 87db184d..90ec9fc2 100644
--- a/src/python/doc/cubical_complex_sum.inc
+++ b/src/python/doc/cubical_complex_sum.inc
@@ -1,14 +1,17 @@
 .. table::
    :widths: 30 40 30
 
-   +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+
-   | .. figure::                                                              | The cubical complex represents a grid as a cell complex with         | :Author: Pawel Dlotko       |
-   |      ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | cells of all dimensions.                                             |                             |
-   |      :alt: Cubical complex representation                                |                                                                      | :Since: GUDHI 2.0.0         |
-   |      :figclass: align-center                                             |                                                                      |                             |
-   |                                                                          |                                                                      | :License: MIT               |
-   |                                                                          |                                                                      |                             |
-   +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+
-   | * :doc:`cubical_complex_user`                                            | * :doc:`cubical_complex_ref`                                                                       |
-   |                                                                          | * :doc:`periodic_cubical_complex_ref`                                                              |
-   +--------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+
+   | .. figure::                                                              | The cubical complex represents a grid as a cell complex with         | :Author: Pawel Dlotko                                   |
+   |      ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | cells of all dimensions.                                             |                                                         |
+   |      :alt: Cubical complex representation                                |                                                                      | :Since: GUDHI 2.0.0                                     |
+   |      :figclass: align-center                                             |                                                                      |                                                         |
+   |                                                                          |                                                                      | :License: MIT                                           |
+   |                                                                          |                                                                      |                                                         |
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+
+   | * :doc:`cubical_complex_user`                                            | * :doc:`cubical_complex_ref`                                                                                                   |
+   |                                                                          | * :doc:`periodic_cubical_complex_ref`                                                                                          |
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+
+   |                                                                          | * :doc:`cubical_complex_tflow_itf_ref`                               | :requires: `TensorFlow <installation.html#tensorflow>`_ |
+   |                                                                          |                                                                      |                                                         |
+   +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+
diff --git a/src/python/doc/cubical_complex_tflow_itf_ref.rst b/src/python/doc/cubical_complex_tflow_itf_ref.rst
new file mode 100644
index 00000000..b32f5e47
--- /dev/null
+++ b/src/python/doc/cubical_complex_tflow_itf_ref.rst
@@ -0,0 +1,40 @@
+:orphan:
+
+.. To get rid of WARNING: document isn't included in any toctree
+
+TensorFlow layer for cubical persistence
+########################################
+
+.. include:: differentiation_sum.inc
+
+Example of gradient computed from cubical persistence
+-----------------------------------------------------
+
+.. testcode::
+
+    from gudhi.tensorflow import CubicalLayer
+    import tensorflow as tf
+
+    X = tf.Variable([[0.,2.,2.],[2.,2.,2.],[2.,2.,1.]], dtype=tf.float32, trainable=True)
+    cl = CubicalLayer(homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = cl.call(X)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+
+    grads = tape.gradient(loss, [X])
+    print(grads[0].numpy())
+
+.. testoutput::
+
+    [[ 0.   0.   0. ]
+     [ 0.   0.5  0. ]
+     [ 0.   0.  -0.5]]
+
+Documentation for CubicalLayer
+------------------------------
+
+.. autoclass:: gudhi.tensorflow.CubicalLayer
+   :members:
+   :special-members: __init__
+   :show-inheritance:
diff --git a/src/python/doc/datasets_generators.inc b/src/python/doc/datasets.inc
index 8d169275..95a87678 100644
--- a/src/python/doc/datasets_generators.inc
+++ b/src/python/doc/datasets.inc
@@ -2,7 +2,7 @@
    :widths: 30 40 30
 
    +-----------------------------------+--------------------------------------------+--------------------------------------------------------------------------------------+
-   | .. figure::                       | Datasets generators (points).              | :Authors: Hind Montassif                                                             |
+   | .. figure::                       | Datasets either generated or fetched.      | :Authors: Hind Montassif                                                             |
    |     img/sphere_3d.png             |                                            |                                                                                      |
    |                                   |                                            | :Since: GUDHI 3.5.0                                                                  |
    |                                   |                                            |                                                                                      |
@@ -10,5 +10,5 @@
    |                                   |                                            |                                                                                      |
    |                                   |                                            | :Requires: `CGAL <installation.html#cgal>`_                                          |
    +-----------------------------------+--------------------------------------------+--------------------------------------------------------------------------------------+
-   | * :doc:`datasets_generators`                                                                                                                                          |
+   | * :doc:`datasets`                                                                                                                                                     |
    +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+
diff --git a/src/python/doc/datasets_generators.rst b/src/python/doc/datasets.rst
index 260c3882..2d11a19d 100644
--- a/src/python/doc/datasets_generators.rst
+++ b/src/python/doc/datasets.rst
@@ -3,12 +3,14 @@
 
 .. To get rid of WARNING: document isn't included in any toctree
 
-===========================
-Datasets generators manual
-===========================
+================
+Datasets manual
+================
 
-We provide the generation of different customizable datasets to use as inputs for Gudhi complexes and data structures.
+Datasets generators
+===================
 
+We provide the generation of different customizable datasets to use as inputs for Gudhi complexes and data structures.
 
 Points generators
 ------------------
@@ -103,3 +105,29 @@ Example
 
 
 .. autofunction:: gudhi.datasets.generators.points.torus
+
+
+Fetching datasets
+=================
+
+We provide some ready-to-use datasets that are not available by default when getting GUDHI, and need to be fetched explicitly.
+
+By **default**, the fetched datasets directory is set to a folder named **'gudhi_data'** in the **user home folder**.
+Alternatively, it can be set using the **'GUDHI_DATA'** environment variable.
+
+.. autofunction:: gudhi.datasets.remote.fetch_bunny
+
+.. figure:: ./img/bunny.png
+     :figclass: align-center
+
+     3D Stanford bunny with 35947 vertices.
+
+
+.. autofunction:: gudhi.datasets.remote.fetch_spiral_2d
+
+.. figure:: ./img/spiral_2d.png
+     :figclass: align-center
+
+     2D spiral with 114562 vertices.
+
+.. autofunction:: gudhi.datasets.remote.clear_data_home
diff --git a/src/python/doc/differentiation_sum.inc b/src/python/doc/differentiation_sum.inc
new file mode 100644
index 00000000..3aec33df
--- /dev/null
+++ b/src/python/doc/differentiation_sum.inc
@@ -0,0 +1,12 @@
+.. list-table::
+   :widths: 40 30 30
+   :header-rows: 0
+
+   * - :Since: GUDHI 3.5.0
+     - :License: MIT
+     - :Requires: `TensorFlow <installation.html#tensorflow>`_
+
+We provide TensorFlow 2 models that can handle automatic differentiation for the computation of persistence diagrams from complexes available in the Gudhi library. 
+This includes simplex trees, cubical complexes and Vietoris-Rips complexes. Detailed example on how to use these layers in practice are available
+in the following `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-optimization.ipynb>`_. Note that even if TensorFlow GPU is enabled, all 
+internal computations using Gudhi will be done on CPU. 
diff --git a/src/python/doc/img/bunny.png b/src/python/doc/img/bunny.png
new file mode 100644
index 00000000..769aa530
--- /dev/null
+++ b/src/python/doc/img/bunny.png
diff --git a/src/python/doc/img/spiral_2d.png b/src/python/doc/img/spiral_2d.png
new file mode 100644
index 00000000..abd247cd
--- /dev/null
+++ b/src/python/doc/img/spiral_2d.png
diff --git a/src/python/doc/index.rst b/src/python/doc/index.rst
index 2d7921ae..35f4ba46 100644
--- a/src/python/doc/index.rst
+++ b/src/python/doc/index.rst
@@ -92,7 +92,7 @@ Clustering
 
 .. include:: clustering.inc
 
-Datasets generators
-*******************
+Datasets
+********
 
-.. include:: datasets_generators.inc
+.. include:: datasets.inc
diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst
index cff84691..4eefd415 100644
--- a/src/python/doc/installation.rst
+++ b/src/python/doc/installation.rst
@@ -175,7 +175,7 @@ A complete configuration would be :
     Scikit-learn version 1.0.1 
     POT version 0.8.0 
     HNSWlib found
-    PyKeOps version [pyKeOps]: 1.5 
+    PyKeOps version [pyKeOps]: 2.1
     EagerPy version 0.30.0 
     TensorFlow version 2.7.0 
     Sphinx version 4.3.0 
@@ -396,7 +396,11 @@ mathematics, science, and engineering.
 TensorFlow
 ----------
 
-`TensorFlow <https://www.tensorflow.org>`_ is currently only used in some automatic differentiation tests.
+The :doc:`cubical complex </cubical_complex_tflow_itf_ref>`, :doc:`simplex tree </ls_simplex_tree_tflow_itf_ref>`
+and :doc:`Rips complex </rips_complex_tflow_itf_ref>` modules require `TensorFlow <https://www.tensorflow.org>`_
+for incorporating them in neural nets. 
+
+`TensorFlow <https://www.tensorflow.org>`_ is also used in some automatic differentiation tests.
 
 Bug reports and contributions
 *****************************
diff --git a/src/python/doc/ls_simplex_tree_tflow_itf_ref.rst b/src/python/doc/ls_simplex_tree_tflow_itf_ref.rst
new file mode 100644
index 00000000..9d7d633f
--- /dev/null
+++ b/src/python/doc/ls_simplex_tree_tflow_itf_ref.rst
@@ -0,0 +1,53 @@
+:orphan:
+
+.. To get rid of WARNING: document isn't included in any toctree
+
+TensorFlow layer for lower-star persistence on simplex trees
+############################################################
+
+.. include:: differentiation_sum.inc
+
+Example of gradient computed from lower-star filtration of a simplex tree
+-------------------------------------------------------------------------
+
+.. testcode::
+
+    from gudhi.tensorflow import LowerStarSimplexTreeLayer
+    import tensorflow as tf
+    import gudhi as gd
+
+    st = gd.SimplexTree()
+    st.insert([0, 1]) 
+    st.insert([1, 2]) 
+    st.insert([2, 3]) 
+    st.insert([3, 4]) 
+    st.insert([4, 5]) 
+    st.insert([5, 6]) 
+    st.insert([6, 7]) 
+    st.insert([7, 8]) 
+    st.insert([8, 9]) 
+    st.insert([9, 10]) 
+
+    F = tf.Variable([6.,4.,3.,4.,5.,4.,3.,2.,3.,4.,5.], dtype=tf.float32, trainable=True)
+    sl = LowerStarSimplexTreeLayer(simplextree=st, homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = sl.call(F)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+
+    grads = tape.gradient(loss, [F])
+    print(grads[0].indices.numpy())
+    print(grads[0].values.numpy())
+
+.. testoutput::
+
+    [2 4]
+    [-1.  1.]
+
+Documentation for LowerStarSimplexTreeLayer
+-------------------------------------------
+
+.. autoclass:: gudhi.tensorflow.LowerStarSimplexTreeLayer
+   :members:
+   :special-members: __init__
+   :show-inheritance:
diff --git a/src/python/doc/rips_complex_sum.inc b/src/python/doc/rips_complex_sum.inc
index 2cb24990..6931ebee 100644
--- a/src/python/doc/rips_complex_sum.inc
+++ b/src/python/doc/rips_complex_sum.inc
@@ -11,4 +11,7 @@
    |                                                                |                                                                        |                                                                                  |
    +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+
    | * :doc:`rips_complex_user`                                     | * :doc:`rips_complex_ref`                                                                                                                                 |
-   +----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+
+   |                                                                | * :doc:`rips_complex_tflow_itf_ref`                                    | :requires: `TensorFlow <installation.html#tensorflow>`_                          |
+   |                                                                |                                                                        |                                                                                  |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+
diff --git a/src/python/doc/rips_complex_tflow_itf_ref.rst b/src/python/doc/rips_complex_tflow_itf_ref.rst
new file mode 100644
index 00000000..3ce75868
--- /dev/null
+++ b/src/python/doc/rips_complex_tflow_itf_ref.rst
@@ -0,0 +1,48 @@
+:orphan:
+
+.. To get rid of WARNING: document isn't included in any toctree
+
+TensorFlow layer for Vietoris-Rips persistence
+##############################################
+
+.. include:: differentiation_sum.inc
+
+Example of gradient computed from Vietoris-Rips persistence
+-----------------------------------------------------------
+
+.. testsetup::
+
+    import numpy
+    numpy.set_printoptions(precision=4)
+
+.. testcode::
+
+    from gudhi.tensorflow import RipsLayer
+    import tensorflow as tf
+
+    X = tf.Variable([[1.,1.],[2.,2.]], dtype=tf.float32, trainable=True)
+    rl = RipsLayer(maximum_edge_length=2., homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = rl.call(X)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+
+    grads = tape.gradient(loss, [X])
+    print(grads[0].numpy())
+
+.. testcleanup::
+
+    numpy.set_printoptions(precision=8)
+
+.. testoutput::
+
+    [[-0.5 -0.5]
+     [ 0.5  0.5]]
+
+Documentation for RipsLayer
+---------------------------
+
+.. autoclass:: gudhi.tensorflow.RipsLayer
+   :members:
+   :special-members: __init__
+   :show-inheritance:
diff --git a/src/python/doc/simplex_tree_sum.inc b/src/python/doc/simplex_tree_sum.inc
index a8858f16..3ad1292c 100644
--- a/src/python/doc/simplex_tree_sum.inc
+++ b/src/python/doc/simplex_tree_sum.inc
@@ -1,13 +1,16 @@
 .. table::
    :widths: 30 40 30
 
-   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+
-   | .. figure::                                                    | The simplex tree is an efficient and flexible data structure for       | :Author: Clément Maria      |
-   |      ../../doc/Simplex_tree/Simplex_tree_representation.png    | representing general (filtered) simplicial complexes.                  |                             |
-   |      :alt: Simplex tree representation                         |                                                                        | :Since: GUDHI 2.0.0         |
-   |      :figclass: align-center                                   | The data structure is described in                                     |                             |
-   |                                                                | :cite:`boissonnatmariasimplextreealgorithmica`                         | :License: MIT               |
-   |                                                                |                                                                        |                             |
-   +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+
-   | * :doc:`simplex_tree_user`                                     | * :doc:`simplex_tree_ref`                                                                            |
-   +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------+
+   +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+
+   | .. figure::                                                    | The simplex tree is an efficient and flexible data structure for       | :Author: Clément Maria                                  |
+   |      ../../doc/Simplex_tree/Simplex_tree_representation.png    | representing general (filtered) simplicial complexes.                  |                                                         |
+   |      :alt: Simplex tree representation                         |                                                                        | :Since: GUDHI 2.0.0                                     |
+   |      :figclass: align-center                                   | The data structure is described in                                     |                                                         |
+   |                                                                | :cite:`boissonnatmariasimplextreealgorithmica`                         | :License: MIT                                           |
+   |                                                                |                                                                        |                                                         |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+
+   | * :doc:`simplex_tree_user`                                     | * :doc:`simplex_tree_ref`                                                                                                        |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+
+   |                                                                | * :doc:`ls_simplex_tree_tflow_itf_ref`                                 | :requires: `TensorFlow <installation.html#tensorflow>`_ |
+   |                                                                |                                                                        |                                                         |
+   +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+
diff --git a/src/python/example/rips_complex_diagram_persistence_from_correlation_matrix_file_example.py b/src/python/example/rips_complex_diagram_persistence_from_correlation_matrix_file_example.py
index ea2eb7e1..0b35dbc5 100755
--- a/src/python/example/rips_complex_diagram_persistence_from_correlation_matrix_file_example.py
+++ b/src/python/example/rips_complex_diagram_persistence_from_correlation_matrix_file_example.py
@@ -40,7 +40,7 @@ parser.add_argument(
 args = parser.parse_args()
 
 if not (-1.0 < args.min_edge_correlation < 1.0):
-    print("Wrong value of the treshold corelation (should be between -1 and 1).")
+    print("Wrong value of the threshold corelation (should be between -1 and 1).")
     sys.exit(1)
 
 print("#####################################################################")
diff --git a/src/python/gudhi/datasets/remote.py b/src/python/gudhi/datasets/remote.py
new file mode 100644
index 00000000..f6d3fe56
--- /dev/null
+++ b/src/python/gudhi/datasets/remote.py
@@ -0,0 +1,223 @@
+# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+# Author(s):       Hind Montassif
+#
+# Copyright (C) 2021 Inria
+#
+# Modification(s):
+#   - YYYY/MM Author: Description of the modification
+
+from os.path import join, split, exists, expanduser
+from os import makedirs, remove, environ
+
+from urllib.request import urlretrieve
+import hashlib
+import shutil
+
+import numpy as np
+
+def _get_data_home(data_home = None):
+    """
+    Return the path of the remote datasets directory.
+    This folder is used to store remotely fetched datasets.
+    By default the datasets directory is set to a folder named 'gudhi_data' in the user home folder.
+    Alternatively, it can be set by the 'GUDHI_DATA' environment variable.
+    The '~' symbol is expanded to the user home folder.
+    If the folder does not already exist, it is automatically created.
+
+    Parameters
+    ----------
+    data_home : string
+        The path to remote datasets directory.
+        Default is `None`, meaning that the data home directory will be set to "~/gudhi_data",
+        if the 'GUDHI_DATA' environment variable does not exist.
+
+    Returns
+    -------
+    data_home: string
+        The path to remote datasets directory.
+    """
+    if data_home is None:
+        data_home = environ.get("GUDHI_DATA", join("~", "gudhi_data"))
+    data_home = expanduser(data_home)
+    makedirs(data_home, exist_ok=True)
+    return data_home
+
+
+def clear_data_home(data_home = None):
+    """
+    Delete the data home cache directory and all its content.
+
+    Parameters
+    ----------
+    data_home : string, default is None.
+        The path to remote datasets directory.
+        If `None` and the 'GUDHI_DATA' environment variable does not exist,
+        the default directory to be removed is set to "~/gudhi_data".
+    """
+    data_home = _get_data_home(data_home)
+    shutil.rmtree(data_home)
+
+def _checksum_sha256(file_path):
+    """
+    Compute the file checksum using sha256.
+
+    Parameters
+    ----------
+    file_path: string
+        Full path of the created file including filename.
+
+    Returns
+    -------
+        The hex digest of file_path.
+    """
+    sha256_hash = hashlib.sha256()
+    chunk_size = 4096
+    with open(file_path,"rb") as f:
+        # Read and update hash string value in blocks of 4K
+        while True:
+            buffer = f.read(chunk_size)
+            if not buffer:
+                break
+            sha256_hash.update(buffer)
+    return sha256_hash.hexdigest()
+
+def _fetch_remote(url, file_path, file_checksum = None):
+    """
+    Fetch the wanted dataset from the given url and save it in file_path.
+
+    Parameters
+    ----------
+    url : string
+        The url to fetch the dataset from.
+    file_path : string
+        Full path of the downloaded file including filename.
+    file_checksum : string
+        The file checksum using sha256 to check against the one computed on the downloaded file.
+        Default is 'None', which means the checksum is not checked.
+
+    Raises
+    ------
+    IOError
+        If the computed SHA256 checksum of file does not match the one given by the user.
+    """
+
+    # Get the file
+    urlretrieve(url, file_path)
+
+    if file_checksum is not None:
+        checksum = _checksum_sha256(file_path)
+        if file_checksum != checksum:
+            # Remove file and raise error
+            remove(file_path)
+            raise IOError("{} has a SHA256 checksum : {}, "
+                        "different from expected : {}."
+                        "The file may be corrupted or the given url may be wrong !".format(file_path, checksum, file_checksum))
+
+def _get_archive_path(file_path, label):
+    """
+    Get archive path based on file_path given by user and label.
+
+    Parameters
+    ----------
+    file_path: string
+        Full path of the file to get including filename, or None.
+    label: string
+        Label used along with 'data_home' to get archive path, in case 'file_path' is None.
+
+    Returns
+    -------
+        Full path of archive including filename.
+    """
+    if file_path is None:
+        archive_path = join(_get_data_home(), label)
+        dirname = split(archive_path)[0]
+        makedirs(dirname, exist_ok=True)
+    else:
+        archive_path = file_path
+        dirname = split(archive_path)[0]
+        makedirs(dirname, exist_ok=True)
+
+    return archive_path
+
+def fetch_spiral_2d(file_path = None):
+    """
+    Load the spiral_2d dataset.
+
+    Note that if the dataset already exists in the target location, it is not downloaded again,
+    and the corresponding array is returned from cache.
+
+    Parameters
+    ----------
+    file_path : string
+        Full path of the downloaded file including filename.
+
+        Default is None, meaning that it's set to "data_home/points/spiral_2d/spiral_2d.npy".
+
+        The "data_home" directory is set by default to "~/gudhi_data",
+        unless the 'GUDHI_DATA' environment variable is set.
+
+    Returns
+    -------
+    points: numpy array
+        Array of shape (114562, 2).
+    """
+    file_url = "https://raw.githubusercontent.com/GUDHI/gudhi-data/main/points/spiral_2d/spiral_2d.npy"
+    file_checksum = '2226024da76c073dd2f24b884baefbfd14928b52296df41ad2d9b9dc170f2401'
+
+    archive_path = _get_archive_path(file_path, "points/spiral_2d/spiral_2d.npy")
+
+    if not exists(archive_path):
+        _fetch_remote(file_url, archive_path, file_checksum)
+
+    return np.load(archive_path, mmap_mode='r')
+
+def fetch_bunny(file_path = None, accept_license = False):
+    """
+    Load the Stanford bunny dataset.
+
+    This dataset contains 35947 vertices.
+
+    Note that if the dataset already exists in the target location, it is not downloaded again,
+    and the corresponding array is returned from cache.
+
+    Parameters
+    ----------
+    file_path : string
+        Full path of the downloaded file including filename.
+
+        Default is None, meaning that it's set to "data_home/points/bunny/bunny.npy".
+        In this case, the LICENSE file would be downloaded as "data_home/points/bunny/bunny.LICENSE".
+
+        The "data_home" directory is set by default to "~/gudhi_data",
+        unless the 'GUDHI_DATA' environment variable is set.
+
+    accept_license : boolean
+        Flag to specify if user accepts the file LICENSE and prevents from printing the corresponding license terms.
+
+        Default is False.
+
+    Returns
+    -------
+    points: numpy array
+        Array of shape (35947, 3).
+    """
+
+    file_url = "https://raw.githubusercontent.com/GUDHI/gudhi-data/main/points/bunny/bunny.npy"
+    file_checksum = 'f382482fd89df8d6444152dc8fd454444fe597581b193fd139725a85af4a6c6e'
+    license_url = "https://raw.githubusercontent.com/GUDHI/gudhi-data/main/points/bunny/bunny.LICENSE"
+    license_checksum = 'b763dbe1b2fc6015d05cbf7bcc686412a2eb100a1f2220296e3b4a644c69633a'
+
+    archive_path = _get_archive_path(file_path, "points/bunny/bunny.npy")
+
+    if not exists(archive_path):
+        _fetch_remote(file_url, archive_path, file_checksum)
+        license_path = join(split(archive_path)[0], "bunny.LICENSE")
+        _fetch_remote(license_url, license_path, license_checksum)
+        # Print license terms unless accept_license is set to True
+        if not accept_license:
+            if exists(license_path):
+                with open(license_path, 'r') as f:
+                    print(f.read())
+
+    return np.load(archive_path, mmap_mode='r')
diff --git a/src/python/gudhi/hera/wasserstein.cc b/src/python/gudhi/hera/wasserstein.cc
index 1a21f02f..fa0cf8aa 100644
--- a/src/python/gudhi/hera/wasserstein.cc
+++ b/src/python/gudhi/hera/wasserstein.cc
@@ -29,7 +29,7 @@ double wasserstein_distance(
   if(std::isinf(internal_p)) internal_p = hera::get_infinity<double>();
   params.internal_p = internal_p;
   params.delta = delta;
-  // The extra parameters are purposedly not exposed for now.
+  // The extra parameters are purposely not exposed for now.
   return hera::wasserstein_dist(diag1, diag2, params);
 }
 
diff --git a/src/python/gudhi/persistence_graphical_tools.py b/src/python/gudhi/persistence_graphical_tools.py
index 7ed11360..21275cdd 100644
--- a/src/python/gudhi/persistence_graphical_tools.py
+++ b/src/python/gudhi/persistence_graphical_tools.py
@@ -332,7 +332,7 @@ def plot_persistence_diagram(
             axes.plot([axis_start, axis_end], [infinity, infinity], linewidth=1.0, color="k", alpha=alpha)
             # Infinity label
             yt = axes.get_yticks()
-            yt = yt[np.where(yt < axis_end)]  # to avoid ploting ticklabel higher than infinity
+            yt = yt[np.where(yt < axis_end)]  # to avoid plotting ticklabel higher than infinity
             yt = np.append(yt, infinity)
             ytl = ["%.3f" % e for e in yt]  # to avoid float precision error
             ytl[-1] = r"$+\infty$"
diff --git a/src/python/gudhi/representations/vector_methods.py b/src/python/gudhi/representations/vector_methods.py
index 7f311b3b..8c8b46db 100644
--- a/src/python/gudhi/representations/vector_methods.py
+++ b/src/python/gudhi/representations/vector_methods.py
@@ -455,26 +455,20 @@ class Entropy(BaseEstimator, TransformerMixin):
         new_X = BirthPersistenceTransform().fit_transform(X)        
 
         for i in range(num_diag):
-            orig_diagram, diagram, num_pts_in_diag = X[i], new_X[i], X[i].shape[0]
-            try:
-                new_diagram = DiagramScaler(use=True, scalers=[([1], MaxAbsScaler())]).fit_transform([diagram])[0]
-            except ValueError:
-                # Empty persistence diagram case - https://github.com/GUDHI/gudhi-devel/issues/507
-                assert len(diagram) == 0
-                new_diagram = np.empty(shape = [0, 2])
-
+            orig_diagram, new_diagram, num_pts_in_diag = X[i], new_X[i], X[i].shape[0]
+                
+            p = new_diagram[:,1]
+            p = p/np.sum(p)
             if self.mode == "scalar":
-                ent = - np.sum( np.multiply(new_diagram[:,1], np.log(new_diagram[:,1])) )
+                ent = -np.dot(p, np.log(p))
                 Xfit.append(np.array([[ent]]))
-
             else:
                 ent = np.zeros(self.resolution)
                 for j in range(num_pts_in_diag):
                     [px,py] = orig_diagram[j,:2]
                     min_idx = np.clip(np.ceil((px - self.sample_range[0]) / step_x).astype(int), 0, self.resolution)
                     max_idx = np.clip(np.ceil((py - self.sample_range[0]) / step_x).astype(int), 0, self.resolution)
-                    for k in range(min_idx, max_idx):
-                        ent[k] += (-1) * new_diagram[j,1] * np.log(new_diagram[j,1])
+                    ent[min_idx:max_idx]-=p[j]*np.log(p[j])
                 if self.normalized:
                     ent = ent / np.linalg.norm(ent, ord=1)
                 Xfit.append(np.reshape(ent,[1,-1]))
diff --git a/src/python/gudhi/simplex_tree.pxd b/src/python/gudhi/simplex_tree.pxd
index 4f229663..5642f82d 100644
--- a/src/python/gudhi/simplex_tree.pxd
+++ b/src/python/gudhi/simplex_tree.pxd
@@ -63,7 +63,6 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi":
         bool prune_above_filtration(double filtration) nogil
         bool make_filtration_non_decreasing() nogil
         void compute_extended_filtration() nogil
-        vector[vector[pair[int, pair[double, double]]]] compute_extended_persistence_subdiagrams(vector[pair[int, pair[double, double]]] dgm, double min_persistence) nogil
         Simplex_tree_interface_full_featured* collapse_edges(int nb_collapse_iteration) nogil except +
         void reset_filtration(double filtration, int dimension) nogil
         bint operator==(Simplex_tree_interface_full_featured) nogil
@@ -81,7 +80,7 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi":
         void expansion_with_blockers_callback(int dimension, blocker_func_t user_func, void *user_data)
 
 cdef extern from "Persistent_cohomology_interface.h" namespace "Gudhi":
-    cdef cppclass Simplex_tree_persistence_interface "Gudhi::Persistent_cohomology_interface<Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_full_featured>>":
+    cdef cppclass Simplex_tree_persistence_interface "Gudhi::Persistent_cohomology_interface<Gudhi::Simplex_tree_interface<Gudhi::Simplex_tree_options_full_featured>>":
         Simplex_tree_persistence_interface(Simplex_tree_interface_full_featured * st, bool persistence_dim_max) nogil
         void compute_persistence(int homology_coeff_field, double min_persistence) nogil except +
         vector[pair[int, pair[double, double]]] get_persistence() nogil
@@ -92,3 +91,4 @@ cdef extern from "Persistent_cohomology_interface.h" namespace "Gudhi":
         vector[pair[vector[int], vector[int]]] persistence_pairs() nogil
         pair[vector[vector[int]], vector[vector[int]]] lower_star_generators() nogil
         pair[vector[vector[int]], vector[vector[int]]] flag_generators() nogil
+        vector[vector[pair[int, pair[double, double]]]] compute_extended_persistence_subdiagrams(double min_persistence) nogil
diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx
index 2c53a872..05bfe22e 100644
--- a/src/python/gudhi/simplex_tree.pyx
+++ b/src/python/gudhi/simplex_tree.pyx
@@ -474,8 +474,7 @@ cdef class SimplexTree:
             del self.pcohptr
         self.pcohptr = new Simplex_tree_persistence_interface(self.get_ptr(), False)
         self.pcohptr.compute_persistence(homology_coeff_field, -1.)
-        persistence_result = self.pcohptr.get_persistence()
-        return self.get_ptr().compute_extended_persistence_subdiagrams(persistence_result, min_persistence)
+        return self.pcohptr.compute_extended_persistence_subdiagrams(min_persistence)
 
     def expansion_with_blocker(self, max_dim, blocker_func):
         """Expands the Simplex_tree containing only a graph. Simplices corresponding to cliques in the graph are added
@@ -488,9 +487,9 @@ cdef class SimplexTree:
         otherwise it is kept. The algorithm then proceeds with the next candidate.
 
         .. warning::
-            Several candidates of the same dimension may be inserted simultaneously before calling `block_simplex`, so
-            if you examine the complex in `block_simplex`, you may hit a few simplices of the same dimension that have
-            not been vetted by `block_simplex` yet, or have already been rejected but not yet removed.
+            Several candidates of the same dimension may be inserted simultaneously before calling `blocker_func`, so
+            if you examine the complex in `blocker_func`, you may hit a few simplices of the same dimension that have
+            not been vetted by `blocker_func` yet, or have already been rejected but not yet removed.
 
         :param max_dim: Expansion maximal dimension value.
         :type max_dim: int
diff --git a/src/python/gudhi/tensorflow/__init__.py b/src/python/gudhi/tensorflow/__init__.py
new file mode 100644
index 00000000..1599cf52
--- /dev/null
+++ b/src/python/gudhi/tensorflow/__init__.py
@@ -0,0 +1,5 @@
+from .cubical_layer import CubicalLayer
+from .lower_star_simplex_tree_layer import LowerStarSimplexTreeLayer
+from .rips_layer import RipsLayer
+
+__all__ = ["LowerStarSimplexTreeLayer", "RipsLayer", "CubicalLayer"]
diff --git a/src/python/gudhi/tensorflow/cubical_layer.py b/src/python/gudhi/tensorflow/cubical_layer.py
new file mode 100644
index 00000000..3304e719
--- /dev/null
+++ b/src/python/gudhi/tensorflow/cubical_layer.py
@@ -0,0 +1,82 @@
+import numpy               as np
+import tensorflow          as tf
+from ..cubical_complex  import CubicalComplex
+
+######################
+# Cubical filtration #
+######################
+
+# The parameters of the model are the pixel values.
+
+def _Cubical(Xflat, Xdim, dimensions, homology_coeff_field):
+    # Parameters: Xflat (flattened image),
+    #             Xdim (shape of non-flattened image)
+    #             dimensions (homology dimensions)
+
+    # Compute the persistence pairs with Gudhi
+    # We reverse the dimensions because CubicalComplex uses Fortran ordering
+    cc = CubicalComplex(dimensions=Xdim[::-1], top_dimensional_cells=Xflat)
+    cc.compute_persistence(homology_coeff_field=homology_coeff_field)
+
+    # Retrieve and ouput image indices/pixels corresponding to positive and negative simplices    
+    cof_pp = cc.cofaces_of_persistence_pairs()
+    
+    L_cofs = []
+    for dim in dimensions:
+
+        try:
+            cof = cof_pp[0][dim]
+        except IndexError:
+            cof = np.array([])
+
+        L_cofs.append(np.array(cof, dtype=np.int32))
+
+    return L_cofs
+
+class CubicalLayer(tf.keras.layers.Layer):
+    """
+    TensorFlow layer for computing the persistent homology of a cubical complex
+    """
+    def __init__(self, homology_dimensions, min_persistence=None, homology_coeff_field=11, **kwargs):
+        """
+        Constructor for the CubicalLayer class
+
+        Parameters:
+            homology_dimensions (List[int]): list of homology dimensions
+            min_persistence (List[float]): minimum distance-to-diagonal of the points in the output persistence diagrams (default None, in which case 0. is used for all dimensions)
+            homology_coeff_field (int): homology field coefficient. Must be a prime number. Default value is 11. Max is 46337.
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.dimensions = homology_dimensions
+        self.min_persistence = min_persistence if min_persistence != None else [0.] * len(self.dimensions)
+        self.hcf = homology_coeff_field
+        assert len(self.min_persistence) == len(self.dimensions)
+
+    def call(self, X):
+        """
+        Compute persistence diagram associated to a cubical complex filtered by some pixel values 
+
+        Parameters:
+            X (TensorFlow variable): pixel values of the cubical complex
+
+        Returns:
+            List[Tuple[tf.Tensor,tf.Tensor]]: List of cubical persistence diagrams. The length of this list is the same than that of dimensions, i.e., there is one persistence diagram per homology dimension provided in the input list dimensions. Moreover, the finite and essential parts of the persistence diagrams are provided separately: each element of this list is a tuple of size two that contains the finite and essential parts of the corresponding persistence diagram, of shapes [num_finite_points, 2] and [num_essential_points, 1] respectively. Note that the essential part is always empty in cubical persistence diagrams, except in homology dimension zero, where the essential part always contains a single point, with abscissa equal to the smallest value in the complex, and infinite ordinate
+        """
+        # Compute pixels associated to positive and negative simplices 
+        # Don't compute gradient for this operation
+        Xflat = tf.reshape(X, [-1])
+        Xdim, Xflat_numpy = X.shape, Xflat.numpy()
+        indices_list = _Cubical(Xflat_numpy, Xdim, self.dimensions, self.hcf)
+        index_essential = np.argmin(Xflat_numpy) # index of minimum pixel value for essential persistence diagram
+        # Get persistence diagram by simply picking the corresponding entries in the image
+        self.dgms = []
+        for idx_dim, dimension in enumerate(self.dimensions):
+            finite_dgm = tf.reshape(tf.gather(Xflat, indices_list[idx_dim]), [-1,2])
+            essential_dgm = tf.reshape(tf.gather(Xflat, index_essential), [-1,1]) if dimension == 0 else tf.zeros([0, 1])
+            min_pers = self.min_persistence[idx_dim]
+            if min_pers >= 0:
+                persistent_indices = tf.where(tf.math.abs(finite_dgm[:,1]-finite_dgm[:,0]) > min_pers)
+                self.dgms.append((tf.reshape(tf.gather(finite_dgm, indices=persistent_indices), [-1,2]), essential_dgm))
+            else:
+                self.dgms.append((finite_dgm, essential_dgm))
+        return self.dgms
diff --git a/src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py b/src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py
new file mode 100644
index 00000000..5a8e5b75
--- /dev/null
+++ b/src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py
@@ -0,0 +1,87 @@
+import numpy               as np
+import tensorflow          as tf
+
+#########################################
+# Lower star filtration on simplex tree #
+#########################################
+
+# The parameters of the model are the vertex function values of the simplex tree.
+
+def _LowerStarSimplexTree(simplextree, filtration, dimensions, homology_coeff_field):
+    # Parameters: simplextree (simplex tree on which to compute persistence)
+    #             filtration (function values on the vertices of st),
+    #             dimensions (homology dimensions),
+    #             homology_coeff_field (homology field coefficient)
+    
+    simplextree.reset_filtration(-np.inf, 0)
+
+    # Assign new filtration values
+    for i in range(simplextree.num_vertices()):
+        simplextree.assign_filtration([i], filtration[i])
+    simplextree.make_filtration_non_decreasing()
+    
+    # Compute persistence diagram
+    simplextree.compute_persistence(homology_coeff_field=homology_coeff_field)
+    
+    # Get vertex pairs for optimization. First, get all simplex pairs
+    pairs = simplextree.lower_star_persistence_generators()
+    
+    L_indices = []
+    for dimension in dimensions:
+    
+        finite_pairs = pairs[0][dimension] if len(pairs[0]) >= dimension+1 else np.empty(shape=[0,2])
+        essential_pairs = pairs[1][dimension] if len(pairs[1]) >= dimension+1 else np.empty(shape=[0,1])
+        
+        finite_indices = np.array(finite_pairs.flatten(), dtype=np.int32)
+        essential_indices = np.array(essential_pairs.flatten(), dtype=np.int32)
+
+        L_indices.append((finite_indices, essential_indices))
+
+    return L_indices
+
+class LowerStarSimplexTreeLayer(tf.keras.layers.Layer):
+    """
+    TensorFlow layer for computing lower-star persistence out of a simplex tree
+    """
+    def __init__(self, simplextree, homology_dimensions, min_persistence=None, homology_coeff_field=11, **kwargs):
+        """
+        Constructor for the LowerStarSimplexTreeLayer class
+  
+        Parameters:
+            simplextree (gudhi.SimplexTree): underlying simplex tree. Its vertices MUST be named with integers from 0 to n-1, where n is its number of vertices. Note that its filtration values are modified in each call of the class.
+            homology_dimensions (List[int]): list of homology dimensions
+            min_persistence (List[float]): minimum distance-to-diagonal of the points in the output persistence diagrams (default None, in which case 0. is used for all dimensions)
+            homology_coeff_field (int): homology field coefficient. Must be a prime number. Default value is 11. Max is 46337.
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.dimensions  = homology_dimensions
+        self.simplextree = simplextree
+        self.min_persistence = min_persistence if min_persistence != None else [0. for _ in range(len(self.dimensions))]
+        self.hcf = homology_coeff_field
+        assert len(self.min_persistence) == len(self.dimensions)
+
+    def call(self, filtration):
+        """
+        Compute lower-star persistence diagram associated to a function defined on the vertices of the simplex tree
+
+        Parameters:
+            F (TensorFlow variable): filter function values over the vertices of the simplex tree. The ith entry of F corresponds to vertex i in self.simplextree
+
+        Returns:
+            List[Tuple[tf.Tensor,tf.Tensor]]: List of lower-star persistence diagrams. The length of this list is the same than that of dimensions, i.e., there is one persistence diagram per homology dimension provided in the input list dimensions. Moreover, the finite and essential parts of the persistence diagrams are provided separately: each element of this list is a tuple of size two that contains the finite and essential parts of the corresponding persistence diagram, of shapes [num_finite_points, 2] and [num_essential_points, 1] respectively
+        """
+        # Don't try to compute gradients for the vertex pairs
+        indices = _LowerStarSimplexTree(self.simplextree, filtration.numpy(), self.dimensions, self.hcf)
+        # Get persistence diagrams
+        self.dgms = []
+        for idx_dim, dimension in enumerate(self.dimensions):
+            finite_dgm = tf.reshape(tf.gather(filtration, indices[idx_dim][0]), [-1,2])
+            essential_dgm = tf.reshape(tf.gather(filtration, indices[idx_dim][1]), [-1,1])
+            min_pers = self.min_persistence[idx_dim]
+            if min_pers >= 0:
+                persistent_indices = tf.where(tf.math.abs(finite_dgm[:,1]-finite_dgm[:,0]) > min_pers)
+                self.dgms.append((tf.reshape(tf.gather(finite_dgm, indices=persistent_indices),[-1,2]), essential_dgm))
+            else:
+                self.dgms.append((finite_dgm, essential_dgm))
+        return self.dgms
+
diff --git a/src/python/gudhi/tensorflow/rips_layer.py b/src/python/gudhi/tensorflow/rips_layer.py
new file mode 100644
index 00000000..2a73472c
--- /dev/null
+++ b/src/python/gudhi/tensorflow/rips_layer.py
@@ -0,0 +1,93 @@
+import numpy               as np
+import tensorflow          as tf
+from ..rips_complex     import RipsComplex
+
+############################
+# Vietoris-Rips filtration #
+############################
+
+# The parameters of the model are the point coordinates.
+
+def _Rips(DX, max_edge, dimensions, homology_coeff_field):
+    # Parameters: DX (distance matrix), 
+    #             max_edge (maximum edge length for Rips filtration), 
+    #             dimensions (homology dimensions)
+
+    # Compute the persistence pairs with Gudhi
+    rc = RipsComplex(distance_matrix=DX, max_edge_length=max_edge)
+    st = rc.create_simplex_tree(max_dimension=max(dimensions)+1)
+    st.compute_persistence(homology_coeff_field=homology_coeff_field)
+    pairs = st.flag_persistence_generators()
+
+    L_indices = []
+    for dimension in dimensions:
+
+        if dimension == 0:
+            finite_pairs = pairs[0]
+            essential_pairs = pairs[2]
+        else:
+            finite_pairs = pairs[1][dimension-1] if len(pairs[1]) >= dimension else np.empty(shape=[0,4])
+            essential_pairs = pairs[3][dimension-1] if len(pairs[3]) >= dimension else np.empty(shape=[0,2])
+        
+        finite_indices = np.array(finite_pairs.flatten(), dtype=np.int32)
+        essential_indices = np.array(essential_pairs.flatten(), dtype=np.int32)
+
+        L_indices.append((finite_indices, essential_indices))
+
+    return L_indices
+
+class RipsLayer(tf.keras.layers.Layer):
+    """
+    TensorFlow layer for computing Rips persistence out of a point cloud
+    """
+    def __init__(self, homology_dimensions, maximum_edge_length=np.inf, min_persistence=None, homology_coeff_field=11, **kwargs):
+        """
+        Constructor for the RipsLayer class
+
+        Parameters:
+            maximum_edge_length (float): maximum edge length for the Rips complex 
+            homology_dimensions (List[int]): list of homology dimensions
+            min_persistence (List[float]): minimum distance-to-diagonal of the points in the output persistence diagrams (default None, in which case 0. is used for all dimensions)
+            homology_coeff_field (int): homology field coefficient. Must be a prime number. Default value is 11. Max is 46337.
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.max_edge = maximum_edge_length
+        self.dimensions = homology_dimensions
+        self.min_persistence = min_persistence if min_persistence != None else [0. for _ in range(len(self.dimensions))]
+        self.hcf = homology_coeff_field
+        assert len(self.min_persistence) == len(self.dimensions)
+        
+    def call(self, X):
+        """
+        Compute Rips persistence diagram associated to a point cloud
+
+        Parameters:   
+            X (TensorFlow variable): point cloud of shape [number of points, number of dimensions]
+
+        Returns:
+            List[Tuple[tf.Tensor,tf.Tensor]]: List of Rips persistence diagrams. The length of this list is the same than that of dimensions, i.e., there is one persistence diagram per homology dimension provided in the input list dimensions. Moreover, the finite and essential parts of the persistence diagrams are provided separately: each element of this list is a tuple of size two that contains the finite and essential parts of the corresponding persistence diagram, of shapes [num_finite_points, 2] and [num_essential_points, 1] respectively
+        """    
+        # Compute distance matrix
+        DX = tf.norm(tf.expand_dims(X, 1)-tf.expand_dims(X, 0), axis=2)
+        # Compute vertices associated to positive and negative simplices 
+        # Don't compute gradient for this operation
+        indices = _Rips(DX.numpy(), self.max_edge, self.dimensions, self.hcf)
+        # Get persistence diagrams by simply picking the corresponding entries in the distance matrix
+        self.dgms = []
+        for idx_dim, dimension in enumerate(self.dimensions):
+            cur_idx = indices[idx_dim]
+            if dimension > 0:
+                finite_dgm = tf.reshape(tf.gather_nd(DX, tf.reshape(cur_idx[0], [-1,2])), [-1,2])
+                essential_dgm = tf.reshape(tf.gather_nd(DX, tf.reshape(cur_idx[1], [-1,2])), [-1,1])
+            else:
+                reshaped_cur_idx = tf.reshape(cur_idx[0], [-1,3])
+                finite_dgm = tf.concat([tf.zeros([reshaped_cur_idx.shape[0],1]), tf.reshape(tf.gather_nd(DX, reshaped_cur_idx[:,1:]), [-1,1])], axis=1)
+                essential_dgm = tf.zeros([cur_idx[1].shape[0],1])
+            min_pers = self.min_persistence[idx_dim]
+            if min_pers >= 0:
+                persistent_indices = tf.where(tf.math.abs(finite_dgm[:,1]-finite_dgm[:,0]) > min_pers)
+                self.dgms.append((tf.reshape(tf.gather(finite_dgm, indices=persistent_indices),[-1,2]), essential_dgm))
+            else:
+                self.dgms.append((finite_dgm, essential_dgm))
+        return self.dgms
+
diff --git a/src/python/gudhi/wasserstein/barycenter.py b/src/python/gudhi/wasserstein/barycenter.py
index d67bcde7..bb6e641e 100644
--- a/src/python/gudhi/wasserstein/barycenter.py
+++ b/src/python/gudhi/wasserstein/barycenter.py
@@ -37,7 +37,7 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False):
     :param init: The initial value for barycenter estimate.
         If ``None``, init is made on a random diagram from the dataset.
         Otherwise, it can be an ``int`` (then initialization is made on ``pdiagset[init]``)
-        or a `(n x 2)` ``numpy.array`` enconding a persistence diagram with `n` points.
+        or a `(n x 2)` ``numpy.array`` encoding a persistence diagram with `n` points.
     :type init: ``int``, or (n x 2) ``np.array``
     :param verbose: if ``True``, returns additional information about the barycenter.
     :type verbose: boolean
@@ -45,7 +45,7 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False):
         (local minimum of the energy function).
         If ``pdiagset`` is empty, returns ``None``.
         If verbose, returns a couple ``(Y, log)`` where ``Y`` is the barycenter estimate,
-        and ``log`` is a ``dict`` that contains additional informations:
+        and ``log`` is a ``dict`` that contains additional information:
 
         - `"groupings"`, a list of list of pairs ``(i,j)``. Namely, ``G[k] = [...(i, j)...]``, where ``(i,j)`` indicates that `pdiagset[k][i]`` is matched to ``Y[j]`` if ``i = -1`` or ``j = -1``, it means they represent the diagonal.
 
@@ -73,7 +73,7 @@ def lagrangian_barycenter(pdiagset, init=None, verbose=False):
 
     nb_iter = 0
 
-    converged = False  # stoping criterion
+    converged = False  # stopping criterion
     while not converged:
         nb_iter += 1
         K = len(Y)  # current nb of points in Y (some might be on diagonal)
diff --git a/src/python/include/Persistent_cohomology_interface.h b/src/python/include/Persistent_cohomology_interface.h
index e5a3dfba..945378a0 100644
--- a/src/python/include/Persistent_cohomology_interface.h
+++ b/src/python/include/Persistent_cohomology_interface.h
@@ -12,6 +12,8 @@
 #define INCLUDE_PERSISTENT_COHOMOLOGY_INTERFACE_H_
 
 #include <gudhi/Persistent_cohomology.h>
+#include <gudhi/Simplex_tree.h>  // for Extended_simplex_type
+
 
 #include <cstdlib>
 #include <vector>
@@ -223,6 +225,44 @@ persistent_cohomology::Persistent_cohomology<FilteredComplex, persistent_cohomol
     return out;
   }
 
+  using Filtration_value = typename FilteredComplex::Filtration_value;
+  using Birth_death = std::pair<Filtration_value, Filtration_value>;
+  using Persistence_subdiagrams = std::vector<std::vector<std::pair<int, Birth_death>>>;
+
+  Persistence_subdiagrams compute_extended_persistence_subdiagrams(Filtration_value min_persistence){
+    Persistence_subdiagrams pers_subs(4);
+    auto const& persistent_pairs = Base::get_persistent_pairs();
+    for (auto pair : persistent_pairs) {
+      std::pair<Filtration_value, Extended_simplex_type> px = stptr_->decode_extended_filtration(stptr_->filtration(get<0>(pair)),
+                                                                                                        stptr_->efd);
+      std::pair<Filtration_value, Extended_simplex_type> py = stptr_->decode_extended_filtration(stptr_->filtration(get<1>(pair)),
+                                                                                                        stptr_->efd);
+      std::pair<int, Birth_death> pd_point = std::make_pair(stptr_->dimension(get<0>(pair)),
+                                                            std::make_pair(px.first, py.first));
+      if(std::abs(px.first - py.first) > min_persistence){
+        //Ordinary
+        if (px.second == Extended_simplex_type::UP && py.second == Extended_simplex_type::UP){
+          pers_subs[0].push_back(pd_point);
+        }
+        // Relative
+        else if (px.second == Extended_simplex_type::DOWN && py.second == Extended_simplex_type::DOWN){
+          pers_subs[1].push_back(pd_point);
+        }
+        else{
+          // Extended+
+          if (px.first < py.first){
+            pers_subs[2].push_back(pd_point);
+          }
+          //Extended-
+          else{
+            pers_subs[3].push_back(pd_point);
+          }
+        }
+      }
+    }
+    return pers_subs;
+  }
+
  private:
   // A copy
   FilteredComplex* stptr_;
diff --git a/src/python/include/Simplex_tree_interface.h b/src/python/include/Simplex_tree_interface.h
index 7f9b0067..3848c5ad 100644
--- a/src/python/include/Simplex_tree_interface.h
+++ b/src/python/include/Simplex_tree_interface.h
@@ -132,36 +132,6 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> {
     return;
   }
 
-  std::vector<std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>> compute_extended_persistence_subdiagrams(const std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>& dgm, Filtration_value min_persistence){
-    std::vector<std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>> new_dgm(4);
-    for (unsigned int i = 0; i < dgm.size(); i++){
-      std::pair<Filtration_value, Extended_simplex_type> px = this->decode_extended_filtration(dgm[i].second.first, this->efd);
-      std::pair<Filtration_value, Extended_simplex_type> py = this->decode_extended_filtration(dgm[i].second.second, this->efd);
-      std::pair<int, std::pair<Filtration_value, Filtration_value>> pd_point = std::make_pair(dgm[i].first, std::make_pair(px.first, py.first));
-      if(std::abs(px.first - py.first) > min_persistence){
-        //Ordinary
-        if (px.second == Extended_simplex_type::UP && py.second == Extended_simplex_type::UP){
-          new_dgm[0].push_back(pd_point);
-        }
-        // Relative
-        else if (px.second == Extended_simplex_type::DOWN && py.second == Extended_simplex_type::DOWN){
-          new_dgm[1].push_back(pd_point);
-        }
-        else{
-          // Extended+
-          if (px.first < py.first){
-            new_dgm[2].push_back(pd_point);
-          }
-          //Extended-
-          else{
-            new_dgm[3].push_back(pd_point);
-          }
-        }
-      }
-    }
-    return new_dgm;
-  }
-
   Simplex_tree_interface* collapse_edges(int nb_collapse_iteration) {
     using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>;
     std::vector<Filtered_edge> edges;
diff --git a/src/python/test/test_diff.py b/src/python/test/test_diff.py
new file mode 100644
index 00000000..dca001a9
--- /dev/null
+++ b/src/python/test/test_diff.py
@@ -0,0 +1,78 @@
+from gudhi.tensorflow import *
+import numpy as np
+import tensorflow as tf
+import gudhi as gd
+
+def test_rips_diff():
+
+    Xinit = np.array([[1.,1.],[2.,2.]], dtype=np.float32)
+    X = tf.Variable(initial_value=Xinit, trainable=True)
+    rl = RipsLayer(maximum_edge_length=2., homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = rl.call(X)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+    grads = tape.gradient(loss, [X])
+    assert tf.norm(grads[0]-tf.constant([[-.5,-.5],[.5,.5]]),1) <= 1e-6
+
+def test_cubical_diff():
+
+    Xinit = np.array([[0.,2.,2.],[2.,2.,2.],[2.,2.,1.]], dtype=np.float32)
+    X = tf.Variable(initial_value=Xinit, trainable=True)
+    cl = CubicalLayer(homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = cl.call(X)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+    grads = tape.gradient(loss, [X])
+    assert tf.norm(grads[0]-tf.constant([[0.,0.,0.],[0.,.5,0.],[0.,0.,-.5]]),1) <= 1e-6
+
+def test_nonsquare_cubical_diff():
+
+    Xinit = np.array([[-1.,1.,0.],[1.,1.,1.]], dtype=np.float32)
+    X = tf.Variable(initial_value=Xinit, trainable=True)
+    cl = CubicalLayer(homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = cl.call(X)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+    grads = tape.gradient(loss, [X])
+    assert tf.norm(grads[0]-tf.constant([[0.,0.5,-0.5],[0.,0.,0.]]),1) <= 1e-6
+
+def test_st_diff():
+
+    st = gd.SimplexTree()
+    st.insert([0])
+    st.insert([1]) 
+    st.insert([2]) 
+    st.insert([3]) 
+    st.insert([4]) 
+    st.insert([5]) 
+    st.insert([6]) 
+    st.insert([7]) 
+    st.insert([8]) 
+    st.insert([9]) 
+    st.insert([10]) 
+    st.insert([0, 1]) 
+    st.insert([1, 2]) 
+    st.insert([2, 3]) 
+    st.insert([3, 4]) 
+    st.insert([4, 5]) 
+    st.insert([5, 6]) 
+    st.insert([6, 7]) 
+    st.insert([7, 8]) 
+    st.insert([8, 9]) 
+    st.insert([9, 10]) 
+
+    Finit = np.array([6.,4.,3.,4.,5.,4.,3.,2.,3.,4.,5.], dtype=np.float32)
+    F = tf.Variable(initial_value=Finit, trainable=True)
+    sl = LowerStarSimplexTreeLayer(simplextree=st, homology_dimensions=[0])
+
+    with tf.GradientTape() as tape:
+        dgm = sl.call(F)[0][0]
+        loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0])))
+    grads = tape.gradient(loss, [F])
+
+    assert tf.math.reduce_all(tf.math.equal(grads[0].indices, tf.constant([2,4])))
+    assert tf.math.reduce_all(tf.math.equal(grads[0].values, tf.constant([-1.,1.])))
+
diff --git a/src/python/test/test_dtm.py b/src/python/test/test_dtm.py
index e46d616c..b276f041 100755
--- a/src/python/test/test_dtm.py
+++ b/src/python/test/test_dtm.py
@@ -91,11 +91,11 @@ def test_density():
 
 def test_dtm_overflow_warnings():
     pts = numpy.array([[10., 100000000000000000000000000000.], [1000., 100000000000000000000000000.]])
-
-    with warnings.catch_warnings(record=True) as w:
-        # TODO Test "keops" implementation as well when next version of pykeops (current is 1.5) is released (should fix the problem (cf. issue #543))
-        dtm = DistanceToMeasure(2, implementation="hnsw")
-        r = dtm.fit_transform(pts)
-        assert len(w) == 1
-        assert issubclass(w[0].category, RuntimeWarning)
-        assert "Overflow" in str(w[0].message)
+    impl_warn = ["keops", "hnsw"]
+    for impl in impl_warn:
+        with warnings.catch_warnings(record=True) as w:
+            dtm = DistanceToMeasure(2, implementation=impl)
+            r = dtm.fit_transform(pts)
+            assert len(w) == 1
+            assert issubclass(w[0].category, RuntimeWarning)
+            assert "Overflow" in str(w[0].message)
diff --git a/src/python/test/test_remote_datasets.py b/src/python/test/test_remote_datasets.py
new file mode 100644
index 00000000..e5d2de82
--- /dev/null
+++ b/src/python/test/test_remote_datasets.py
@@ -0,0 +1,87 @@
+# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+# Author(s):       Hind Montassif
+#
+# Copyright (C) 2021 Inria
+#
+# Modification(s):
+#   - YYYY/MM Author: Description of the modification
+
+from gudhi.datasets import remote
+
+import shutil
+import io
+import sys
+import pytest
+
+from os.path import isdir, expanduser, exists
+from os import remove, environ
+
+def test_data_home():
+    # Test _get_data_home and clear_data_home on new empty folder
+    empty_data_home = remote._get_data_home(data_home="empty_folder_for_test")
+    assert isdir(empty_data_home)
+
+    remote.clear_data_home(data_home=empty_data_home)
+    assert not isdir(empty_data_home)
+
+def test_fetch_remote():
+    # Test fetch with a wrong checksum
+    with pytest.raises(OSError):
+        remote._fetch_remote("https://raw.githubusercontent.com/GUDHI/gudhi-data/main/points/spiral_2d/spiral_2d.npy", "tmp_spiral_2d.npy", file_checksum = 'XXXXXXXXXX')
+    assert not exists("tmp_spiral_2d.npy")
+
+def _get_bunny_license_print(accept_license = False):
+    capturedOutput = io.StringIO()
+    # Redirect stdout
+    sys.stdout = capturedOutput
+
+    bunny_arr = remote.fetch_bunny("./tmp_for_test/bunny.npy", accept_license)
+    assert bunny_arr.shape == (35947, 3)
+    del bunny_arr
+    remove("./tmp_for_test/bunny.npy")
+
+    # Reset redirect
+    sys.stdout = sys.__stdout__
+    return capturedOutput
+
+def test_print_bunny_license():
+    # Test not printing bunny.npy LICENSE when accept_license = True
+    assert "" == _get_bunny_license_print(accept_license = True).getvalue()
+    # Test printing bunny.LICENSE file when fetching bunny.npy with accept_license = False (default)
+    with open("./tmp_for_test/bunny.LICENSE") as f:
+        assert f.read().rstrip("\n") == _get_bunny_license_print().getvalue().rstrip("\n")
+    shutil.rmtree("./tmp_for_test")
+
+def test_fetch_remote_datasets_wrapped():
+    # Test fetch_spiral_2d and fetch_bunny wrapping functions with data directory different from default (twice, to test case of already fetched files)
+    # Default case is not tested because it would fail in case the user sets the 'GUDHI_DATA' environment variable locally
+    for i in range(2):
+        spiral_2d_arr = remote.fetch_spiral_2d("./another_fetch_folder_for_test/spiral_2d.npy")
+        assert spiral_2d_arr.shape == (114562, 2)
+
+        bunny_arr = remote.fetch_bunny("./another_fetch_folder_for_test/bunny.npy")
+        assert bunny_arr.shape == (35947, 3)
+
+    # Check that the directory was created
+    assert isdir("./another_fetch_folder_for_test")
+    # Check downloaded files
+    assert exists("./another_fetch_folder_for_test/spiral_2d.npy")
+    assert exists("./another_fetch_folder_for_test/bunny.npy")
+    assert exists("./another_fetch_folder_for_test/bunny.LICENSE")
+
+    # Remove test folders
+    del spiral_2d_arr
+    del bunny_arr
+    shutil.rmtree("./another_fetch_folder_for_test")
+
+def test_gudhi_data_env():
+    # Set environment variable "GUDHI_DATA"
+    environ["GUDHI_DATA"] = "./test_folder_from_env_var"
+    bunny_arr = remote.fetch_bunny()
+    assert bunny_arr.shape == (35947, 3)
+    assert exists("./test_folder_from_env_var/points/bunny/bunny.npy")
+    assert exists("./test_folder_from_env_var/points/bunny/bunny.LICENSE")
+    # Remove test folder
+    del bunny_arr
+    shutil.rmtree("./test_folder_from_env_var")
diff --git a/src/python/test/test_representations.py b/src/python/test/test_representations.py
index 5f29740f..2ca72d07 100755
--- a/src/python/test/test_representations.py
+++ b/src/python/test/test_representations.py
@@ -152,7 +152,26 @@ def test_vectorization_empty_diagrams():
     scv = Entropy(mode="vector", normalized=False, resolution=random_resolution)(empty_diag)
     assert not np.any(scv)
     assert scv.shape[0] == random_resolution
-
+    
+def test_entropy_miscalculation():
+    diag_ex = np.array([[0.0,1.0], [0.0,1.0], [0.0,2.0]])
+    def pe(pd):
+        l = pd[:,1] - pd[:,0]
+        l = l/sum(l)
+        return -np.dot(l, np.log(l))
+    sce = Entropy(mode="scalar")
+    assert [[pe(diag_ex)]] == sce.fit_transform([diag_ex])
+    sce = Entropy(mode="vector", resolution=4, normalized=False)
+    pef = [-1/4*np.log(1/4)-1/4*np.log(1/4)-1/2*np.log(1/2),
+           -1/4*np.log(1/4)-1/4*np.log(1/4)-1/2*np.log(1/2),
+           -1/2*np.log(1/2), 
+           0.0]
+    assert all(([pef] == sce.fit_transform([diag_ex]))[0])
+    sce = Entropy(mode="vector", resolution=4, normalized=True)
+    pefN = (sce.fit_transform([diag_ex]))[0]
+    area = np.linalg.norm(pefN, ord=1)
+    assert area==1
+        
 def test_kernel_empty_diagrams():
     empty_diag = np.empty(shape = [0, 2])
     assert SlicedWassersteinDistance(num_directions=100)(empty_diag, empty_diag) == 0.
diff --git a/src/python/test/test_simplex_tree.py b/src/python/test/test_simplex_tree.py
index 688f4fd6..54bafed5 100755
--- a/src/python/test/test_simplex_tree.py
+++ b/src/python/test/test_simplex_tree.py
@@ -320,6 +320,10 @@ def test_extend_filtration():
     ]
 
     dgms = st.extended_persistence(min_persistence=-1.)
+    assert len(dgms) == 4
+    # Sort by (death-birth) descending - we are only interested in those with the longest life span
+    for idx in range(4):
+        dgms[idx] = sorted(dgms[idx], key=lambda x:(-abs(x[1][0]-x[1][1])))
 
     assert dgms[0][0][1][0] == pytest.approx(2.)
     assert dgms[0][0][1][1] == pytest.approx(3.)
@@ -528,7 +532,7 @@ def test_expansion_with_blocker():
 
     def blocker(simplex):
         try:
-            # Block all simplices that countains vertex 6
+            # Block all simplices that contain vertex 6
             simplex.index(6)
             print(simplex, ' is blocked')
             return True
diff --git a/src/python/test/test_subsampling.py b/src/python/test/test_subsampling.py
index 4019852e..3431f372 100755
--- a/src/python/test/test_subsampling.py
+++ b/src/python/test/test_subsampling.py
@@ -91,7 +91,7 @@ def test_simple_choose_n_farthest_points_randomed():
     assert gudhi.choose_n_farthest_points(points=[], nb_points=1) == []
     assert gudhi.choose_n_farthest_points(points=point_set, nb_points=0) == []
 
-    # Go furter than point set on purpose
+    # Go further than point set on purpose
     for iter in range(1, 10):
         sub_set = gudhi.choose_n_farthest_points(points=point_set, nb_points=iter)
         for sub in sub_set:
@@ -117,7 +117,7 @@ def test_simple_pick_n_random_points():
     assert gudhi.pick_n_random_points(points=[], nb_points=1) == []
     assert gudhi.pick_n_random_points(points=point_set, nb_points=0) == []
 
-    # Go furter than point set on purpose
+    # Go further than point set on purpose
     for iter in range(1, 10):
         sub_set = gudhi.pick_n_random_points(points=point_set, nb_points=iter)
         for sub in sub_set:
author	wreise <wojciech.reise@epfl.ch>	2022-08-10 10:28:26 +0200
committer	wreise <wojciech.reise@epfl.ch>	2022-08-10 10:28:26 +0200
commit	b9a31fed2b90ee69a5c23047fd2ff1c264ad9605 (patch)
tree	c7a6e319c5cc6ba9c7963b08f7a4cdf3c776c922
parent	60e57f9c86a7aae67c2931200066aba059ec2721 (diff)
parent	4f83706aa1263c04cb5e8763e1e8eb6c580bed3c (diff)